modern fourier transform infrared spectroscopy (comprehensive analytical chemistry)
TRANSCRIPT
Series Editor's Preface
This book on Modern Fourier Transform Infrared Spectroscopy is auseful addition to the Comprehensive Analytical Chemistry series. Thework contains different chapters that cover both fundamental andapplied aspects of infrared spectroscopy. Particular attention is givento fundamentals of vibrational spectroscopy and to the recent develop-ments of hyphenated chromatographic techniques. In addition, themajor portion of the applications described in this book deal withpolymeric and biological materials. Chemometric interpretation anddata analysis are also described in detail in the last chapter of the book,indicating their relevance in infrared spectroscopy. The book can beused as an academic text and as reference book either for those withmore expertise or for those starting with this technique. Overall, thebook covers an important technique increasingly used in analyticalchemistry.
Finally I would like to thank the authors of the book for their timeand efforts in preparing their contributions. Without their engagementthis reference work on infrared spectroscopy would certainly not havebeen possible.
D. Barcel6
xvii
Acknowledgements
Writing a book needs a lot of reading, careful planning and writing. Theprocess is time consuming and requires the assistance of people onwhom we can rely. During the process of writing this book many havehelped us with physical work, ideas and support. It is not possible tothank everyone who has contributed to the book. However, there aresome who have contributed to elevate the quality of the book and we aregrateful for their efforts. In this respect, we would like to thankProfessor Rolf Manne, Department of Chemistry, Agder UniversityCollege for critically reviewing Chapter 4. We would like to thank Dr.Hideki Kandori (Kyoto University) for critically reviewing parts ofChapter 8 and Ms. Seiko Hino for polishing the English in Chapters 3,5, 7, and parts of Chapters 8 and 9. In addition one of the authors (VGG)would like to thank Sheila E. Rodman of Polaroid Corporation for thecollection of some of the materials used in Chapters 6, 7 and 8.
Finally, we would like to thank our families and friends who havegiven us moral support and helped us through some difficult timesduring the writing of the book.
xviii
Authors' Preface
Infrared spectroscopy has a history of more than a century: the charact-eristic absorptions of functional groups in the infrared region wereknown even in the 19th century; the first infrared atlas was published in1905, twenty years before the birth of quantum mechanics. However,even though infrared spectroscopy is a relatively old technique, it hasalways been a popular technique for chemical analysis. Developmentsin computer technology, sensitive detectors and accessories for newsampling methodologies in the infrared region have made infraredspectroscopy one of the most powerful and widespread spectroscopictools of the 20th and 21st centuries. The applications of infraredspectroscopy, and of Fourier transform infrared spectroscopy (FT-IR)in particular, are ever expanding, due to its versatile nature. Theenormous number of articles and research papers published every yearthat deal with infrared spectroscopy and its applications is clearevidence to this.
The book "Modern Fourier Transform Infrared Spectroscopy" hasbeen written to reflect the popularity of infrared spectroscopy in sev-eral different fields of science. The chapters are designed to give thereader not only the understanding of the basics of infrared spectroscopybut also ideas on how to apply the technique in these different fields.
The book is suitable for students at graduate level as well asexperienced researchers in academia and industry. The first threechapters deal with the fundamentals of vibrational spectroscopy. Sincespectroscopy is the study of the interaction of electromagnetic radiationwith matter, the first two chapters deal with the characteristics,properties and absorption of electromagnetic radiation. Chapter 3provides the basis for vibrations in molecules from both classical andquantum mechanical points of view. The absorption of infraredradiation by a vibration in a molecule depends on the symmetry of themolecule and the symmetry of the vibrations. As this aspect is notusually treated in textbooks on infrared spectroscopy, Chapter 4 dealswith the symmetry aspects of molecules and illustrates how the readercan determine the vibrations that are infrared active.
Chapter 6 is an overview of the instrumentation used to perform themajority of Fourier transformed infrared spectroscopic experiments
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today. The chapter starts with an overview of the history of FT-IRspectroscopy from the construction of the first interferometers in 1880to the present day and continues with a description of the componentsof an interferometer and the various scanning techniques (continuous-scan and step-scan). Chapter 7 first describes sampling techniquesused in transmission and reflection spectroscopy and then a variety ofthe so-called hyphenated techniques that combine the use of FT-IRspectroscopy with another analytical technique. Thermogravimetricanalysis (TGA/FT-IR), liquid chromatography (LC/FT-IR), gas chroma-tography (GC/FT-IR) and supercritical fluid chromatography (SFC/FT-IR) are the combinations discussed in this book.
Chapter 8 depicts certain applications of FT-IR spectroscopic tech-niques to basic and industrial research. Specifically, a large portion ofthe chapter deals with the characterization of polymers and polymericsurfaces, whereas the remaining part describes applications to organicthin films and biological molecules. One subcategory treated in detail isthe determination of molecular orientation in polymers via static anddynamic FT-IR experiments. Another subcategory is the applicationsthat involve optically active materials and conducting polymers. Inaddition, very significant developments have recently taken place inthe area of infrared microspectroscopy and especially in infrared imag-ing with the introduction of focal plane array detection. Part of thischapter is dedicated to an explanation of the experimental proceduresassociated with these imaging experiments along with selectedexamples from the recent literature.
Finally, Chapter 9 deals with some modern analytical methods ininfrared spectroscopy. Again, the methods described here are not verycommon in books on infrared spectroscopy. The first part of the chapterdeals with chemometric techniques that can be applied to semi-quanti-tative and quantitative analysis of infrared spectroscopic profiles. Thetext is designed to give the theoretical basis of these techniques and inparticular how they can be applied to infrared spectroscopic dataprofiles. In this chapter, the subject of two-dimensional correlationspectroscopy (2D-IR) is also discussed. The principles of the techniquealong with selected examples of the applications of the 2D-IR treat-ment are presented.
Alfred A. ChristyYukihiro Ozaki
Vasilis G. GregoriouApril 2001
xx
Chapter 1
Electromagnetic radiation and theelectromagnetic spectrum
We have come across people talking about microwave, UV radiation,radio waves, x-rays, radar, cosmic rays and so on. We understand thedangers of UV radiations from the sun and the use of microwave inheating food. What do we associate with all these different terms? Weunderstand without learning the physics of these different radiationsthat they are associated with different energies. For example, whitelight is a form of energy and it comprises a mixture or spectrum of sevendifferent colours, which are all visible to the human eye. All thesecolours of which white light is composed have different energies in thedescending order: violet, indigo, blue, green, yellow, orange, red. Aphotographic plate is readily affected by violet light, unlike red lightwhich has almost no effect.
From the above discussion, it is clear that the spectrum of differentradiations falls into a larger scale of spectrum where white light is avery small part. The larger scale containing the spectrum of differentradiations is called electromagnetic spectrum.
The physical properties of radiations cannot be explained by asingle theory. Some properties such as propagation of radiationthrough a medium, diffraction and reflection are better explained by atheory called wave theory and properties like momentum are betterexplained by particle theory. The propagation of radiation throughspace involves electric and magnetic components of the radiation andhence the term "electromagnetic".
Spectroscopy generally deals with the interaction of electromag-netic radiation and matter. In order to understand this interaction, wemust understand the characteristics of the electromagnetic radiationand the matter involved in the interaction.
1
1.1 WAVE NATURE OF ELECTROMAGNETIC RADIATION-WAVECHARACTERISTICS AND WAVE PARAMETERS
According to electromagnetic theory, electromagnetic radiation is aform of energy that is composed of oscillating electric and magneticfields acting in planes that are perpendicular to each other and to thedirection of propagation (Fig. 1.1). The oscillating electric field is simpleharmonic and propagates as waves with a velocity (c) 3x108 m s- invacuum. The propagation velocity varies with the refractive index of themedium.
In a two-dimensional representation, the variation of the electricfield strength of an electromagnetic radiation with propagation time inspace can be paralleled to the variation of the y co-ordinate of the traceof a particle moving around a circle of radius A with a constant angularvelocity o radians per second (Fig. 1.2).
Let us assume that OX and OY represent the positive directions ofthe x and y axes and O represents the origin of these axes. Let us alsoassume that at time zero the particle passes through x and thenconsider the position of the particle after t seconds. The angle traversedby the particle in t seconds is ot radians. The y co-ordinate of theposition of the particle can be given by equation
y =A sin ot (1.1)
Electric field streng~
Direction of propagation
Fig. 1.1. Oscillating electric and magnetic fields of electromagnetic radiation.
2
ct=r/2
act=r
s-1
wt= 3r12
Fig. 1.2. Trace of a particle moving around a circle of radius A with an angular velocityrads-1.
At time zero (i.e. ot = 0) the particle is at x and this function isminimum with a value 0. At time 7d/20 (i.e ot = c/2) the particle is at yand the function is maximum with a value A, the amplitude of thefunction.
At time nl/c (i.e cot = g), the particle is at Z and the function hasanother minimum. Similarly the function will have another maximumand another minimum at times 3/2co (cot = 37/2) and 2/co (ot = 2),respectively. The particle takes 2/o seconds (remember one circle is 2i7radians) to complete the journey through the circular path once (onecycle). This is called the period of the motion and denoted by . Thenumber of cycles the particle traces through in one second is o/2t {1/(2t/o)} and is called the frequency (v) of the motion. The frequency isabbreviated by the symbol Hz. The angular velocity of the motion canthen be written in terms of the frequency as
co = 2v (1.2)
A two-dimensional plot of the variation of the y co-ordinate of theposition of the particle with time is shown in Fig 1.3. Equation (1.1) canbe written to include the frequency of the motion and time as
y =A sin 2vt (1.3)
3
A
O.5 A A
>1 0--
-0.5A
-A
Time in seconds
Fig. 1.3. A two-dimensional plot of the variation of the y co-ordinate moving in a circle asshown in Fig. 1.2.
0.SA
0
-0.5A
-A
Propagation distance in metres
Fig. 1.4. The propagation of electromagnetic radiation.
The propagation of the electromagnetic radiation in space is 3x108 ms l. Figure 1.3 can be redrawn (Fig. 1.4) in a similar manner torepresent the distance of propagation of electromagnetic radiationalong the x axis.
When the x axis represents the distance, we can define some otherparameters characteristic to electromagnetic radiation. In the
4
preceding discussion, we learnt that the y co-ordinate of the particlehas zero values at times 0, n/co and 27/co. That is at distances 0, rc/lo and2nc/o, the propagating electric field of the electromagnetic radiationwill have zero field strength. But the distance between the extremepoints, that is, the distance travelled during a complete cycle of oscilla-tion is called wavelength (k). However, because of the symmetry of thesine wave, the wavelength can be defined as the distance between twosimilar points in the wave. The wave has a frequency v and thereforethe velocity of propagation can be written as
kv = c (in metres per second) (1.4)
This implies that the wavelength has dimension m (metre). Theinverse of the wavelength, when the wavelength is expressed in centi-metres is called wavenumber and is denoted by v. The dimension forwavenumber is cm-1 .
v = 1/k cm-1 (1.5)
The wavenumber can also be thought of as the number of waves in 1 cmlength. The above two equations combined give Eq. (1.6).
v = Vc (c in centimetres per second) (1.6)
The propagation distance s of an electromagnetic radiation in t secondsis given by
s = kvt = ct (1.7)
Equation (1.7) can be combined with Eq. (1.1) to give a relationshipdescribing the variation of the field strength of an electromagneticradiation with the distance of propagation and its wavelength asfollows
y =A sin (2nrs/k) (1.8)
The flux of energy of an electromagnetic radiation along the direction ofpropagation is equally divided between electric and magnetic fields.
Electromagnetic radiations are produced by accelerating electriccharges and electric charge accelerations are produced when
5
electromagnetic radiations are absorbed. Electromagnetic radiations ofdifferent energies are produced when the energy involved in the accel-eration of electric charges is different. We shall see later that y-rays tomicrowaves are produced during oscillations of charges at differentstates in matter.
1.2 QUANTUM CONCEPT AND PARTICLE NATURE OFELECTROMAGNETIC RADIATION
Not all properties of electromagnetic radiation can be explained by thewave theory. Electromagnetic radiation has particle-like (corpuscular)properties in addition to the wave properties. The corpuscular nature ofelectromagnetic radiation was developed during the early 20th centuryin order explain certain characteristics that classical physics failed toexplain.
Max Planck originated the quantum hypothesis to explain thediscontinuity in the energy of an oscillator of frequency v. Planck'shypothesis suggests that the energy of an oscillator with frequency v isnot continuously variable, but restricted to integral multiples of hv as0, lhv, 2hv, 3hv, ... nhv where hv is a quantum of energy and h is auniversal constant which is known as Planck's constant.
Albert Einstein, in 1905, related Planck's quantum hypothesis tothe photoelectric effect where electrons from metal surfaces wereejected by ultraviolet radiation. Einstein explained that the electronsfrom a metal are ejected when they receive energy at least equivalent totheir binding energy. Furthermore, the energy of the radiation must beconfined to a small region of space in order to transfer the energyentirely to an electron and eject it instantaneously. The ejection willnot be instantaneous if the energy is spread evenly across the entirewave front. This leads to an understanding that the energy of electro-magnetic radiation can be considered as packets (quanta) of energy hv(Fig. 1.5). The quantum of radiant energy was named photon by Lewisin 1926.
The corpuscular nature of photons was explained by theirpossession of momentum. The relativistic expression shown in Eq. (1.9)
Fig. 1.5. Energy packets (quanta) of photons.
6
leads to a value of hv/c for linear momentum (p) of a photon which hasno mass (m = 0).
E = m2c4 +p2c 2 (1.9)
The scattering of photons (electromagnetic radiation) during collisionswith electrons is a clear indication that the photons possessmomentum.
1.3 UNITS OF WAVE PARAMETERS
The SI unitary system requires that the dimensions of length, massand time are specified in metres (m), kilograms (kg) and seconds (s),respectively. Table 1.1 shows the units of some parameters and con-stants we have come across during our discussion.
TABLE 1.1Symbols and dimensions of wave parameters and related terms
Parameter Symbol Dimensions of units
Energy J (Joule) kg m2 s-2
Wavelength mFrequency Hz (Hertz) s-1 (cycles per second)Velocity of light 3x108 m s- 1
Planck's constant 6.626x1034 J s
1.4 ORIGIN OF ELECTROMAGNETIC RADIATION ANDELECTROMAGNETIC SPECTRUM: y-RAYS TO MICROWAVE
The origin of electromagnetic radiation varies widely. The universecontains radiations ranging from y-rays to microwaves. A system thatemits radiation is also capable of absorbing that radiation. An exampleof this is the absorption and emission of yellow light by sodium atomsby which sodium is quantitatively determined by atomic spectrometry.We use a sodium lamp that emits light at a particular frequency which
7
visible
infraredradiation
Y-rays
Fig. 1.6. Oscillators in an atom and a molecule.
is produced when an excited electron relaxes from an excited state tothe ground state to excite an electron from a ground state to the samecorresponding excited state in another sodium atom.
As mentioned earlier, the electromagnetic radiations originate fromoscillators arising from the acceleration of electric charges. Gamma-rays are produced by the oscillators in the atomic nuclei; x-rays areproduced by the oscillators arising from the tightly bound electrons inthe vicinity of the nucleus of atoms; visible and ultraviolet radiationsare produced by the oscillators arising from the outer electrons in themolecules and atoms; infrared radiation is produced by the oscillatorsarising from the vibration and rotation of molecules.
Now we should be able to understand why electromagnetic radi-ations of different dimensions are used in studying nuclear, electronic,vibrational and rotational transitions in matter.
TABLE 1.2
Electromagnetic spectrum: yrays to radio waves, their approximate frequency and energyrange
Radiation Wavelength(m)
y-rays 5x10-12_10 -1 2
x-rays 10-S-5x10 - 12
Far UV 1.8x10 7-10 8
Near UV 3.5x10-7-1.8x10- 7
Visible 7.7x10-7-3.5x10- 7
Near IR 2.5x10-6-7.7x10 - 7
Mid IR 5x10-5-2.5x106
Far IR 10-3-5x105
Microwave 3x10-1 -10 -3
Frequency range Energy range per Energy range(Hz) photon (J) per mole (kJ)
6xl103x1O20 4x10-12x10- 1 3 24x106-1.2x10 s
3x1016 -6x101 9 2x 10-18 -4x 10 - 14 1200-24x10 6
1.7x 101 5-3X101 6 1.13x10 1 8 -2x10 18 680-1200
8.6x1014-1.7x1015 5.7x10-19-1.13x 10-18 343-680
3.9x1014 -8.6x1014 2.58x10-19-5.7x10 -l 9 155-343
1.2x10' 4 -3.9x1014 8x10-20 2.58x10 1 9 48-155
6x 1012 -1.2x1014 4x10-2_8x 10 - 2.4-48
3x10 -6101 2 2x10- 22 -4x10 -2 1 0.12-2.4
10 9-3x10 11 6.6x10-2-2x10- 2 2 0.0004-0.12
8
Electromagnetic radiation spectrum in the larger scale is given inTable 1.2. It is difficult to define precise limits between differentdivisions and the reader should understand that the divisions areapproximate and may slightly vary with the limits given in othertextbooks.
GENERAL BIBLIOGRAPHY
P.W. Atkins, Molecular Quantum Mechanics. Oxford University Press,London, 1984.
C.N. Banwell and E.M. McCash, Fundamentals of Molecular Spectroscopy.McGraw-Hill, London, 1994.
W. Kemp, Organic Spectroscopy. Macmillan, London and Basingstoke, 1978.J.H. Vander Maas, Basic Infrared Spectroscopy. Heydon & Sons, London, 1972.
9
Chapter 2
Interaction of electromagnetic radiationwith matter
2.1 ABSORPTION OF ELECTROMAGNETIC RADIATION
Matter is composed of molecules or atoms. Atoms are composed ofnuclei containing protons, neutrons and electrons surrounding thenucleus. This means that matter is full of oscillators of very differentdimensions. Any of these can be excited to a higher level using electro-magnetic radiation of appropriate energy. For example, vibration in amolecule containing two atoms is equivalent to a simple oscillator. Thisvibration can be excited to the next vibrational level by irradiating themolecule with infrared radiation of appropriate energy (i.e. appropriatefrequency). Here, we shall just assume that absorption takes place (Fig.2.1) without considering the conditions for infrared absorption, whichwe shall consider in Chapter 3.
If the energy of the radiation does not match the energy differencebetween the excited and ground states of the molecule, no absorptionwill take place. If the frequency of the radiation that is absorbed by themolecule is v, then the energy difference between the ground state andexcited state is given by the Eq. (2.1).
Ee-Eg = AE = hv = hc =hvc (2.1)
where Ee, Eg are absolute energies of the excited and ground states.For example, if the wavenumber of the radiation needed to excite a
vibrational mode in a molecule is 3000 cm-l, then the energy absorbedby one molecule is
11
I - E x.tedx
Fig. 2.1. Absorption of electromagnetic radiation.
AEmoiecule = hvc = 6.626x 10-3 4 J s x3000 cm- l 3x 101 cm s- l (2.2)= 5.963x10-2 0 J
If we are interested in the energy absorbed by a mole of the substancethen we have to multiply the answer by the Avogadro's number NA =
6.023x10 2 3 mol-1. That is, the energy absorbed by a mole of thesubstance is
AEmole = 5.963x1020 J x 6.023x 1023 mol- = 35.9x 10 J mol-' (2.3)= 35.9 kJ mol-
2.2 PRESENTATION OF DATA: A LINE SPECTRUM
In absorption spectroscopy, the information sought for is theabsorption of radiant power from a source by the sample. In infraredspectroscopy, this is done in practice by a spectrometer; the constructionof this instrument will be dealt with in a later chapter. The idea behindthe technique is to send radiation through (or interact with) a sampleand measure the characteristics of the radiation emerging from thesample.
Let us assume that monochromatic radiation (only one-frequencyradiation) with sufficient intensity and of a frequency that matches thefrequency of absorption is passed through a sample. A part of theradiation will be absorbed and the intensity of the radiation emergingfrom the sample, the transmitted radiation, will be of reduced
12
AE = hp
100
0v
Frequency, Hz
Fig. 2.2. A transmittance spectrum.
1
aW
0V
Frequency, Hz
Fig. 2.3. A line spectrum of absorption.
intensity. If we plot the percent of the intensity of the transmittedradiation relative to the source intensity against frequency, then theexpected plot should contain a single line as shown in Fig. 2.2.Similarly an absorption spectrum will be as shown in Fig. 2.3.
2.3 LINE BROADENING IN INFRARED ABSORPTION SPECTROMETRY
The real absorption spectrum of a diatomic molecule, which has only asingle vibrational mode, is not a line spectrum, but an absorptionspectrum containing a broad peak with a maximum at the frequency ofabsorption as shown in Fig. 2.4.
The line broadening in spectrometry arises because of character-istics adherent to molecules in different phases and uncertainty in the
13
1
Q
A
-E
11
V
Frequency, Hz
Fig. 2.4. A broad peak representing an absorption.
energy levels due to the limited residence time of the particle in theexcited state.
In solids, liquids and gases the particle velocities are different. Theparticles collide more frequently in the gas phase than in the liquidphase. The vibrational and rotational energy levels are perturbed fromtheir actual values and lead to small variations in the ground stateenergy levels. This implies that solids should give sharp bands. This istrue, but the bands are split because of electronic interactions. Spectralline broadening arises also due to the Doppler effect. The infraredmeasurements are made in cells where the radiation is allowed to passthrough or interact with the sample. Molecules that are in motiontowards the source will absorb radiation of higher frequency comparedwith the molecules that are moving away from the source (lowerfrequency).
One of the important effects that cause spectral line broadening isthe uncertainty effect. The uncertainty principle proposed by WernerHeisenberg suggests that there is natural limitation on how precise apair of physical parameters can be made. In vibrational spectrometrythe uncertainty in the energy level of the excited state, AE, anduncertainty in the lifetime of the molecule at an excited vibrationalstate, At is related by the uncertainty relationship as follows.
AE At 2 h/2 (2.4)
This can be rewritten to include frequency v as follows
A(hv)At 2 h/2t (2.5)
14
ii
i.e.
AvAt > 1/2xT (2.6)
If the residence times at the excited vibrational states are infinite thenthe uncertainty in the frequency of absorption is zero and the frequencycan be determined precisely. The molecules that undergo vibrationaltransitions have a finite time of residence of 10-8 s and this leads to anuncertainty in the frequency
Av > h/(2xAt) = 1/(2x3.14x 10-8) s 108 (2.7)
This uncertainty is small compared to the radiation frequency ofinfrared radiation 1012-104. This leads us to conclude that absorptionby a single vibrational mode will be a band spectrum with a finitefrequency width as shown in Fig. 2.4.
2.4 MEASURED SPECTRA OF DIATOMIC MOLECULES
The measured infrared spectra of diatomic molecules do not show asingle band as we expected but fine spectra with several fine peaksspaced at equal intervals with a space in the middle. The fine spectraarise from the rotational spectra of diatomic molecules. When a di-atomic molecule is excited the rotational levels are also excited and therotational absorptions are superimposed on the vibrational spectra ofthe diatomic molecules. The vibrational spectrum of carbon monoxideat high resolution is shown in Fig. 2.5.
2.5 NORMAL OR FUNDAMENTAL VIBRATIONS
Molecules of a substance are in continuous motion. They move(translation) and rotate. Each atom in a molecule assumes a newposition with time.
Each atom in a molecule can be represented by three co-ordinates (x,y, z) in a Cartesian system. We say that the atom has three degrees offreedom. When we consider a molecule containing N atoms, the atomshave a total of 3N degrees of freedom. The result of the movements of
15
o
o -
Co
C
gO g
C
o
C0
o -~
CC
C,
0O -
Co -E:
:1 O
N CC
. o
O UC
oC
N E
g
-~C
M CC
o
rl i
r
cIF,
the individual atoms can be represented by the movement of the centreof mass of the molecule.
The position of the centre of mass-the position of the molecule inspace-can then be represented by three co-ordinates, i.e., threedegrees of freedom. The molecule rotates about its centre of mass, andthe rotations about three mutually perpendicular axes passing throughthe centre of mass require three more degrees of freedom. The freemovement of the atoms is restricted by the bonds between the atoms,but they vibrate from their equilibrium positions. These are repre-sented by the remaining 3N - 6 degrees of freedom. These vibrationalmotions are called normal or fundamental vibrations. Linear moleculesneed only two degrees of freedom to specify rotations of the molecules inspace. Therefore, the linear molecules have 3N - 5 fundamental vibra-tional modes.
2.6 INFRARED SPECTRUM OF POLYATOMIC MOLECULES
Fortunately, the energy needed to excite most of the vibrational modesin organic molecules falls in the infrared spectral frequency region7.5x101 2-1.2x101 4 (250-4000 cm-l). In infrared spectroscopy, it is
tK
3.0-
2.5
i 2.0
w 1.5
1.0.
0.5.
0.05I
- GroYp requencies -
i AAA, )L I i
1350
f- Fierprt --
eI n.
, Aid
900
kA
17
4000.0 3000 2000 1500 1000 450,0
Wavenumber cm-1
Fig. 2.6. An infrared absorption spectrum of polyatomic molecule (polystyrene).
I 1}Y I 1v, VCLU v ·. I I I
X - V ,. . . . ..
customary to give the excitation energy needed in terms of wave-number v which has a directly proportional relationship with frequencyv as v = v/c. The region 4000-1350 cm-l contains group frequencies andthe region 1350-900 cm-l contains low energy vibrations. This region ischaracteristic of the molecule and is called the fingerprint region.
If the molecule is polyatomic and the radiation is polychromatic,then the vibrational modes absorbing in the region 4000-250 cm-l willresult in considerable overlap and the plot between absorbance andwavenumber will be a mixture of sharp and broad bands over the wholerange. Wavenumbers are usually plotted from higher wavenumbers tolower wavenumbers and the plot is called an infrared absorptionspectrum (Fig. 2.6).
GENERAL BIBLIOGRAPHY
P.W. Atkins, Molecular Quantum Mechanics. Oxford University Press,London, 1984.
C.N. Banwell and E.M. McCash, Fundamentals of Molecular Spectroscopy.McGraw-Hill, London, 1994.
W. Kemp, Organic Spectroscopy. Macmillan, London and Basingstoke, 1978.J.H. Vander Maas, Basic Infrared Spectroscopy. Heydon & Sons, London, 1972.
18
Chapter 3
Theory of infrared spectroscopy
3.1 PRINCIPLES OF INFRARED SPECTROSCOPY
When irradiated with infrared light, a molecule absorbs it under someconditions. The energy hv of the absorbed infrared light is equal to anenergy difference between a certain energy level of vibration of themolecule (having an energy Em) and another energy level of vibration ofthe molecule (having an energy En). In the form of an equation,
hv=En-Em (3.1)
holds. In other words, absorption of infrared light occurs principallybased on a transition between energy levels of molecular vibration.This is why an infrared absorption spectrum is a vibrational spectrumof a molecule.
Satisfying Eq. (3.1) does not always cause infrared absorption.There are transitions which are allowed by a selection rule (i.e., allowedtransition) and those which are not allowed by the same rule (i.e.,forbidden transition). In general, transitions with a change in thevibrational quantum number by +1 are allowed transitions and othertransitions are forbidden transitions. This is what is known as aselection rule with respect to infrared absorption. Another selectionrule with respect to infrared absorption is one which is defined by thesymmetry of a molecule. This selection rule is, in other words, "a rulethat infrared light is absorbed when the electric dipole moment of amolecule changes as a whole in accordance with a molecular vibration."
The two selection rules are developed from quantum-mechanicalconsiderations. According to quantum mechanics, for a molecule totransit from a certain state m to another state n by absorbing or
19
emitting infrared light, it is necessary that the following definiteintegral:
(P)mn = f W.tln mdQ (3.2)
or at least one of (py)mn, and (z),, which are expressed by a similarequation is not 0, where Px denotes an x-component of the electric dipolemoment; v denotes the eigenfunction of the molecule in its vibrationalstate; and Q denotes a normal coordinate (i.e., a normal vibration; seeSection 3.3) expressed as a single coordinate. Now, let us consider only(px)mn. A distribution of electrons in the ground state changes as thecoordinate expressing a vibration changes and, therefore, the electricdipole moment is a function of the normal coordinate Q. Hence, Px canbe expanded as follows:
PX =( )o (d /Q)oQ+ 1(82 /Q2)Q2+... (33)2
Expressed by a displacement of atoms during the vibration, Q has asmall value. This allows us to omit Q2 and the subsequent terms in theequation above. Substituting the terms up to Q of Eq. (3.3) in Eq. (3.2)
(p.x)m, =(Pi)oWVm dQ+ 8 x f QydQ (3.4)
is obtained. Due to the orthogonality of the eigenfunction, the first termof this equation is 0 except when m = n holds. The first term denotes themagnitude of the permanent dipole of the molecule. For the secondterm to have a value other than 0, both (p /taQ)o # 0 and lJynQ /mdQ • 0must be satisfied. These two conditions lead to the two selection rules.The nature of the eigenfunction permits the integral to have a valueother than 0 only when n = m 1 holds. (Considering Q2 and thesubsequent terms of Eq. (3.3) as well, we can prove that even when n =m + 1 fails to hold, (x)mn has a value, even though small, other than 0).The first selection rule regarding infrared absorption is thus proved.The other selection rule, which is based upon the symmetry of amolecule, is obtained from (JcdQ) 0 • 0. The relationship (pJaQ)o X 0indicates that infrared absorption occurs only when certain vibrationchanges the electric dipole moment. The vibration is infrared active
20
when (pJaQ)0 0 holds, but is infrared inactive when (p 1JcaQ)0 = 0holds.
Since most molecules are in the ground vibrational state at roomtemperature, a transition from the state v" = 0 to the state v" = 1 (firstexcited state) is possible. Absorption corresponding to this transition iscalled the fundamental. Although most bands which are observed ininfrared absorption spectra arise from the fundamental, in some cases,we can find bands which correspond to transitions from the state v" = 0to the state v" = 2, 3, 4 ... (i.e., overtone transitions). However, sinceovertones are forbidden, overtone bands are very weak.
The horizontal axis and the vertical axis of an infrared absorptionspectrum must now be explained. A frequency is indicated along thehorizontal axis in the units of wavenumber (cm-1 ) (with higher wave-numbers always on the left-hand side) (Fig. 3.1). On the other hand, atransmittance T (%) (Fig. 3.1a) or an absorbance E (Fig. 3.1b) isexpressed along the vertical axis. While infrared spectra includereflectance spectra and emission spectra in addition to absorption
(a)
80
60
40
20
01.0
(b)
0.8
0.6
0.4
0.2
04000 3200 2400 1600 800
Fig. 3.1. Examples of infrared spectra: (a) transmittance spectrum; (b) absorbancespectrum.
21
spectra, a reflectance, an emission intensity, etc. are expressed alongthe vertical axis in the case of a reflectance spectrum, an emissionspectrum, etc.
3.2 CHARACTERISTICS OF INFRARED SPECTROSCOPY
Infrared spectroscopy provides detailed information about vibrations ofa molecule. Since molecular vibrations readily reflect chemical featuresof a molecule, such as an arrangement of nuclei and chemical bondswithin the molecule, infrared spectroscopy contributes considerablynot only to identification of the molecule but also to study of themolecule structure. Furthermore, an interaction with a surroundingenvironment also causes a change in molecule vibrations, and hence,infrared spectroscopy is useful in studying the interaction, too.Infrared spectroscopy has many uses from basic research to variousapplications. Why is infrared spectroscopy useful? The answer issimple. It is spectroscopy which probes a vibration of a functionalgroup. Infrared spectroscopy can be used not only for the identificationof a functional group, but also for the investigation of the chemical bondand environment of the functional group. For example, C=O groups of-C=C-C=O and -CH2 -CH2 -C=O give different frequencies. Of course,a -C=O group and -C=O .. H-O- also yield different frequencies. Wecan summarize the characteristics of infrared spectroscopy as follows:
1. Using an electromagnetic wave having a low energy, infrared spec-troscopy rarely damages a sample. In addition, infrared spectro-scopy may be used for non-destructive analysis of a sample.
2. Infrared spectroscopy is applicable to a sample in various states,e.g., solid, crystal, fibre, film, liquid, solution and gas. Furthermore,measurements of infrared spectra of a sample in a solution and in asolid state, allow us to compare its structure in the solution withthat in the solid.
3. Infrared spectroscopy uses not only so-called infrared absorption,but can utilize infrared reflection, emission, photoacoustic spectro-scopy as well.
4. Connection with an optical microscope, a gas chromatograph, aliquid chromatograph or other instrument is relatively easy, whichallows hyphenated analysis.
22
3.3. MOLECULAR VIBRATIONS
Knowledge about vibrations of a molecule is crucially important forunderstanding infrared spectroscopy. It is useful also for Raman andnear-infrared spectroscopy. While vibrations of a polyatomic moleculeare generally complex, according to harmonic oscillator approximation(i.e., an approximation on the premise that the force which restores adisplacement of a nucleus from its equilibrium position complies withHooke's law; vibrations in harmonic oscillator approximation are calledharmonic vibrations), any vibrations of the molecule are expressed ascompositions of simple vibrations called normal vibrations. Normalvibrations are vibrations of nuclei within a molecule, and translationalmotions and rotational motions of the molecule as a whole are notincluded in normal vibrations. In each normal vibration, all atomsvibrate with the same frequency (normal frequency), and they passthrough their equilibrium positions simultaneously. In general, a mole-cule which consists of N atoms has 3N - 6 normal vibrations (3N - 5normal vibrations if the molecule is a linear molecule). Since normalvibrations are determined by the molecular structure, the atomicweight and the force constant, when these three are known, we cancalculate the normal frequencies and the normal modes.
3.4 A VIBRATION OF A DIATOMIC MOLECULE
As the simplest example of molecular vibrations, a vibration of adiatomic molecule will now be considered. Being always a linear mole-cule, a diatomic molecule has only one normal vibration (3 x 2 - 5 = 1).Needless to say, this vibration is a stretching vibration that the mole-cule stretches and contracts (Fig. 3.2a). We will describe the stretchingvibration in accordance with classic mechanics. Assuming that thenuclei are masses, m1 and min, and the chemical bond is the "spring" as
k
m, m2
(a) (b)
Fig. 3.2. (a) A stretching mode of a diatomic molecule. (b) A model for a diatomic molecule(two masses combined by a spring).
23
in Hooke's law (with the spring constant k) (Fig. 3.2b), we can explainthe vibration of the molecule based on classic mechanics.
Now, assume that the masses m and m2 deviate Ax 1 and Ax2,respectively, from their equilibrium positions. Then, the potentialenergy of the system shown in Fig. 3.2b is:
V = k(Ax2 -Ax 1 )2 (3.5)
Meanwhile, the kinetic energy of the system is:
1 2 1 dx('. i>T =-m~lx - m2 x 2 = dt) (3.6)
Now that V and T are known, motions of the system are determined bysolving Lagrange's equation of motion:
d(aT + =0 (3.7)dt (ai ax i
However, before solving Lagrange's equation of motion, we introducenew coordinates Q and X.
Q= pL(Ax 2 -Ax 1 ) (3.8)
X = mAx + mAx2 (3.9)Vm + m2
Now,
= m2 (where i is a reduced mass) (3.10)m +M2
Q is a coordinate of the displacement of a distance between the twomasses, while X is a coordinate of the displacement of the centre ofgravity of the system. Using Q and X, the potential energy V and thekinetic energy T are written as:
24
T 1 Q2 + 1x2 (3.11)2 2
v= k 2 (3.12)2 p
We substitute V and T in the Lagrange equation of motion (3.7). First,applying to the coordinate X (xi = X), we obtain
X=0 (3.13)
This expresses a free translational motion which is not bounded by thepotential energy. On the other hand, from the Lagrange equation ofmotion regarding the coordinate Q(xi = Q), we obtain
dQ + k Q =O (3.14)dt2 pL
From the differential equation like Eq. (3.14), we can find a solution asfollows:
Q = Q0 cos2Tvt (3.15)
Equation (3.15) implies that the system illustrated in Fig. 3.2b has asimple harmonic motion with the frequency v and the amplitude Q0.Substituting Eq. (3.15) in Eq. (3.14),
(-42v2 +k)Q=0 (3.16)
Finally, we find the frequency of the spring as:
v = I 1k (3.17)2n
Since the frequency of the spring corresponds to the frequency of themolecular vibration and the spring constant corresponds to the force
25
TABLE 3.1
Stretching frequencies and force constants of diatomic molecules
Reduced mass (p)(1.66x10 -2 4)
0.50
0.67
1.00
17.50
7.00
8.00
0.95
0.97
0.98
0.99
7.46
6.85
Force constants(105 dyne/cm)(N cm 1)
5.73
5.77
5.77
3.21
22.9
11.8
9.17
5.16
4.06
3.12
15.9
19.0
constant of the chemical bond, it can be seen from Eq. (3.17) that thefrequency of the molecular vibration is proportional to the square rootof the force constant and inversely proportional to the square root of thereduced mass of the atoms. Table 3.1 shows the stretching frequenciesand the force constants of some diatomic molecules. As can clearly beseen in the table, the stronger a chemical bond is and the smaller themasses of atoms are, the higher the stretching frequency of a moleculebecomes.
As diatomic molecules, there are those like H2, which consist of thesame atoms (homonuclear diatomic molecules) and those like HCl,which consist of different atoms (heteronuclear diatomic molecules). Ofthese, vibrations of only heteronuclear diatomic molecules appear ininfrared absorption spectra. This is because while the electric dipolemoment of a heteronuclear diatomic molecule changes with a moleculevibration, that of a homonuclear diatomic molecule is always 0.
26
Molecule
H2
HD
D2
35C1 2
N2
02
HF
H3 5C1
HBr
HI
NO
CO
G(v)(cm- l )
4160
3631
2944
556
2331
1555
3962
2886
2558
2233
1877
2143
3.5 QUANTUM MECHANICAL TREATMENT OF A VIBRATION OF ADIATOMIC MOLECULE
Quantum mechanics allows us to describe energy levels of vibrations ofdiatomic molecules. In quantum mechanics, the first step is to writedown Schridinger's equation, HI = Ey. The second step is to solve theequation to calculate an eigen value and an eigen function. In terms ofclassic mechanics, the total energy H of a vibration of a diatomicmolecule is the sum of a kinetic energy 1/2Q2 (Eq. 3.11) and a potentialenergy (1/2)k.(Q2/p) (Eq. 3.12),
H=T +V =2 Q2 +_ Q2 (3.18)
Replacing Q with an operator -ih/2z.dldQ, H is calculated as:
h 2 d2 lkH -- d + -kQ2 (3.19)
8n 2 dQ2 2
Substituting this in Hy = Ey and processing the formula, a Schrod-inger equation on harmonic oscillator of a diatomic molecule isobtained.
d2 Y 872 I Q2>+- E- k -j) =0 (3.20)
dQ2 h 2 2 )
As how to solve this equation is described in detail in a number ofbooks, we will explain only a result. The formula (3.20) has a solutiononly to the following eigen value Ev:
Ev =(V +-hv (3.21)
where V is a quantum number of a vibration (V = 0, 1, 2, ...).An eigen function to each value of Ev is expressed as:
Wv =Nv Hv(, Q)exp - (3.22)
27
where Nv denotes a normalization constant, Hv is a Hermite poly-nomial, and a = 4i72!v/h.
Wave functions to V = 0, 1, and 2 are as follows.
v/o =(a / 7) 4 exp(-aQ2 /2) (3.23a)
p1 =(a / 7)14 (2a)V2 Q exp(_aQ 2 / 2) (3.23b)
,2 =(al /t)" 4 (1/ 2)(2aQ2 - 1)exp(-aQ2 /2) (3.23c)
As is clearly understood from these formulas, a wave function of aharmonic oscillator is an even function when a quantum number is aneven number but is an odd function when a quantum number is an oddnumber. Figure 3.3 shows a potential energy, wave functions, v,existence probabilities, x' and energy eigen values, E, of theharmonic oscillator.
When we treat vibrations of diatomic molecules in accordance withquantum mechanics, we will find different results from when we treatthe same in accordance with classic mechanics. Firstly, the lowestvibrational energy is not 0 but Eo = (1/2)hv. Energies have discretevalues E = (3/2)hv, E2 = (5/2)hv, E3 = (7/2)hv, ..., and an energydifference between adjacent energy levels is always hv. Another major
(a) (b)
Fig. 3.3. A potential energy, wave functions, and probabilities of existence of harmonicoscillator.
28
-Q-0- +
difference between a conclusion we obtain from quantum mechanicsand a conclusion from classic mechanics is the amplitude of molecularvibrations. While classic mechanics never allows us to assume that theamplitude, namely, the existence probability of a diatomic moleculeextends beyond a potential energy, quantum mechanics permits us tofind a slight existence probability outside a potential energy in eachstate (Fig. 3.3b).
3.6 VIBRATIONS OF POLYATOMIC MOLECULES
We will consider normal vibrations of carbon dioxide (CO,; linear tri-atomic molecule) and water (H20; non-linear triatomic molecule) asexamples of the simplest polyatomic molecules. CO2 has 3x3 - 5 = 4normal vibrations. Figure 3.4 shows the four normal vibrations 1, 3, 2aand 2b (see Section 4.8.1 for labelling rules). The normal vibrations 1and 2 are vibrations that two CO bonds stretch and contract in phase(1) and out of phase (3), respectively, called symmetric and anti-symmetric stretching vibrations. Meanwhile, the vibrations 2a and 2bare both vibrations that the angle of OCO changes and are calledbending vibrations. While the vibrations 2a, 2b are independent of eachother, energies required for the vibrations are in principle equal to eachother, only with planes of the vibrations differing by 90 degrees fromeach other. That is, the two types of vibrations have the same energy.Such vibrations which have principally the same energy are calleddegenerate vibrations.
1 0
3 _ 0
2a ?
2b DO
Fig. 3.4. Molecular vibrations of CO2: (1) symmetric stretching vibration; (3) anti-symmetric stretching vibration; (2a, 2b) degenerate vibrations.
29
9 q
V, C2 V3
Fig. 3.5. Molecular vibrations of water: (1) symmetric stretching vibration (vl); (2)bending vibration (v2); (3) antisymmetric stretching vibration (V3).
To know whether the normal vibrations 1, 3, 2a and 2b are infraredactive or not, we examine a change in the electric dipole moment atequilibrium positions (prJQ),. In the normal vibration 1, the electricdipole moment is always 0. Hence, the normal vibration 1 is infraredinactive. Conversely, the electric dipole moment largely changes in thenormal vibration 3, and thus it is infrared active. In a similar manner,the normal vibrations 2a and 2b accompany a change in the electricdipole moment, and therefore, are infrared active (see also Section 4.8.5and Fig. 4.28). With respect to a molecule such as a CO 2 molecule whichhas the centre of symmetry, a general rule holds true that an infraredactive vibration is Raman inactive and a Raman active vibration isinfrared inactive. This rule is called the mutual exclusion rule.
Water, being a nonlinear triatomic molecule, has three normalvibrations, as shown in Fig. 3.5. The normal vibrations 1 and 3 havedifferent frequencies from each other, because of different H1... H2interactions between the two (see also Section 4.7.4 and Fig. 4.23).
In the cases of CO 2 and H20 molecules, the frequency of a stretchingvibration is higher than that of a bending vibration. This indicates thatthe stretching vibration requires a higher energy than the bendingvibration.
Next, let us consider vibrations of atomic groups. Figure 3.6 showssix vibrational modes of an AX 2 group (e.g., CH2, NH2). Of the six, twovibration modes are stretching vibrations, one being a symmetricstretching vibration and the other an antisymmetric stretching vibra-tion. The remaining four are bending vibrations, i.e., scissoring, rock-ing, wagging, and twisting vibrations. Of the four bending vibrations,scissoring and rocking vibrations are bending vibrations in the plane ofCH2 (in-plane vibrations), while wagging and twisting vibrations arevibrations which displace vertically to the plane of CH2 (out-of-planevibrations).
30
1
1 2 3
4 5 6
+ T + +
Fig. 3.6. Molecular vibrations of AX2 group: (1) symmetric stretching vibration; (2)antisymmetric stretching vibration; (3) scissoring vibration; (4) rocking vibration; (5)
wagging vibration; (6) twisting vibration.
In general, group frequencies are useful to consider vibrations of apolyatomic molecule which includes three or more atoms (see Chapter5). Group frequencies are vibrations of particular atomic groups(functional groups), such as rocking, symmetric and antisymmetricvibrations of a CH2 group, C=O stretching vibration of a carbonyl groupand stretching vibration of an OH group. (Bands due to groupfrequencies are called characteristic absorption bands.) The concept ofgroup frequencies hold true when certain normal vibrations are sub-stantially determined by movements of two or a plurality of atoms(atomic group). Group frequencies play prominent roles in the analysisof infrared and Raman spectra. A more detailed description of groupfrequencies is given in Chapter 5.
3.7 QUANTUM MECHANICAL TREATMENT OF VIBRATIONS OFPOLYATOMIC MOLECULES
We will now explore vibrations of polyatomic molecules in accordancewith quantum mechanics. A kinetic energy T and a positional energy Vare expressed as:
T = 2 (3.24)2 i=1
31
V2 i;iQi (3.25)2 i=1
Hence, a total energy H is:
1 n 2V 1 H=T+V= 1Qi +Z-YiQi2 (3.26)
2 i 2 i=,
Replacing Q with -ih/2w.d/dQ again and calculating Ht, we can yield awave equation (3.27) regarding vibrations of polyatomic molecules.
h2 a 2 +i -2 E + riQ2 V =EW (3.27)87 , CqQ2 2 -1
Since normal vibrations are independent of each other, the formulaabove can be separated into n wave equations which, respectively,correspond to the respective normal vibrations, an eigen value E isexpressed as the sum of eigen values Ei of the respective normalvibrations, and an eigen function yv is expressed as a product of eigenfunctions yi representing the respective normal vibrations. In short,since the formula (3.27) has the same style as formula (3.20), the eigenvalue Ei is also the same as formula (3.21).
Hence, a total of vibrational energies whose frequencies are v1, v2, ...,Vn is:
E i =(V i +1/2)hv i (3.28)
Ev =E1 + E2 + .+En
=iV1 + )hv, +iV 2 +)hv 2 + +Vn +2 hv (3.29)
Figure 3.7 shows energy levels of v1, v2, and v3 modes (Fig. 3.5) of awater molecule. In Fig. 3.7 (0, 0, 0) denotes the lowest ground state and(1, 0, 0), (0, 1, 0), (0, 0, 1) denote fundamental levels at which v1, v2 andv3, respectively, have a quantum number of 1. Transitions between thelowest ground state and the fundamental levels are fundamentals.Next, (2, 0, 0), (0, 2, 0), (0, 0, 2) denote that vj, v2, and v3 have a quantumnumber of 2, respectively, and are called ouertone levels. (3, 0, 0) ... are
32
12000
7 80000
4000
A~
(,,
(1 11)
I_______ _ -(1 0 1)(0 2 1)
(O 11)
(O 0 1)I--____ _ -(1 0 0)
(0 2 0)
-- - (O 1 0)
(0 0 0)
Fig. 3.7. Energy levels of vl, vl, and V3 modes of water.
also overtone levels. Overtones are transitions between these overtonelevels and the lowest ground state. Combination mode levels are levels,such as (1, 0, 1) and (0, 1, 1), at which two or more normal vibrations areexcited. Transitions between combination mode levels and the lowestground state are called combination modes.
3.8 ANHARMONICITY
So far, we have treated molecular vibrations as harmonic oscillators.However, except for the vicinity of the bottom of a potential energycurve, the harmonic oscillator model is not a good model on molecularvibrations in reality. If the harmonic oscillator model were correct, aswe can clearly see in Fig. 3.3, dissociation of molecules should neveroccur, no matter how large the amplitude is. Hence, it is necessary toconsider a potential energy function V(r) (r denotes an inter-nucleardistance) which more accurately expresses vibrations of molecules. In
33
-Q-- o - +Q(re)
Fig. 3.8. Morse's function.
accordance with our instinct, V(r) must be a function such that itrapidly increases when r approaches zero but gradually comes close to adissociation energy, De, where r >> re (re is an equilibrium distance)holds. As a function which satisfies this condition, Morse's functionexpressed as below is well known:
V(r) = De[1 - exp(-a(r - re))]2 (3.30)
In formula (3.30), a is a constant. Figure 3.8 shows Morse's function.Assuming that Q = r - re is always smaller than r and expanding V(r) byTaylor's series into a polynomial with respect to Q in the vicinity of re,
, Q + I IQ+-re 2 r 6( d3 (3. 31)) 6\ ~" or ~(3.31)
+-( Q4 +24 a 8r4 ),
Since the first term on the right-hand side is a constant term, this termis regarded as 0. With respect to the second term as well, since V is
34
extremely small to re, the second term is also regarded as 0. Now,ignoring the fourth and higher-order terms and applying (32V ar2 )re = k,the following formula holds:
V(r)= 1kQ2 (3.32)2
In other words, Morse's function is equivalent to a function whichexpresses harmonic oscillator approximation in the region close to theequilibrium inter-nuclear distance re (a second derivative on formula(3.30) yields k = 2a2De).
A potential energy V is generally expressed as:
V= k2Q2 + k3Q3 + k4Q4 + ... (3.33)
The high-order terms such as Q3 and Q4 are called anharmonic terms.Calculating an eigen value Ev' considering up to the Q3 term, we obtain,
EV =V + hre-IV + 2hvexe (3.34)
where v, =a / D/ 2 n. The symbol Xe is a constant called an an-harmonic constant.
It is possible to approximately assume the degree of anharmonicityfrom the value of this constant. Table 3.2 shows the values of an-harmonic constants for major diatomic molecules. While the constant xehas a value of 0.01 approximately, if a molecule contains a hydrogenatom which has a light mass, the constant xe increases (Table 3.2).Since the anharmonic constant xe holds the following relationship withrespect to a, De, etc., it is possible to calculate the shape of Morse'sfunction and a dissociation energy of the molecules, etc.
hve haXe= hv - ha (3.35)4De 4 2c1*D
From formula (3.34), one can calculate a difference, AEv, betweenenergy levels of vibrational quantum numbers V and V + 1.
AE= hv, - 2hvexe(V + 1) (3.36)
35
TABLE 3.2
Anharmonicity constants of diatomic molecules
Anharmonicity constant
0.02685
0.02055
0.02176
0.01741
0.01706
0.01720
0.007081
0.002857
0.006122
0.007639
0.007337
Formula (3.36) shows that the larger V is, the smaller AEv is.In this formula, a transition u = 0 - 1 is:
(3.37)
Hence, AE = hv, does not hold. The value Vobs (which is an observedvalue) is obtained as AE v = hvob,. We will now describe a method ofcalculating ve from Vob.
HCI exhibits a strong band at 2886 cm -1 due to a fundamental (V = 0to 1) and a weak band at 5668 cm-1 due to a first overtone (V = 0 to 2). Itis possible to calculate an absorption wavenumber ve and an anharm-onic constant xe from these observed values.
With respect to V = 0 - 1 and V = 0 -> 2,
(3.38a)
(3.38b)
Hence,
2886 = v(1-2x ) (3.39a)
Molecules
H2
D2
HF
HC
HBr
H1
C12I2
N2
02NO
AEv = hve, - 2hvexe = hve(1 - 2xe)
AE (1) = hv( (1- 2 x )
36
AE, (,-,) = 2hv,(1 -3x, )
5668 = 2v,(l- 3xe )
Solving these simultaneous equations, we obtain xe = 0.0174 and ve =2990 cm - . We must consider Ve to discuss the strength of a chemicalbond, since considering Vob, is not sufficient for this purpose.
3.9 OVERTONES AND COMBINATION MODES
It is anharmonicity that allows overtones and combination modes to beobserved. Let us consider selection rules regarding infrared spectraonce again. This time, we will consider anharmonicity on a dipolemoment.
I I Q-L-! Q2±. (3.40)DQ )o 2y Q
() =( 4)Of edQ+ j J JnQy-dQ(~ Ix =1xlv m +Q |v m(3.41)
2(,9Q2 )9Q 2 Q 0dQ+
The third term has a value other than 0 when ( 2 pjdQ 2 ) 0 andynQQ2 PmdQ X 0 both hold. The latter integral has a value other than 0
when V' V and V + 2. Hence, even a first overtone is no longerforbidden if we consider the term Q2 as well. In a similar manner,second, third, etc. overtones are no longer forbidden as we take higher-order terms into consideration. However, the intensities of these over-tones are far weaker than those of fundamentals. The frequencies offirst, second, third, etc. overtones are smaller than double, triple,quadruple of the frequencies of fundamentals, respectively. This isbecause the differences between the vibrational energy levels becomenarrower as the quantum number u increases, as clearly shown in Fig.3.9 and indicated by formula (3.36). Anharmonicity excludes combina-tion modes as well from those forbidden in a similar manner. Theintensities of combination bands are also weak.
37
(3.39b)
3.10 FERMI RESONANCE
In some cases, overtones and combination modes are as strong asfundamentals. This occurs when we have Fermi resonance. Fermiresonance is developed by anharmonicity, when the frequency of anovertone or a combination mode by chance happens to be approx-imately the same as that of a fundamental (or when an overtone and acombination mode have very close frequencies with each other). Whenwe have Fermi resonance, two relatively strong bands appear in aregion where we are supposed to observe only one strong fundamental,one on the high-wavenumber side to the fundamental or the overtoneand the other on the low-wavenumber side to the fundamental or theovertone. These two bands both contain contributions from the funda-mental and the overtone. In other words, Fermi resonance occurs whenthe fundamental and the overtone are mixed together because ofanharmonicity.
Figure 3.9 shows an infrared spectrum of benzaldehyde as anexample of Fermi resonance. In general, aldehyde yields a band due toa CH in-plane bending vibration in the vicinity of 1400 cm l. Anovertone of this band is expected to appear in the vicinity of 2800 cm l,and its frequency is close to the frequency of CH stretching vibration ofaldehyde. In the real spectrum, we find one band on a somewhat higherwavenumber side and another band on the lower wavenumber side to2800 cm-l (Fig. 3.9). These bands are created because of Fermi reson-ance between the overtone of the CH in-plane bending vibration andthe CH stretching vibration.
Isd
000 00-__
10000 F5T II JW- Al~~~J'LL L
3200 2800 2400 2000 bU I&0/cml
Fig. 3.9. An infrared spectrum of benzaldehyde as an example of Fermi resonance
38
,,
CUN
2
I�1- - ( - -
Let us now consider why Fermi resonance occurs. Assume we havesmall terms (such as a potential energy due to anharmonicity) whichprovide perturbations to two energy levels, El, E2 (El > E2). We cancalculate changes in E1 and E2 caused by the perturbations if we solvethe following formula with respect to W.
E 1 + al -W 0=0 (3.42)
D3 E 2 +a 2 -W
where al, a2, P are the small terms which provide the perturbations. Aswe expand formula (3.42), we obtain,
W 2 -(E 1 +E 2 + 1 + a2)W +-(E1 + a,)(E + a2)-P2 =0 (3.43)
As we solve this formula (assuming that a, a2, p are sufficientlysmaller than E1, E2), we obtain,
W=E1 +a 1 + D or E2 +a 2 (3.44)E 1 - E,2 E - E2
Changes in E1 and E2 are extremely small if E1 - E2 >> 0. However,when E1 - E 2 = 0, that is, when E1 and E2 are close to each other, a typeof resonance occurs, thereby considerably changing the values of E andE2.
When we consider Fermi resonance, we must note that only thosehaving the same vibrational symmetry cause Fermi resonance betweenthem. For instance, although two OH stretching vibrations v1 and V3(Fig. 3.5) of a water molecule do not cause resonance between themsince the vibrations have different symmetries from each other, theirovertones (2v1 and 2v3 ) have the same symmetry and therefore causeFermi resonance (see also Section 4.9.2).
GENERAL READING
Theory of molecular vibrationsG. Herzberg, Molecular Spectra and Molecular Structure I. Spectra of Diatomic
Molecules, 2nd edn. Van Nostrand, Amsterdam, 1950.
39
G. Herzberg. Molecular Spectra and Molecular Structure II: Infrared andRaman Spectra of Polyatomic Molecules. Van Nostrand, Amsterdam,1945.
K. Nakamoto, Infrared and Raman Spectra of Inorganic and CoordinationCompounds, 5th edn. Wiley-Interscience, New York, 1997.
E.B. Wilson, Jr., J.C. Decius and P.C. Cross, Molecular Vibrations. McGraw-Hill, New York, 1955.
L.A. Woodward, Introduction to the Theory of Molecular Vibrations andVibrational Spectroscopy. Oxford University Press, London, 1972.
Infrared spectroscopyL.J. Bellamy, The Infrared Spectra of Complex Molecules, Vol. 1, 3rd edn.
Chapman and Hall, London, 1975; Vol. 2, 2nd edn. Chapman and Hall,London, 1980.
N.B. Colthup, L.H. Daly and S.E. Wiberley, Introduction to Infrared andRaman Spectroscopy, 3rd edn. Academic Press, San Diego, CA, 1990.
P.R. Griffiths and J.A. deHaseth, Fourier Transform Infrared Spectroscopy.Wiley-Interscience, New York, 1986.
40
Chapter 4
Symmetry of molecules, group theory andits applications in vibrationalspectroscopy
In Chapter 3, we learnt that a molecule is infrared active if the dipolemoment changes during the vibrational motion and that a molecule isRaman active if the polarizability changes during the vibrationalmotion.
In the case of diatomic molecules, the number of degrees of freedomcorresponding to the vibrational motions in the molecule is 3x2 - 5 = 1.This motion is the stretching vibration along the axis of the molecule.We saw in Chapter 3 that the dipole moment of a heteroatomic diatomicmolecule changes during its vibration and the molecule is infraredactive, and that the dipole moment of a homonuclear diatomic moleculedoes not change and the molecule is infrared inactive. We then went onto discuss carbon dioxide molecule and identified that the normalvibrations 2, 3a and 3b are infrared active because of the change indipole moment during these vibrational motions in the molecule.Furthermore, we found that the normal vibration 1 is infrared inactivebecause the dipole moment does not change during this motion..
However, by the general mutual exclusion principle, as we saw inChapter 3, we know that this rule holds for molecules with centre ofsymmetry. That is, the vibrational motions that are infrared active areRaman inactive and the motions that are infrared inactive are Ramanactive (this must be seen as a rule of thumb not as an absoluteprinciple). To determine whether a motion is Raman active, we mustfind out whether there is change in the polarizability during thismotion. Symmetric vibrational modes in a molecule that lead to achange in the size of the molecule generally involve changes in thepolarizability and are Raman active. For example, symmetric stretch-
41
ing in carbon dioxide leads to a change in the size of the molecule andinvolves a change in polarizability and the motion is Raman active.
For the polyatomic molecules, it is often difficult to determinewhether a mode is infrared active or Raman active. The selection rulesfor infrared and Raman absorption can be arrived at by considering thesymmetry of the molecules. In order to do this, we have to learn thesymmetry aspects of the molecules, their group and symmetries of thedifferent molecular vibrations.
4.1 SYMMETRY OF MOLECULES: SYMMETRY ELEMENTS ANDSYMMETRY OPERATIONS
Geometrical figures such as equilateral triangles, squares, cubes etc.possess symmetry. A visual inspection of these shapes leads us toperceive that there are some symmetrical features in them. Forexample, in a square figure cut out from a white sheet of paper, all thesides are equal. Their diagonals bisect at the centre of the square, thecorners of the square are at equal distances from the centre, the squarecan be divided into two halves along the axis passing through the midpoints of any two opposite sides or along their diagonals. Furthermore,the figure can be rotated in several ways about its centre, along thediagonal axes and along the axes passing through the middle points ofany two opposite sides to get the same figure without any apparentchange. We say that this figure has several symmetry elements. Whencertain operations are made, the figure seems apparently unchanged.We call these operations symmetry operations.
In polyatomic molecules, the orientation of atoms in space mayreveal certain symmetry features in the molecules. We can identifyvarious symmetry elements, and symmetry operations that can beperformed on molecules. Identifying symmetry elements and under-standing symmetry operations are important to classify molecules intodifferent point groups, which we shall consider in the next section.
4.1.1 Identifying symmetry elements and symmetryoperations
We will take the benzene molecule as an example; it possesses all thesymmetry elements we will come across in discussing molecularsymmetry and we will try to understand the symmetry elements and
42
6
5
2 Rotationby60 °5
C63 4
2
4
Fig. 4.1. A clockwise rotation of the benzene molecule by an angle of 60 ° (C6) about an axispassing through the centre and normal to the plane of the molecule.
symmetry operations. We mark the corners as 1, 2, 3, 4, 5, and 6 (Fig.4.1). These numbers will help us to identify any changes in the orienta-tion of the corners representing the carbon atoms in space.
Let us assume that the plane of the molecule lies on the plane of thepaper. Then we imagine an axis passing through the centre and normalto the plane of the molecule, and consider some rotations of the figurealong this axis. A rotation of the molecule (clockwise) about this axisthrough an angle of 60° (2x/6) is performed on the molecule and the newpositions of the corners are shown in Fig. 4.1. The molecule is in-distinguishable if the numbers indicating the positions of the cornersare removed.
We can repeat the same operation five more times leaving themolecule apparently unchanged (Fig. 4.2). After the sixth operation,the molecule assumes its original position. The rotation axis is thesymmetry element and the rotation about this axis is the operation.This rotation axis is called proper rotation axis (we shall see later thatthere is defined another rotation axis called improper rotation axis). Itis given the symbol C and the order of the axis is written as the suffix.The six-fold proper rotation axis in benzene can be written as C6. Theoperation generated by this element has also the same symbol. Theoperations generated by the C6 symmetry element are C6, C6
2 , C63, C6
4 ,C6
5 and C66. As mentioned above, the molecule assumes its original
position after the C66 operation. This is thus the same as doing nothing
to the molecule (C66 = E). The operation is called the identical operation
and denoted by E.The molecule also has a three-fold (Fig. 4.3) rotation axis C,, and a
two-fold (Fig. 4.4) rotation axis C2, coinciding with the proper rotationaxis we identified earlier. The proper rotation axis of highest order iscalled the principal axis. It is also important to identify equivalent
43
5
C6
2
4 66 C6 3
! 23
3
C6I
4
5
4 C6 5 (f)C6
C64
Fig. 4.2. Multiple C6 rotations. (a) Benzene molecule = C66; (b) C6; (c) C6
2; (d) C63; (e) C6
4;(f) C65.
TABLE 4.1
Rotation axes, operations generated and equivalent operations
Operation
C, C6 C62
C63
C4
C5
66
E
C, C, C32 C33
C2 C2 C22
rotations at this stage. Some of the repeated operations generated bythe C6 symmetry element may be equal or identical to the symmetryoperations generated by the other symmetry elements. For example,the symmetry operations generated by the C6, C3 and C2 can be com-pared. The operations C6
2, C63, C6
4, C66 are equal to operations C3, C2, C3
2
44
5
4
(b
5
6
(d)
6
6
5
(a) (e)0
6 4
1
6
5
2 Rotation by1200
C33
6
1
(a)
2
1
4
5
6
(c)
Fig. 4.3. C3 operations about the same axis as in Fig. 4.2.
1 Rotation by 180 4
C22 *
3
lnttinn iv lRl0
5
6
4 1C2
Fig. 4.4. C2 operations about the same axis as in Fig. 4.2.
and E, respectively. Table 4.1 summarises the operations generated bythe rotation axes and some of their equivalent operations. The tableshows that the distinct operations generated by the C6 rotation axis areC6 and C6
5. The rotation axis C3 generates C3 and C32, and C2 produces
only one distinct operation.
45
1
-
6
5
C2 62 - . 2 6
3 '3
(a)4 4
SC2 \Cc 2
(b)
C2 XC 2
C2"
(c)
Fig. 4.5. (a) C2 operations about an axis lying on the plane of the molecule and passingthrough two opposite corners of the molecule; (b) different C2 as above; and (c) C2operations about an axes lying on the plane of the molecule and passing through the
middle points of two opposite sides of the molecule.
There are other two-fold proper rotation axes lying in the plane ofthe molecule as shown in Figs. 4.5a, b and c. There are three such axes.We give them the symbols C2 ' and C2 " to differentiate from the two-fold
46
A
1
6
5
2 i 3
3 2
I
5
6
4 t
Fig. 4.6. Inversion operation about the middle point of the benzene molecule.
axis shown in Fig. 4.4. We use the same symbol for all three axes of eachtype because of our understanding that the operations generated bythese axes are equivalent. When specifying symmetry elements, wecollect them together. There are six C2 axes lying in the plane of themolecule. As discussed above, it is also clear that the operations C2
2
generate the identity (C22 = E).
Now, we shall consider other symmetry elements in the molecule.Any point on the molecule can be inverted (reflected in the midpoint ofthe molecule) through the centre of the benzene molecule without anyapparent change in the molecule (Fig 4.6). We call this symmetryelement inversion centre and the operation inversion. The symbol forthe inversion operation is i. The molecule assumes its identical positionwhen operated on twice with i. That is i2 = E.
The molecule has several symmetry planes. The symmetry element,symmetry plane generates reflection of the molecule in the plane. Thesymbol for the symmetry operation is . These planes of symmetry canbe differentiated as h, V or Cd. GCh is a horizontal mirror plane lyingperpendicular to the principal axis. ov is a vertical mirror plane con-taining the principal axis which is conventionally taken as vertical.There are three such mirror planes in the benzene molecule (Figs. 4.7aand b). This plane contains the molecular plane of the benzene mole-cule. d is dihedral mirror plane, a special case of a vertical planebisecting two C2 axes that lie perpendicular to the principal axis. In thecase of benzene there are three dihedral planes, as shown in Fig. 4.7c.Each mirror plane generates reflection and the molecule assumes itsidentical position when operated on twice with a mirror plane; that is
v2 = E, oh2 = E and Cd2= E.
There is another symmetry element called improper rotation axis orrotation reflection axis. The axis generates a combined operationconsisting of an n-fold rotation followed by a horizontal reflection. The
47
4
cv C v
(a)
5
Fig. 4.7. (a) Reflection operation about a vertical mirror plane containing the principalaxis and passing through two opposite corners of the molecule; (b) three such verticalmirror planes; (c) three vertical mirror planes containing the principal axis and passingthrough the middle points of the opposite sides of the molecule; and (d) horizontal mirror
plane lying on the plane of the molecule.
benzene molecule has two improper rotation axes S6 and S,3 as shown inFigs. 4.8a and b. Figure 4.8a shows the effect after the first operation. Itis important to note that the molecule is in reflected form after the
48
6'6
6
5
1'
2'
3 A4 3 a4
I S6
(a)
1 5 5'
6
5
2
3
6'
1'
4 2 2'
S3
(b)
Fig. 4.8. Rotation reflection operation.
rotation and indicated by the numbers with primes. The improperrotation axis generates operations S6 , S6
2 , S63, S64, S6
5, and 566. A careful
study of the resulting molecule after each operation S6 will reveal thatsome of the above operations are not distinctive. They are equivalent tothe operations generated by other symmetry elements of the benzenemolecule. The improper rotation axes and their equivalent operationsare given in Table 4.2.
As in the case of the rotation axes, the distinct operations generatedby the improper rotation axis S6 are S, and S6
5 . The independentoperations generated by the S3 axis are S3 and S3
5. Identifying distinct-ive operations generated by the symmetry elements is important in ourdiscussion of reducible representations.
49
I
i ]_ .
I
TABLE 4.2
Improper rotation axes, operations generated and equivalent operations
Operation
S6 S6 S62 S63 S6
4
C3 i C32
Operation
S, S, S32 S33 S34
C32 h C3
S,5 S66
E
S, 5 S36
E
Now it is time to summarise the symmetry elements of the benzenemolecule. We have identified the identity E, rotation axes C6, C3, C2,3C2', 3C2", mirror planes Gh, 3v, 3 d, inversion centre i and improperrotation axes S6 and S3. Among these symmetry elements, inversioncentre and symmetry planes generate one operation each. However,the proper and improper rotation axes generate more than oneoperation. These operations and their equivalent single operations aregiven in Tables 4.1 and 4.2. We can now summarise all the symmetryoperations that can be generated by these elements as E, C6, C6
5, C3,C32, C2, 3C2', 3C2", i, S3, S 3
5, S6, S6 5 oh, 3V and 3 d. We have selectedhere a molecule with high symmetry and most of the molecules we willbe dealing with in this chapter will be simpler than this.
TABLE 4.3
Some examples
Symmetry elements
Only E
E and a mirror plane
E, C2, v' and %c"
E, C3, 3ov
E, C3 , 3C 2, Gch, 3%v and S3
E, C. and Dcv
E, C_, ooc and nCh
Examples
CHFC1Br
CHCl2Br, (CH 3)2CHC1
HO, HS, CH20, COC12, (CH 3 )2C=O,CH 2C12, C6H5 X, CH 5 N etc.
NH3, CHX3, POC13BF3 , PF,
HCN
CO 2
Figure
4.9a
4.9b
4.10a and b
4.11a and b
4.12a and b
4.13a
4.13b
50
4.1.2 Identifying symmetry elements: some examples
Figures 4.9-4.13 illustrate some models of molecules possessing cer-tain common symmetry elements. Table 4.3 summarises the symmetryelements and some examples of molecules possessing these.
(b
Fig. 4.9. Type of molecules (a) possessing E as the only symmetry element, (b) possessingsymmetry elements E and a.
/1 C20V'- / /
(a)
C2
(b)
Fig. 4.10. Type of molecules possessing symmetry elements E, C2, %cy' and c%".
51
Fig. 4.11. Type of molecules possessing symmetry elements E, C3, 3 v.
C
C
C2
%C
C2
Fig. 4.12. Types of molecules possessing symmetry elements E, C3, 3C2 , Gh, 3%, and S3.
52
:YY
l
be
B
p
Coo-principal axis
B
I
I
A
Cw-principal axis
infinite number ofvertical planes throughthe principal axis
(b)
-
infinite number ofvertical planes throughthe principal axis
(a)
Fig. 4.13. Type of molecules possessing symmetry elements (a) E, C, and cOOv, and (b) E,C,, ooo, and h.
4.1.3 The classification of molecules, point groups
The discussion on symmetry elements and inspection of the examplesreveal that the molecules containing a different number of atoms maycontain the same symmetry elements. For example, the moleculeslisted in row 3 of the Table 4.3 have the same symmetry elements E, C2,oyv' and ov". The molecules that have the same symmetry elements canbe shown to have several properties in common. Therefore, it isadvantageous to put all these different molecules into a specific group.The symmetry operations corresponding to the symmetry elements of amolecule leave at least one point invariant (unmoved). We call thesegroups point groups.
53
C--roUDL
C,
Fig. 4.14. Example of a molecule belonging to C2 point group.
The molecules are assigned to different point groups according totheir symmetry elements. We start with molecules with few symmetryelements and special groups. Molecules of the types shown in Fig. 4.9apossess only the identity element E; they belong to group C. Themolecules of the type shown in Fig. 4.9b have E and a vertical mirrorplane and they belong to group C,. We see that the molecules of the typeshown in Fig. 4.10a and b possess more symmetry elements (E, C2, ,v'and ov' ) and belong to group C2v. Likewise, the molecules of the typeshown in Fig. 4.11 possess E, C3, v,' and v,", v'"' and are said to belongto the point group C3v. We can clearly see that the classification followsthe symmetry elements. Generally, if a molecule has a Cn rotation axis(principal axis) and n vertical planes passing through the principalaxis, then it is said to belong to the point group Cnv.
Linear molecules of the type shown in Fig. 4.13a have an infinite-order principal axis and infinite number of vertical planes; the typeshown in Fig. 4.13b have, in addition to the above symmetry elements,a mirror plane normal to the principal axis. These belong to the pointgroups C, and Dih, respectively.
Classifying molecules into different point groups does not requirethe identification of all the symmetry elements. The presence of certainsymmetry elements in a molecule implies the presence of certain othersymmetry elements. Scheme 4.1 helps us to assign molecules intodifferent point groups (without identifying all the symmetry elementsin several cases).
54
-
no
Scheme 4.1.
TABLE 4.4
Some examples and their point groups
Molecules Symmetry elements Point group
NH2 -NH2, H202 E, C2 (Fig. 4.14) C2
NH3, PH3, POC13 E, Ca and 3%7 C3v
Trans CIH=ClH E, C2 , h and i (Fig. 4.15) C2h
C2H6 (staggered) E, C3, 3C2 (horizontal), 3o d (Fig. 4.16) D3d
C2H2 E, C2, 2C 2 (horizontal) and ch (Fig. 4.17) D2h
BF3, PC15 E, C3, 3C2 (horizontal) and Gh D3h
C6H 6 E, 2C6, 2C3, C2 , 3C2', 3C2", i, 2S3, 2S6 , oh, 3Gd D6h
and 3oh
55
C2h- group
Fig. 4.15. Example of a molecule belonging to C2h point group.
p) - 0C2f
D3 d-group
C2
C2 I C2
Od
Fig. 4.16. Example of a molecule belonging to D3d point group.
4.2 GROUP THEORY AND SYMMETRY OPERATIONS AS ELEMENTSOF A GROUP
Mathematically, a set (G) of abstract elements, on which a binaryoperation o is defined is said to form a group with respect to thisoperation if the elements of the group obey the following four rules.1. The product of any two elements A and B and the square of every
element is a member of the set.
56
Oh
6 C /
(K(-U-,
I U
D2 h-group
Fig. 4.17. Example of a molecule belonging to D2h point group.
2. The set contains an identity element E for which EoA = A.3. The elements follow associative law. That is (AoB)oC = Ao(BoC)4. For each element A of the set, there exists an inverse in the set such
that AoA -1 = E.Mathematically, the binary operation can be defined in several ways.For the purpose of our discussion of symmetry operations, we definethis operation as a product operation (one operation followed byanother). Furthermore, to avoid confusion with the symmetryelements, we refer the "elements of a group" as "members of the group".
Our aim in this section is to show that the set containing symmetryoperations as members forms a group. We can make use of the watermolecule with four symmetry elements for this purpose. The molecule(Fig. 4.18) has the symmetry elements E, C2, (v') and % (v"). Thesymmetry operations are also E, C2, oz and o%. We must be aware ofthe difference between the symmetry elements and symmetryoperations. Symmetry operations contain all the individual operationsthat can be performed about the symmetry elements (see the benzeneexample).
According to the first rule the product of two symmetry operationsin the set is a symmetry operation. We shall follow the steps shown inFig. 4.18 to identify whether the product of the symmetry operations xfollowed by C2 yields a symmetry operation. It is evident from theillustrations that the product of the above operations leaves the atomsin the molecule in positions that can be transformed by a singleoperation. This can be simply written as follows.
57
Xz
C2
%yz
Fig. 4.18. Symmetry operations and products of symmetry operations. water molecule isused as an example.
C2( = oyz (4.1)
Similarly, from Fig. 4.18
CC2C = E (4.2)
A product table (Table 4.5) can be set up to show that this is true for allthe operations. This table will also help us to investigate the remainingrules. For example, the following two equations (the multiplicationtable mentioned above will help here) confirm that the symmetryoperations follow associative law.
58
TABLE 4.5
Product table of operations
The operation performed first
E C2 aF, cy2
E E C2 a_ 1yz
C2 C2 E ayZ (z2
aOxz a7 ayZ E C2
y yz aZ C2 E
(yz C2)xz = xz z = E (4.3)
G2 (C2 Gxz) = yz yz = E (4.4)
The above equations also explain that the elements cv and 2yz haveinverses yGx and cy, respectively. This is true for all the symmetryoperations in the set.
At this stage, it is necessary to mention that the symmetryoperations may not be commutative. This means that the result of twosuccessive operations may not be the same if their operation order isreversed.
The symmetry operations can be represented by several ways. Ifthere exists a group with other members P, Q, R and S that satisfy thesame multiplication table shown above, the group is said to behomomorphous with the group containing symmetry operations.
4.3 MATRIX REPRESENTATION OF THE SYMMETRY OPERATIONS
In a Cartesian co-ordinate system the position vector a of a point A canbe written as the product of a row vector containing the unit vectorsalong the co-ordinate axes and a column vector containing the co-ordinates of the point.
a= (ij k) y
59
If this vector is rotated anti-clockwise by an angle (p about the z axis,the new co-ordinates of the point can be expressed in terms of theoriginal co-ordinates and the angle (p. The z co-ordinate does not changeduring the rotation. The new x (x') and y (y') co-ordinates can becalculated from the projection of a onto the xy plane. They are
x' = x cosq -y sin(p
y' = x sinmp + y cosp
Z =z
These can be written as a product of a 3x3 matrix and a 3x1 columnmatrix containing the original co-ordinates. Therefore, the newposition vector of the point can be written as the product of a matrixand the original position vector.
x' cosp -sinp 0 xy' = sin cosp OY0
rx' 'cos -sin(p 0 x(i jk)y =(ij k) sinp cosw O Y
z ' O 0 1 z
a' = D(T)a
The matrix D(T) is called the transformation matrix (operation) and inthis case the transformation is rotation by an angle p.
Similarly, symmetry operations and combinations of symmetryoperations in a point group can be relatively simplified by turning tomatrices. For a summary of matrices and their properties see theappendix.
We again use the water molecule Cartesian co-ordinate system asan example. The molecule lies on the XZ plane (a) containing therotation axis C2 along the Z axis. The H, O and H atoms can then berepresented by Cartesian co-ordinates (x1,yi,zl), (x2,y2,z2) and (x3,y3,z,)
60
C2Oyz ayZ
Fxz
Fig. 4.19. Water molecule in three Cartesian co-ordinate systems.
centred at H, O and H atoms respectively. Now we can consider theeffect of identity operation (E) on the molecule (Fig. 4.19).
Identity operation
x1
Y1
Z,3C,
Y2
Z,
X,
Y3
.Z,-
X1
Y1
Z1
X2
Y2
Z2
X3
Y3
y3Z,_z3 _
The operation does not transform any of the co-ordinates and thereforethey remain the same. Now let us consider the Cartesian displace-ments by the operations C2 , az and Gy~ on the molecule. The effects ofthe operations on the co-ordinates are shown below.
61
-
N
C2
--X3
-Y3
z3
-X2
-> -Y2
Z2
-xi
-Y1
L
X1
Y1
Z1
X2
Y2
Z2
X3
YZ3
Z3
rXl
-y1-Yl
Zl3C2
-Y2
Z2
X3
-Y 3
L Z3
F x1 -I
Yz
x2
Y2
I z2
Z3
-X3
Y3
Z3
Y2
Z2
-x 1
Y1
Z1 -
If the new co-ordinates after each transformation are represented by acolumn matrix (X1,Y 1,Z,X 2,Y 2,Z 2,X 3,Y 3,Z3), then this column matrixrepresenting each transformation can be written as the product of a9x9 square matrix containing elements 0, 1 and -1; and the columnmatrix representing the co-ordinates of the atoms before thetransformation.
Matrix representation for identity (E) operation
D(E): Matrix A
100000000
010000000
001000000
000100000
000010000
000001000
000000100
000000010
000000001
xr
Y1
Z1
X2
Y2
Z2
X3
Y3
x1
Y1
Z1
X2
Y2Z,
X3
Y3
_Z3
Xi
Y1Z
X 2
Y2
Z2X3
z3
62
_ _ _ _ _ _
Matrix representation for C2 operation
D(C2 ): Matrix B
X1
Y1Z1
X2
Y
Z2
X3
Y3
Z3
0 0
0 0
0 0
0 0
0 0
0 0
-1 0
0 -1
0 0
0 0
O 0
0 0
0 -1
0 0
0 0
0 0
0 0
1 0
0 0 -1
000
000
000
-1 0 0
0 1 0
000
000
000
Matrix representing oy operation
D(3,,): Matrix C
X,
Y,
z1
Xy2
Y3z3
X3
Y,
4,
1 0 0 0
0 -1 0 0
0 1 0
0 0 0 1
00 00
00 00
00 00
00 00
00 00
0 00
0 00
0 00
0 00
-1 0 0
0 1 0
0 01
0 00
0 00
0
0
0
0
0
0
0
-1
0
O 0
-1 0
0 1
0 0
0 0
O 0
0 0
0 0
0 0
x1
Y1
Z1
X2
Y2
Z2
X3
Y3
Z3
0
0
0
0
0
0
0
0
1
x 1
Yl
Z1
3C2
Y2
Z2
X3
Y3
Z3
63
Matrix representation for a, operation
D(az): Matrix D
0 0 0 0 0 0 -1 0 0
0 O O 000000 1 0
0 0 0 0 000 1
0 O 0 -1 0 0 0 0 0
0 O 0 1 0 0 0 0
0 O 0000 1 000
-1 0 0 0 0 0 0 0 0
0 1 0 0 0 0 0 0 0
00 1 0 0 0 0 0 0
x1
Y1
Z1
X2
Y2
Z2
X3
Y3
_Z3
A group containing the above four matrices A, B, C, D can be shown toobey the multiplication table shown in Table 4.5 and are homomor-phous to the C2, point group containing the symmetry operations E, C2,a and a'.
The dimension of the matrices representing the symmetry operationsdepends on the basis selected. In the above case, we have selectedCartesian co-ordinates as the basis and therefore the matrices are 9-dimensional.
4.4 CHARACTER OF THE SYMMETRY OPERATIONS
The symmetry operations have some symmetry characteristics. Thesecharacteristics can be deduced from the characteristics of the matricesrepresenting the symmetry operations. One such characteristic is thecharacter of a matrix representing a particular symmetry operation.The character is the sum of the diagonal elements (trace) in the matrix.For example, the character of the matrix representing the identityoperation is 9. The characters of the matrices representing the sym-metry operations C2, a(X) and 'a,z) are -1, 3 and 1, respectively. We haveused Cartesian co-ordinates as the basis for this representation andtherefore the set of characters of the symmetry operations is called theCartesian representation. This is written as
C2, E C0 - 1a
r 9 -1 3 1
64
Xi
Y,Z1
X,
Y2Z2
X3
3z 3
-Z'
4.5 CLASSES OF OPERATIONS
Two operations P and Q of a symmetry group are said to belong to aclass if there is a third operation in the group such that
RPR-1 = Q where RR -1 = E
We say that Q is the similarity transform of P and that Q and P areconjugate. Conjugate operations fall into the same class. It can also beshown that the operations belonging to a class has the same character.
The ammonia molecule belongs to the C3v point group and has thesymmetry operations E, C3 , C3
2, I'v V", "V. By using Fig. 4.20a, we canshow that the operations C3, C3
2 belong to a class(Eq. 4.5) and ac'v, v,
Y
t, I 3 ACJ -'2 - ? v
, I
(a)
1
I C3Y I
Y2
(c)
t
r,
X,
C3
¥3
Fig. 4.20. A two-dimensional projection of ammonia molecule and symmetry operations.
65
Y3
Q D' X, -1L -- £
a"'v belong to another class (Eq. 4.6). We know that the inverse of amirror reflection ('v) is the same reflection ('v). Making the reflectiontwice leaves the system unchanged. Let us now consider the operationC3 followed by 'v, and C3
2. The result is equal to the operation (a"v (Eq.4.6).
G'v C3 o'v = C3 2 (4.5)
The operations C32 and C3 are conjugate and belong to the same class.Similarly, the operations ('v, cy"v and "'v can be shown to belong toanother class.
C32 'v C3 = ca", where C3 is the inverse of C32 (C32 C3 = E) (4.6).
Therefore the symmetry operations of the C,3 point group can be simplywritten as E, 2C3 and 3
Gv. We can also work out the characters for thesymmetry operations in the Cartesian representations. A two-dimensional projection of the molecule is shown in Fig. 4.20. The z-axisis chosen as the principal axis passing through the nitrogen atomperpendicular to the plane of the paper. A C3 rotation will be in the anti-clockwise direction for the reader. The effects of operations C3 and a'vare shown in Fig. 4.21. The effects of operations on the co-ordinates andthe matrix representations of the operations are shown below.
The identity operation E
X1
Y1
ZiX 2
Y2
Z 2X 3
y3
Z4
X,
Y,
Z1
X2
Y2
Z2
X3
Y3
z3X4
y4z 4_Z,
66
�
C3
Fig. 4.21. The effect of C3 and Y'v operations on ammonia molecule.
The matrix representation for the identity operation
D(E): Matrix A
100000000000
0 1 0 0 0 0 0 0 0 0 0 0
0 1 0 0 0 0 0 0 0 0 0
000100000000
000010000000
000001000000
000000100000
000000010000
000000001000
000000000100
000000000010
000000000001
67
````\
The C3 operation
-X3 cos 60 - Y3 cos 30
X3 sin60-Y 3 sin30
Z3
-X, cos 60 Y1, cos 30
X1 sin60 -Y, sin30
Z1
-X2 cos60-Y, cos 30
X2 sin60-Y sin30
Z2
-X 4 cos60-X4 cos30
X4 sin60 -Y4 sin30
Z4
The matrix representation of C3 operation
D(C3 ): Matrix B
0 0 0 0 0 0 -1/2 -3/2 0 0 0 00 0 0 0 0 0 -/3/2 -1/2 0 0 0 00 0 0 0 0 0 0 0 1 0 0 0
-1/2 3 /2 0 0 0 0 0 0 0 0 0 03/2 -1/2 0 0 0 0 0 0 0 0 0 00 0 1 0 0 0 0 0 0 0 0 0
0 0 0 -1/2 -,3/2 0 0 0 0 0 0 00 0 0 J3/2 -1/2 0 0 0 0 0 0 00 0 0 0 0 1 0 0 0 0 0 0
0 0 0 0 0 0 -0 0 1/2 /3/2 00 0 0 0 0 0 0 0 0 -,r3/2 -1/2 0
0 0 0 0 0 0 0 0 0 0 0 1
68
X,
Y ,Z,X,Y2
Z,
X,
Y3
Z3
X,
Yll
z1
The cv operation
Xi
Y,
Z1X2
Y2
Z2X3
Y3
z 3X4
Z4
-- xI
Y,
Z1-X3
13
-x 2Y2
Z2
-X 4
y4
Z4
The matrix representing the v operation is:
D(cv): Matrix C
--1 00 0 0 0 0 0 0 0 0 0
0 1 0 0 0 0 0 0 0 0 0 0
O 0 1 0 00 0 0 0 0 0 0
0 O O O O O -1 0 0 0 0 0
0 O O O O 000000 1 0 0 0 0
0 O O O O O 0000000 1 000
0 O O -1 0 0 0 0 0 0 0 0
0 O O 0 1 0 0 0 0 0 0 0
0 O O O 0 1 0 0 0 0 0 0
0 00 0 00 0 0 O 0 -1 0 0
0 O O O O O O O 000000000 1 0
0 0 0 0 0 0 0 0 0 0 0 1
69
The characters of the operations in Cartesian representation are
C3v, E 2C3 3c7v
F 12 0 2
4.6 REDUCIBLE AND IRREDUCIBLE REPRESENTATIONS
We mentioned earlier that the characters of matrix representationsdepend on the basis selected. For example, Cartesian representationsof molecules belonging to a point group would give different charactersdepending on the number of atoms. For example, H2 0 and SO2molecules give representations consisting of 9x9 matrices each; CH 2 0 arepresentation consisting of 12x12 matrices; and CH2 C12 a representa-tion consisting of 15x 15 matrices.
All these representations formed by these matrices are reducible. Toillustrate this, we shall use the matrix representations of the symmetryoperations for the water molecule in the C2,, point group using only x co-ordinate vectors as the basis for the representation. Matrices A, B, Cand D representing the symmetry operations E, C2, oy2 and z,, will thenbe (the reader can work this out):
Fl 0 OJ 0 0 FO 0 - -A 0 1 0 B= 0 -1 0 C= o 1 0 D= 0 -1
001 0- 0 0 0 -1 0 0
The characters for this representation are 3 -1 3 -1. The abovematrices can be similarity transformed using a 3x3 dimensional matrixP such that P-1AP = A', P-1BP = B', P1 CP = C', and PDP = D'. Thetransformation leads to non-zero elements in the leading diagonals ofthe matrices A', B', C' and D'. The characters of these matrices are thesame as the matrices A, B, C and D, respectively (see Appendix III, P).The similarity transformation (reduction) can be continued with A', B',C' and D' until a matrix P is not found to satisfy the above trans-formations. The resulting matrices A', B', C' and D' will have non-zerodiagonal elements. The similarity transformed matrices A', B', C' andD' are:
70
(1 1 1 1)
1 0 0 1 0 O1 10 0 1 0 0
A'= 0 1 0 B'= 0 -1 0 C'= 0 1 0 D'= 0 -1 0
0 1 0 -1 0 1 0 0 -1
(1 -1 1 -1)
The corresponding diagonal elements of the matrices A', B', C' and D'form representations that are called irreducible representations. Fromthe above matrices we have 1 1 1 1, and two 1 -1 1 -1 irreduciblerepresentations.
4.6.1 Irreducible representations and character tables
A molecule belonging to a point group can have infinite numbers ofrepresentations. But all these can be reduced to a combination of a setof irreducible representations. Each point group has a unique set ofirreducible representations and they are presented in the charactertable (see Tables 4.5 and 4.6) of the point group.
The character tables (Tables 4.5 and 4.6) need some explanation.The top left corner of the table shows the symbol for the point group.Different classes of operations of the point group are given on the toprow in the second column. The number appearing in front of theoperations indicates the number of group elements (equivalentoperations) in the class. All the operations belonging to a class have thesame character. The irreducible representations are labelled by theMulliken symbols A1, A2, B1 and B2 in the first column of the charactertable. The following describes their meanings and other symbols wewill be encountering later in character tables of different point groups.A collection of character tables is given in Appendix 2.1. One-dimensional irreducible representations (they have character
1 or -1) are labelled as A or B. The symbol A is used for theirreducible representation that is symmetric with respect torotation about the principal axis (z-axis that has the highest order ofrotation). The symbol B is used if the representation is anti-
71
TABLE 4.5
Character table of the point group Cz2
C2v E C2 xz %z
A1 1 1 1 1
A2 1 1 -1 -1
B1 1 -1 1 -1
B2 1 -1 -1 1
X2 y22
Rz xy
x RX xz
y Ry yz
TABLE 4.6
Character table of the C3v point group
C3v E 2Ca 3v _
Al 1 1 1 Z X2 + y2,2
A2 1 1 -1 Rz
E 2 -1 0 (xy) (Rx,Ry) (x2 - y2,xy)(xz,yz)
symmetric with respect to rotation about the principal axis. Two-dimensional representations (doubly degenerate) are labelled as Eand three-dimensional (triply degenerate) as T.
2. The subscripts 1 and 2 are used respectively depending on whetherthe representation is symmetric or antisymmetric with respect to aC2 rotation axis lying in the plane perpendicular to the principalaxis (or with respect to a vertical plane if the C2 axis is lacking).Primes (') and double primes (") are used respectively depending onwhether the representations are symmetric or antisymmetric withrespect to a horizontal plane of symmetry. Subscripts g (gerade-even) and u (ungerade-uneven) are used respectively depending onwhether they are symmetric or antisymmetric with respect tocentre of inversion (i).
3. The use of subscripts in two-dimensional and three-dimensionalirreducible representations also follows certain rules but we willtake them as given in character tables.
The character table also shows the irreducible representations somedirectional properties belong to. Their meanings are as follows
72
1. The transformation properties of the rotational modes of a moleculeR, R and Rz belong to irreducible representations of the group towhich the molecule belongs. These are classified under therespective irreducible representations to which they belong.
2. The co-ordinates x, y and z in a Cartesian system or dipole momentoperator (p) or translation operator (T) transform in the same wayas the irreducible representations under the symmetry operationsof a group. The transformation properties of the Cartesian co-ordinates under the operations of a group can be easily determined.For example in C2v, an x co-ordinate under the operations E, C2, ,%z transform into x, -x, x and -x (Fig. 4.22). Therefore, the char-acters of this one-dimensional representation are 1, -1, 1, -1 whichare those of the irreducible representation as B1. Similarly the co-ordinates y and z can be shown to span the irreducible repre-sentations B2 and A.
Binary combinations of the co-ordinates (x2, y2 , z 2, X2 -y 2, xy, xz and yz)are also classified in the same way and placed in a separate column.The degenerate pairs are given in brackets. We shall be using theseproperties in determining whether a vibration is infrared active orRaman active. Binary combinations can be calculated from theirreducible representations of the co-ordinates x, y and z. For example,in C2v, the characters of the combination x2 -y 2 (x.x-y.y) can be calcu-lated by using the characters of the co-ordinates x (x spans A withcharacters 1, 1, 1, 1 for the operations) and y (y spans B2 with charac-ters 1, -1, -1, 1). The result 1, 1, 1, 1 leads to the classification ofx 2 -y2
under A.
4.6.2 Reducing representations of a point group
The process of reducing representations can be achieved by usingmatrix representations of the operations as shown in Section 4.6. Forexample, in the case of a water molecule, which belongs to the C2,, pointgroup, the matrices representing the E, C2, =, and %o, operations can betransformed into another set of representations by using similaritytransformations. If the matrices representing these operations are A,B, C and D (as shown above), and if there exists a matrix P and itsinverse p-1 such that PAP = A', P-BP = B', P-1 CP = C' and Pr-DP =D' then these can be transformed into a new set of matrices A', B', C'and D' representing the same operations. Their characters remain thesame (see appendix on matrices). The transformation is repeated until
73
Z
.y
---------- - x
C2
(a) -Y
Z
Y
(b)
z
Y
I -
Z
~X .*--------I
Y
i---------- X
z
I
XZ
z
------
-~- ......-
(c)
Fig. 4.22. The transformation properties of the Cartesian co-ordinates under symmetryoperations.
all the matrices representing the operations are blocked out asmatrices containing non-zero diagonal elements. When such matricesare obtained, each set of corresponding diagonal elements (a'/i, b'ii, c'ii,and d'ii) will belong to one of the irreducible representations of thegroup. Then the reducible representation can be written as the sum ofthe irreducible representations.
74
Y
Usually, similarity transformation of matrices involves long andcomplicated process involving matrices. However, the number ofirreducible representations that form a reducible representation can becalculated using the formula below and the character table of therelevant group.
Ni =(l/h) E NgX(R)Xi(R) (4.7)Over allclasses
where N = number of times each irreducible representation i appear inthe reducible representation; h = order of the group-number ofdistinguishable symmetry operations in the group; Ng = the number ofoperations in each class; (R) = the character of the reducible repre-sentation for the operation R; Xi(R) = The character of the irreduciblerepresentation i for the operation R.
We shall illustrate the reduction of the Cartesian representation ofwater molecule belonging to C2v point group (see Section 4.4).
The character table for the point group is shown in Table 4.5. Byconsidering the number of operations in each class (the number shownin front of each operation), we can calculate how many times theirreducible representation A appears in the above reduciblerepresentation as follows:
N i = (1/h)YNg Xi(R)X(R)
1.E 1.C2 1.a l.cYyz
r 9 -1 3 1
A, 1
N(A1 ) = 1/(1+1+1+1)} [Ng(E) Xi(E)(E) + Ng(C2) Xi(C 2)X(C2) + Ng(xz)Xi(xz) X(xz) + Ng(yz) Xi (Cyz)X( 5yz)]
= {1/4) [1.1.9 + 1.(-1).1 + 1.3.1 + 1.1.1]
= {1/41[9 - 1 + 3 + 1] = 3
75
.E 1.C2 1.a_ l.a
r i9 -1 3 1
N(A2 ) = 1/4[Ng(E) xi(E)x(E) + Ng(C2 ) Xi(C 2)x(C2) + Ng(Qz) Xi(=) X(o=) +Ng(Oyz) Xi(yZ) X(Oyz)
= 1/4[1.1.9 + 1.(1)(-1) + 1.(-1).3 + 1.(-1).1]
= 1/4[9 - 1 - 3 - 1] =
N(B1 ) = {1/4 [Ng() (E) (E) + Ng(C2) zi(C2)z(C2) + Ng(cz) Xi(o,) &() +Ng(%yz) i(yz) X(%yz)]
= {1/41[1.1.9 + 1.(-1).(-1) + 1.1.3 + 1.(-1).1]
= t1/4)[9 + 1+ 3 -1] = 3
1.E 1.C2 l.a= L%,
F 9 -1 3 1
B 2 1 -1 -1 1
N(B1 ) = {1/4} [Ng(E) Xi(E)X(E) + Ng(C2) zi(C2)X(C 2) + Ng(5,) Xi(Tzz) X(xz) +Ng,(yz) Xi((Cyz) X(Gyz)]
= {1/41[1.1.9 + 1.(-1)(-1) + 1.(-1).3 + 1.1.1]
= {1/4}[9 + 1- 3 + 1] = 2
76
These reductions show that the Cartesian representation can bereduced as linear combination of irreducible representations as
F=3A1 +A2 +3Bl+2B2 (4.8)
Similarly, using the C3V character table, the reducible Cartesian repre-sentation of ammonia molecules can be written as linear combinationof the irreducible representations Al, A2 and E.
1.E 2.C3 3.o3
Fr 12 2
A10 1
N(A1 ) = [1/(1+2+3)] [Ng(E) xi(E) X(E) +X(Cv)]
Ng(C3)Xi(C3) x(C3) + Ng(ov) Xi(ov)
= 1/6)[1.1.12 + 2.1.0 + 3.1.2] = 1/6[12 + 6]
=3
1.E 2.C3 3.%y
r 12 0 2
A2 1 1 -1
N(A 2) = 1/(1+2+3)] [Ng(E)Xi(E)X(E) + Ng(C3)Xi(C3)X(C3) + Ng(Gv) Xi(Cv)X(ov)]
= 1/6}[1.1.12 + 2.1.0 + 3.(-1).2] = 1/6[12 - 6]
=1
77
1.E 2.C3 3.c v
F i12 0 2
E 2 0
N(B1 ) = {1/(1+2+3)} [Ng(E)Xi(E) x(E) + Ng(C3)xi(C 3)x(C 3) + Ng(ayv) Xi(v)X(Yv)]
= {1/6}[1.2.12 + 2.(-1).0 + 3.0.2] = 1/6[24]
=4
Therefore,
F=3A,+A2 +4E (4.9)
The total dimensions of the representations are equal to the number ofco-ordinates of the molecule.
4.6.3 Determining characters of operations in Cartesianrepresentations to obtain reducible representations
Applications of symmetry to molecular vibrations require: (1) thedetermination of the group to which the molecule belongs; (2) selectionof a suitable basis for the representation of the operations; and (3)determination of the characters of the different operations with respectto the selected basis.
The identification of the group to which the molecule belongs wasdiscussed in Section 4.1.3. There are several different ways to select thebasis for the representations. However, we will restrict ourselves toCartesian representations. Determination of the characters of differentoperations of a group on a molecule is the tricky part which needs somesimplification. In the examples shown above for water and ammonia,the use of Cartesian representations resulted in matrices of dimensions3Nx3N (N = number of atoms in the molecule). Working with matricesof large dimensions is difficult. However, we could follow certain rulesthat could make the character determination relatively simple: (1) onlythose atoms that are not shifted during a symmetry operationcontribute to the characters (these are the atoms that contribute with
78
non-zero diagonal elements in the matrices; (2) it follows that theidentity has a character equal to 3n.
Therefore, it is enough to look for atoms that are not shifted during asymmetry operation and sum up the numbers representing thecoefficients of the co-ordinates after the operation.
4.7 APPLICATION TO MOLECULAR VIBRATIONS
4.7.1 Vibrational motion, infrared and Raman spectra
We learnt in our earlier discussions that vibrational motions of amolecule lead to infrared and Raman spectra of the molecule.
The infrared absorption arises when the vibrational motion of amolecule produces an oscillating dipole. The oscillating dipole interactswith the electromagnetic radiation of the same frequency and absorbsit. The infrared spectrum measured by irradiating a sample withpolychromatic radiation in the range 4000-250 cm-l contains theabsorption patterns of such vibrations.
The Raman activity arises from the inelastic scattering of photonsfrom the radiation source by a sample. When a sample is irradiated bymonochromatic radiation of visible light, the spectrum measured in themid-infrared region will contain lines with different intensities. Whenphotons collide with molecules of the samples, some photons lose a partof their energy and are scattered as radiation with less energy (withlonger wavelengths). These are called Stokes lines. On the other handmolecules, which are already in an excited state, lose energy and thephotons absorb this energy and the scattered radiation will have higherenergy and would give lines at shorter wavelengths. These are calledanti-Stokes lines. A part of the incident radiation may also passthrough the sample without any change in the wavelength. This iscalled Rayleigh radiation. The infrared region is less energetic than thevisible region and Stokes lines are lines with longer wavelengths thanthe excitation radiation. Therefore, the Raman spectrum measured inthe mid-infrared region contains only Stokes lines.
When a molecule is exposed to electromagnetic radiation, theelectric field component of the radiation distorts the electron distri-bution in the molecule. This distortion induces a dipole moment that isproportional to the electric field E (Eq. (4.10)). The proportionalityconstant is called polarizability.
79
The polarizability ca is a scalar quantity when pi and E are parallel.Otherwise, it is a tensor quantity with nine components:
xx axy xz
IL= ay C yy ay z E
zx zy ( zz,
The polarizability a may oscillate during a vibration and hence theinduced dipole moment. The general selection rule for the Ramanactivity is that the molecule should have an oscillating polarizability.
4.7.2 Vibrational motions and their symmetries
We have seen earlier that the internal motions of a molecule containingN atoms can be described by 3N-6 degrees of freedom (or 3N-5 degreesof freedom for linear molecules). These are called fundamentalvibrations or normal modes of vibrations or normal modes. Some ofthese are infrared active, some are Raman active and some are bothinfrared and Raman active.
The Cartesian representation of a molecule provides us with areducible representation, that can be reduced to a combination of theirreducible representations representing all the modes of the moleculeincluding translation and rotation. In the case of the water molecule,the Cartesian representation is reduced to a linear combination ofirreducible representations as
F = 3A, +A + 3B + 2B,2
The water molecule has three translational modes and three rotationalmodes. A look at the character Table 4.5 shows that the translationsalong the X, Y and Z axes span B, B2 and Al, respectively and rotationsabout the X, Y and Z axes span B1 , B2 and A2, respectively. By sub-tracting these species from the total representation, the modesrepresenting the normal modes of vibrations can be determined.
80
p = aE (4.10)
Total representation: 3A, + A2 + 3B, + 2B 2Translational modes: Al + B, + B2Rotational modes: A2 + B1 + B2
Normal modes: 2A1 +B1
Two of the three normal modes of the water molecule are totallysymmetric.
4.7.3 Wavefunctions representing vibrational motion, andtheir symmetries
In quantum mechanics the vibrational states of an electronic state of amolecule are described by wavefunctions. Any vibrational wave-function of a polyatomic molecule is a product of the wavefunctions ofthe normal modes. The wavefunction of the excited state of a moleculeis also the product of the wavefunctions of all the modes of motion of themolecule. It means that the total wavefunction describing the motion ofa molecule with N atoms in an excited state can be written as theproduct of 3N-6 wavefunctions (or 3N-5 wavefunctions for linearmolecules).
P = 91929393 ... 93N-6 (4.11)
The wavefunction of the molecule in the lowest vibrational state issimilarly composed of 3N-6 wavefunctions. These wavefunctions are ofthe gaussian type (= Ce (1
2)Y2 ).
The wavefunctions describing the normal modes posses a symmetryrelated to the symmetry of the normal mode. The wavefunction of avibrational ground state is totally symmetric (it involves squares of theco-ordinates). In the case of a water molecule, the wavefunctionrepresenting the vibrational ground state is of the symmetry type Al.
The symmetries of the wavefunctions representing the singlyexcited vibrational states are the same as the symmetries of the normalmodes. Therefore, the symmetries of the wavefunctions of the singlyexcited vibrational states of the water molecule are A1 , A1 and B2.
4.7.4 Symmetry and infrared absorption
When a molecule absorbs infrared radiation at normal temperaturesthe molecule is excited from the vibrational ground state to the firstexcited state (Av = ±1 v = 1 - v = 0 and the absorption pattern of the
81
fundamentals falls in the mid IR region. The excitation of afundamental vibration involves transition dipole moment (transitionmoment) which is evaluated by the integral (Eq. (4.12)) involving thewavefunctions of the ground and excited vibrational states (pg and (Pe)and the dipole moment 1p of the molecule. The absorption of infraredradiation takes place only if the transition moment has a non-zerovalue.
Transition moment I = p g Pp ed (4.12)
p g is the conjugate wave function of pg.The dipole moment 11 of a molecule arises from the charge
distribution in the molecule and can be resolved into three componentsalong x, y and z directions.
= + y + Pz (4.13)
PPed =(g(i +iy +plz) ped (4.14)
I=- E JpPi(pdr (4.15)i-x,y,x
If one of the above three components has a non-zero value then thenormal mode is infrared active. For this to happen, the direct product ofthe pg, li and (p should span the totally symmetric irreduciblerepresentation. Since, the vibrational ground state spans a totallysymmetric irreducible representation, the requirement will be met ifthe direct product between p (i i = x or y or z) and (Pe spans the totallysymmetric irreducible representation. In other words i (i = x or y or z)and (Pe must span the same irreducible representation. The dipolemoment p is a vector quantity and the components Px, Py and pz spanthe same irreducible representations as the translation co-ordinates(Fig. 4.22) x, y and z, respectively. This means that if the normal modespans the same irreducible representation as one of the translationalco-ordinates then the mode is infrared active. This is true also for thedoubly degenerate (Table 4.7) and triply degenerate irreducible repre-sentations because the direct products of all representations withthemselves contain the totally symmetric representation. For example,in the case of point group C, the doubly degenerate species has
82
'7
a)b) Ct
= 3651 cm- V2 = 1595 cm-1
Al Al
, c) C)V3 = 3755 cm-
B2
Fig. 4.23. Symmetric and asymmetric stretching of water molecule.
TABLE 4.7
Direct product of doubly degenerate irreducible representations
E 2C3 3a
E 2 -1 0
E 2 -1 0ExE = F 4 1 0
characters x(E) = 2, X(C3) = -1 and X(ov) = 0. The direct product of thecharacters r can be reduced again by using Eq. (4.7) as illustrated inthe examples above to
r =A 1 +A 2 + E (4.16)
83
_
4.7.5 Symmetry and Raman activity
An argument similar to the above can again explain the Raman activityin a molecule. The polarizability is a tensor property and is expressedby a matrix containing 9 elements as shown below. The transitionmoment during absorption can be written as in Eq. (4.15)
I = (P 9 gedr (4.17)
I = (p gaE(p dT (4.18)
a; a a E-
I= ayx ayy a yz Ey (PedT (4.19)
(X Cy O z_ Ez
Because of symmetry axy = a,yc ayz = azy and a = a,,. For Raman activity,the above integral must be non-zero. This is true if one of the compo-nents of the integration is non-zero. An argument similar to infraredactivity can be made here to determine whether one of the componentsis non-zero and hence Raman activity.
This means that if one of the components of a spans the sameirreducible representation as (Pe then the mode is Raman active.
In the above sections, we have simplified the process of identifyingwhether a normal mode is infrared active or Raman active. They can besummarised as follows:1. Identify the symmetry group to which the molecule belongs.2. Develop the Cartesian reducible representation.3. Reduce the representation as a linear combination of irreducible
representations of the group.4. Identify the irreducible representations spanned by translational
and rotational modes.5. Identify the irreducible representations spanned by the normal
modes.6. Use the character table of the group and decide on whether these
normal modes span the same irreducible representation as one ofthe normal co-ordinates or their product functions and hencewhether they are infrared active or Raman active.
84
4.7.6 Measured spectrum and band assignments
The above procedure can tell us the number of bands that might arisewhen the infrared or Raman spectrum of the compound is measured.However, they do not say anything about their assignments in thespectrum. A procedure that could determine the symmetry types of thedifferent absorptions in a measured spectrum would ease the assign-ments of the bands to different modes. Furthermore, the vibrationalmodes of a molecule are determined using harmonic consideration ofthe vibrations. These determinations can be found elsewhere [1].
4.8 EXAMPLES
4.8.1 Water and nonlinear molecules with the generalformulae BAB
We have used the water molecule as an example in our earlier dis-cussions. We shall find out whether the three remaining modes ofmotion representing the vibrations of the water molecule are infraredor Raman or both infrared and Raman active. We found the symmetriesof the vibrations to be 2A1 + B2.
These are two completely symmetric modes and asymmetric modesas shown in Fig. 4.23. A look at the character table for the C2v pointgroup (Table 4.5) shows that the translational co-ordinates z and ytransform in the same way as irreducible representations A, and B2,respectively. Therefore, these modes are infrared active. Furthermore,the product combination of the translational co-ordinates x 2-y2 (and z2)and yz transform in the same way as the irreducible representations A,and B2 , respectively. Therefore, the modes are Raman active. All threenormal modes of the water molecule are both infrared and Ramanactive. The bands in the infrared spectrum coincide with the bands inthe Raman spectrum.
The infrared and Raman spectra of water in a gaseous state containthree bands at 3755, 3651 and 1595 cm-1 . The number of bands is inagreement with our theoretical prediction. However, these do not tellus which of these two bands represents vibrations of A, symmetry.Theoretical calculations show that the Raman scattered light are polar-ised by the symmetry modes of type A. Therefore, by examining theRaman scattered light with a second polariser, the bands can beclassified into different symmetry classes (Fig. 4.23).
85
TABLE 4.8
Fundamental vibrations of water molecule (in gaseous phase) and their characteristics
Frequency in Symmetry type Label Assignmentwavenumber ()/cm 1
3651 A,(totally symmetric) VI Symmetric stretch
1595 Al (totally symmetric) v2 Bending
3755 B2 (nonsymmetric) V3 Asymmetric stretch
TABLE 4.9
The normal modes of some nonlinear molecules with the molecular formulae BAB
Symmetric stretch 7l Symmetric bending Asymmetric stretchcml (Al) V2, cm-1 (Al) V3 cm-1 (B2)IR & Raman IR & Raman IR & Raman
D2O (gas) [2] 2671 1178 2788#
H2S (gas) [3] 2615 1183 2627
H2Se (gas) [4] 2345 1034 2358
NO, (gas) [5] 1318 749 1610
ClO2 (gas) [6] 943 445 1110
The absorption bands are labelled as v1,v2,v3, ... vn etc. in thedecreasing frequency order according to their symmetries (see Table4.8 for water molecule). Note that it is customary in mid-infraredspectrometry to give the frequency in wavenumber (v = cv). Thesymmetric type bands are labelled first starting from the totallysymmetric type. Degenerate vibrations of mode n are labelled as vna,
,,n, etc. The normal modes of some non-linear molecules with a generalformula BAB are given in Table 4.9
4.8.2 Ammonia and pyramidal molecules with the generalformula AB 3
We can again use the reduced Cartesian representation of ammoniamolecule from Eq. (4.9). There are 12 normal modes. The modes repre-sented by reducible representation E are doubly degenerate. The nor-mal modes representing the vibrations can be determined as follows.
86
a) b)
V1 = 3336 cm 1 V2 = 932 cm 1
A, A1
c) d) X
V3a = 3414 cmt V4,, = 1628 cm 1
E E
Fig. 4.24. The normal modes of ammonia molecule.
Total representation: 3A1 + A2 + 4ESymmetries of translational modes: A + ESymmetries of rotational modes: A2 + ESymmetries of vibrational modes: 2A1 + 2E
The molecule should have 3x4-6 = 6 normal modes of vibration. It is inagreement with the above result where normal mode with symmetrytype E is doubly degenerate. The normal modes are shown in Fig. 4.24.A look at the C3v point group shows that z and (x,y) belong to therepresentations A and E respectively. Therefore, all the fourfundamental vibrational modes are infrared active and give four bandsin the spectrum (two of these are doubly degenerate).
Similarly, the character table confirms that these modes are alsoRaman active. Here again the bands in the infrared spectrum are
87
TABLE 4.10
The normal modes of some pyramidal molecules and species with formulae AB 3
Symmetric Symmetric Antisymmetric Antisymmetricstretch. vi cm-' bend. v2 cm-1 stretch. V, cm-' bend. v4 cm-l(A1) IR & (Al ) IR & (E) IR & (E) IR &Raman Raman Raman Raman
PH3 (gas) [7] 2327 990,992* 2421 1121
AsH 3 (gas) [7] 2122 906 2185 1005
[C0 3]- (solid) [8] 939 614 971 489
[S 3]2- (soln.) [9] 967 620 933 469
*Splitting in v2 is due to Fermi resonance (see Section 4.9.2).
coincident with the bands in the Raman spectrum. The normal modesof some pyramidal molecules with general formula AB 3 are given inTable 4.10.
4.8.3 BF3 and planar molecules with formula AX 3
The molecules belong to the D3h point group. The Cartesian represent-ation of the molecule (Fig. 4.25) gives a reducible representation asshown below. The characters were derived with the help of Fig. 4.25.
D3h E 2C3 3C 2 - 2S3 3ov
Frat 12 0 -2 4 -2 2
The Cartesian representation reduces to a combinationA', + A'2 + 3E' +2A"2 + E". Of these, translational modes spanA"2 + E' and the rotation-al modes span A'2 + E". Therefore, the vibrational modes span A'1 + 2E'+ A"2. These represent 6 normal modes of vibration (3x4-6). Thecharacter table for the point group D,, suggests that normal modeswith symmetry A"2 and E' are infrared active because these modestransform the same way as the translational co-ordinates. The normalmodes with symmetry A'1 and E' are Raman active. Thus the modeswith symmetry E' are both infrared and Raman active. These modesare shown in Fig. 4.26. The normal modes of some planar moleculeswith a general formula AX3 are given in Table 4.11.
88
C3 Zt
Y,
C2
F
VI
ZI
-Y,
X,
Xl
Fig. 4.25. The effect of symmetry operations of moleculesgroup.
belonging to the D3h point
TABLE 4.11
The normal modes of some planar molecules and species with formulae AX 3
Symmetric Symmetric Antisymmetric Antisymmetricstretch. v, cm- 1 bend. v2 cm-1 stretch. V, cm- 1 bend. V4 cm-(A' l) Raman (A"2) IR active (E') IR & (E') IR &active Raman Raman
BH 3 (gas) [10] 2623 1132 2820 1610
AlBr 3 (gas) [11] 228 107 450-500 93
A1F3 (matrix) [12] 660 284 960 252
4.8.4 Planar molecules of lower symmetry with four atoms
We have discussed the normal modes of pyramidal and planarmolecules belonging to the C3 V and D3h point groups. If one of the atoms
89
F
0,
I d
I .I� �
-1
t Ji
v1=888 cm V3a
A1
h --
v2 =708 cm-l V3 a 3b =1505 cm -
A2 E
V4a
V4a= V4 b =482 cm t
E
Fig. 4.26. The normal modes of BF3 .
ofX in the planar molecule AX3 is replaced by Y the symmetry elementsof the molecule reduce and the molecule will belong to the C2v pointgroup. If Y and Z replace two of the X atoms, the molecule assumes thesymmetry elements of the Cs point group. However, the number ofnormal modes remains constant. Furthermore, the character tables forthe C2v and C point groups suggest that all the modes in thesemolecules are both infrared and Raman active.
4.8.5 Carbon dioxide and linear molecules with the formulaXYX
The CO2 molecule belongs to the Dh point group. Using the Cartesianco-ordinates a reducible representation of the molecule can be obtain-ed. The characters of the operations for the reducible representationcan be determined using Fig. 4.27. The character for the identityoperation E is (E) = 9 (all the co-ordinates contribute). When the
90
( F
Ae_�
molecule is rotated about the principal axis by a small arbitrary angle4, the new co-ordinates X, Y and Z for each atom will be Yi sin4 + Xi cos4,Yj cos4 - Xi sino and Z i (i = 1, 2 and 3), respectively. Each of the atomswill contribute a character of 1+2coso (see Eq. (4.20)) and therefore,(CQ) = 3(1+2coso).Similarly, for reflection on a vertical plane through
the principal axis X(av) = 3 (see Fig. 4.27d and Eq. (4.21)). The effect ofimproper rotation shifts the co-ordinates of the oxygen atoms and,therefore, it is enough to look at the effect on the carbon atom (Fig.4.27d). The z co-ordinate changes direction and X(S?,)= -1+2coso. Theoperation inversion moves the co-ordinates of oxygen atoms andtherefore, it is enough to look at the character contribution from thecarbon atom. All three co-ordinates are reversed and hence x(i) = -3.Similarly, the (ooC 2)= -1. The Cartesian reducible representation isshown in in the table below.
Effect of CO on one atom:
cos sin 0I l-sino cos 0 Y1 (4.20)
]0 0 Z1
Effect of reflection ov on one atom:
cos 2 sin2 ° 0 Xl
Z= [sin2o -cos2 0 Y (4.21)
The reducible Cartesian representation is:
Dh E 2CQ ... Coov i 2Sj ........ ooC2
F t 9 3+6cos 3 -3 -1+2cos -1
Since the molecule has an infinite number of vertical planes and C?,axes along the principal axis (i.e. the principal axis is of infinite order),reducing the above Cartesian representation is difficult. However, alook at the irreducible representations in the character table gives ussome clue as to how the above representation can be reduced (seeAppendix II for table Dh). In order to obtain a character -1+2cos forthe operation 2S?,, the combination must involve 21-, + Hg + - - - . In
91
Zl
C-.0
b)a)
S.o Principal axis
-.%
Y=Y2 cos -X2 sin O/ Y2
C)
2 + Ylcos 20
Fig. 4.27. The effect of symmetry operations on a carbon-dioxide molecule.
order to get a character +3 for moov operation and -1 for oXC2 operation,there must be a combination 2 + + Zg+. The total reducible repre-sentation reduces to a combination of the irreducible representationsas g + JIg + 2u + + 2u. Of these modes, the translational and rotationalmodes span Yu+ + lu and rIg, respectively. Therefore, the vibrationalmodes of the carbon dioxide span Xg
+ + Eu++ riu. The molecule has fourvibrational modes (note that IIu is a doubly degenerate representation)which is in agreement with our prediction (3x3 - 5 = 4). The normalmodes of the carbon-dioxide molecule are shown in Fig. 4.28. A look at
92
'x
I
Vi= 134 cm3- - _v,= 1340 cm' = 2349 cmt
yg+ (a) (b)
(o 2 > -9 2.V-Z 667 cm-'
Fl u
+ +
o~ .- ) 'V2b= 667 cm -'
+ - (c)
Fig. 4.28. The normal modes of the carbon-dioxide molecule.
TABLE 4.12
Normal modes of some linear molecules and species with formula XYX
Symmetric stretch. v Symmetric bend. v2 Antisymmetriccm - (Zg+ ) Raman cm - 1 (Il) IR active stretch v3 cm 1 (Zu+)
active IR active
CS2 (gas) [13] 658 397 1533
KrF 2 (gas) [14] 449 233 596, 580
[CuCl 2]-(s) [15] 300 109 405
the character table for point group Dh shows that the translational co-ordinates span u+, and Iu. The products x2
+ y 2 and z2 span g+. That is,the anti-symmetric stretching mode and degenerate bending mode areinfrared active and the symmetric mode is infrared inactive but Ramanactive. This example also illustrates the mutual exclusion principle formolecules with a centre of inversion. The normal modes which areinfrared active are Raman inactive and those which are Raman activeare infrared inactive. The normal modes of some linear molecularformula XYX are given in Table 4.12.
93
4.8.6 Linear molecules with formula XYZ
When one of the atoms ofX is replaced by another atom Z, the moleculeassumes symmetry elements of the Cv point group. The charactertable indicates that all the three normal modes are both infrared andRaman active.
4.9 MEASURED VIBRATIONAL SPECTRA OF MOLECULES
We have learnt in this chapter how to predict the vibrational spectra ofmolecules. However, measured spectra often show more bands than thepredicted 3N-6 or 3N-5 fundamental frequencies and, in some cases,there are fundamental frequencies that cannot be observed in theinfrared spectrum.
4.9.1 More bands due to anharmonicity-overtones andcombination bands
One of the reasons for observing more bands than expected arises dueto anharmonicity of the normal vibrations. The normal vibrations of amolecule were assumed to be simple harmonic. However, this is not thecase. The bonds between the atoms behave like anharmonic oscillatorsand transitions between vibrational ground state and higher levelsbecome possible. The selection rule for anharmonic oscillators is Av =+1, +2, +3, .... The transition between vibrational ground state to thesecond excited state (v = 2 - v = 0) is called first overtone (secondharmonic) and to the third excited state (v = 3 - v = 0) is called secondovertone (third harmonic). The frequencies of these transitions are notexact multiples of the fundamental transitions. The frequencies ofthese transitions decrease (i.e., V=2- < 2 V_ o )
There is also another possibility for the transition to occur to acombined level. This can be the sum of the tones such as v, + v2 , v1 + v2
+ V3 , etc. or 2v, + v2 , v1 + 2 V2, etc. or difference tones such as v¾ - v2,v2 - V,, etc. These transitions normally fall in the near infrared regionof the electromagnetic spectrum. However, some of them can beobserved in the mid-infrared region. In such cases the number ofbands in the mid-infrared region exceeds the number of bands pre-dicted by group theory.
94
4.9.2 More bands due to Fermi resonance
Two molecular vibrations may interact with each other if they havefrequencies very close to each other (30 cm-'). For example, one of thefundamental modes and an overtone of another mode or a combinationmode may have frequencies close to each other (accidental degeneracy).These vibrations may interact if their symmetries are the same and theovertone or combined tone is enhanced. The interacting vibrations splitand the vibration with higher frequency is raised in frequency and thevibration with lower frequency is depressed about the average of thetwo vibrations. This is called Fermi resonance (see Section 3.10 fortreatment of Fermi resonance).
An example of Fermi resonance is the interaction between thesymmetric stretch (I) around 1340 cm -' and the first overtone (2v21334 cm-') of the symmetric bending at 667 cm - in a carbon dioxidemolecule. The symmetric stretch has symmetry g+. The symmetricbending is a doubly degenerate vibration with symmetry Ig. The firstovertone of this degenerate vibration splits into two sublevels withsymmetry species g+ and Ag. Fermi resonance arises because of theinteraction between the species Xg+ of the symmetric stretching vibra-tion and the species Eg* of the first overtone (of the symmetric bendingvibration). This interaction results in two bands in the Raman spec-trum at 1388 cm-1 (the frequency is raised about the average 1340 cm-1 )and 1286 cm 1 (the frequency is lowered about the average 1340 cm-1 ).
4.9.3 Overlap of rotational spectrum on vibrational spectrum
The rotational spectrum of some small molecules (diatomic and tri-atomic) falls into the same region as the vibrational spectrum of themolecule. The fine structure of the rotational spectrum can be seen inthe infrared of the molecule. For example, the infrared spectra ofcarbon monoxide (see Fig 2.5) and the ammonia molecule areaccompanied by their rotational spectra. However, this is not a problemin polyatomic molecules because the rotational bands are very close toeach other and hardly visible in the spectra.
REFERENCES
1. G. Herzberg, Infrared and Raman Spectra. Van Nostrand, New York,1945.
2. W.S. Benedict, N. Gailar and P.K. Plyler, J. Chem. Phys., 24 (1956) 1139.
95
3. H.C. Allan and P.K. Plyler, J. Chem. Phys., 25 (1956) 1132.4. D.M. Cameron, W.C. Sears and H.H. Nielsen, J. Chem. Phys., 7 (1939)
994.5. R.V. St. Louis and B.L. Crawford, Jr., J. Chem. Phys., 42 (1965) 857.6. A.H. Nielsen and P.J.H. Woltz, J. Chem. Phys., 20 (1952) 1878.7. E. Lee and C.K. Wu, Trans. Faraday Soc., 35 (1939) 1366.8. W. Sterzel and W.D. Schnee, Z. Anorg. Allg. Chem., 383 (1971) 231.9. J.C. Evans and H.J. Bernstein, Can. J. Chem., 33 (1955) 1270.
10. A. Kaldor and R.F. Porter, J. Am. Chem. Soc., 93 (1971) 2140.11. I.R. Beattie and J.R. Horder, J. Chem. Soc., A (1969) 2655.12. A. Snelson, J. Phys. Chem., 71 (1967) 3202.13. T. Wentink, J. Chem. Phys., 29 (1958) 188.14. H.H. Classen, G.L. Goodman, J.C. Malm and F. Screiner, J. Chem. Phys.,
42 (1965) 1229.15. D.N. Waters and B. Basak, J. Chem. Soc., A (1971) 2733.
GENERAL BIBLIOGRAPHY
P.W. Atkins, Molecular Quantum Mechanics. Oxford University Press,London, 1984.
C.N. Banwell and E.M. McCash, Fundamentals of Molecular Spectroscopy.McGraw-Hill, London, 1994.
M. Ladd, Symmetry and Group Theory in Chemistry. Horwood Publishing,Chichester, 1998.
K. Nakamoto, Infrared and Raman Spectra of Inorganic and Co-ordinationCompounds. Wiley, New York, 1978.
J.D. Ronaldson and S.D. Ross, Symmetry and Stereo Chemistry. IntertextBooks, London, 1972
A. Vincent, Molecular Symmetry and Group Theory. Wiley, London, 1977.
96
Chapter 5
Group frequencies and assignments of theinfrared bands
5.1 GROUP FREQUENCIES
Analysis of normal vibrations of a polyatomic molecule is, in general,complicated because the molecule consists of a number of atoms.Although the vibrations of a polyatomic molecule can be calculated bycalculating a potential energy and a kinetic energy of a system, as inthe case of a diatomic molecule, the calculation is not straightforward.The concept of group frequencies helps the analysis of vibration spectraof a polyatomic molecule. The concept of group frequencies may beapplicable when the amplitudes of nuclei in a particular functionalgroup are very large in a certain normal vibration, while those of theother atoms are very small. Infrared spectroscopy is useful forqualitative and quantitative analysis and structural investigation of acomplex molecule since there are a number of vibrational modes whichcan be regarded as group frequencies. Table 5.1 summarizes groupfrequencies. Group frequencies observed mainly in Raman spectra(e.g., S-S stretching vibration) are also shown in this table.
The idea of group frequencies is beneficial even for a very complexmolecule such as protein. As an example, let us consider normalvibrations of an amide group. Normal vibrations of an amide grouphave been calculated in detail, taking N-methylacetamide (Fig. 5.1) asa model of the amide group [1,2]. Considering a methyl group as oneatom, N-methylacetamide is a six-atom molecule, and hence, hastwelve normal vibrations (3x6 - 6 = 12). Of the twelve, the normalvibrations shown in Fig. 5.1 are amides I, II and III modes which arekey vibrations for studying the structure of proteins. As can clearly beseen in Fig. 5.1, amide I has a strong characteristic of C=O stretching
97
TABLE 5.1
Group frequencies
3500 3000 2500I OH stret
NH stret
CH stret(unsaturated)
CHstret(saturated)
m SH start
* 01
2000 1500 1000
I Casym bend· CI sissor
CIH sym bend
CHl:wag
_ CHbend I JC= C)
str tn P=O- stretI C stret I PO; antisym sret
CLO stret I PO;sym stret
* C=Ostret(COOI)* -CONH-
i C=Cstret* C=-Nstret
_ CO, antisym stret
I NO antisym street
500T
* N=N stretI -CONH-
* N-N stret _ CO2 sym stret
NN atisym stret NO2 sym stret
°(c:Na ~ C-N stretRr.mtgd(p htA C-C street
rmm ~ri~ ~ ~C-O street
Sis
3500 3000 2500 2000 1500 1000 500
Wavenumber I cni'
vibration. Meanwhile, amides II and III are coupling modes of C-Nstretching vibrations and N-H in-plane bending vibrations. Of thethree, amides I and II appear strongly in infrared spectra, and amides Iand III appear intense in Raman spectra. Amides I, II and III bands of
C\, 3 H
C-N0t \CH3
Fig. 5.1. Structure of N-methylacetamide and its amide I, amide II, and amide III modes.(Reproduced from Ref. [2] with permission. Copyright (1984) Academic Press.)
98
I I
TABLE 5.2
Secondary structures of protein and frequencies of amide I, II, and III bands
Secondary Infrared Ramanstructures
Amide I Amide II Amide I Amide III
a-helix 1655-1650 -1540 1660-1645 1300-1265
3-sheet -1690, 1680-1675, -1550 1675-1665 1240-1230structure -1640, -1630
Random coil 1655-1645 1535-1530 1670-1660 1260-1240
P-turna -1680, -1660, -1680 ,-1660, 1330-1290-1640 -1640
310helixa 1645-1640 -1655
31helixa -1640 -1550 -1380, -1335,-1285
aFrom Ref. [4].
proteins are generally found in the range of 1690-1620 cm- l ,1580-1520 cm l and 1320-1220 cm-1 , respectively. The frequencies ofthese modes are known to sensitively reflect secondary structures ofpolyaminoacids, peptides, and proteins [3-6].
Table 5.2 shows relationships between secondary structures ofproteins and the frequencies of amides I, II and III. Measurement ofinfrared (or Raman) spectra of protein allows us to estimate thecontents of secondary structures, which will be explained in Section8.7.1.
5.2 ISOTOPE SHIFT
In analysis of infrared spectra, a shift associated with isotopicsubstitution (isotope shift) gives solid assignment of bands in manycases. In general, force constants may be assumed not to change due toisotopic substitution, and therefore, isotope shifts lead to mass effectsalone. Calculate the magnitude of an isotope shift, taking a diatomicmolecule as an example. The frequency of a stretching vibration of adiatomic molecule is given by Eq. (3.17). Where v' is the frequency forreplacing an atom having a mass ml with an isotope having a mass ml',the following relation holds:
99
Fig. 5.2. Amide I', amide II', and amide III' modes of deuterium-substituted N-methyl-acetamide. (Reproduced from Ref. [2] with permission. Copyright (1984) Academic
Press.)
v= ~ (5.1)
p' = m,' m 2/(m' + m2) holds. As Eq. (5.1) clearly shows, the larger thedifference between ml and m,', the larger is the isotope shift. Since v/v'= 1.36 if H is replaced with D, a C-H stretching vibration of saturatedhydrocarbons, which appears in the vicinity of 2900 cm l, shifts close to2100 cm-l. Figure 5.2 shows amides I, II and III modes of deuterium-substituted (ND) N-methylacetamide (which will be called amides I', II'and III'). While shifts induced by the deuterium substitution are ratherlarge in the amide II and III modes as NH bending vibrations con-tribute to these two modes, amide I mode, being principally a C=Ostretching vibration, gives rise to a very small isotope shift. Whatshould be noted with respect to isotope shifts of polyatomic molecules isthat vibrational modes change more or less in association with isotopicsubstitution, which can be clearly understood from comparison of Fig.5.1 with Fig. 5.2. In studies of infrared spectra, 15N-substitution, 13C-substitution and the like are often utilized in addition to deuteriumsubstitution. Although an isotope shift is small when such a heavyatom is replaced, a change in a vibrational mode associated with theisotopic substitution is also small.
5.3 HOW TO MAKE BAND ASSIGNMENTS IN INFRARED SPECTRA
In general, we observe a number of bands in an infrared spectrum of amolecule. The first consideration to be made when analysing theinfrared spectrum is whether it is necessary to analyze the infraredspectrum as a whole or only a part of the spectrum. For example, if an
100
objective is to examine a secondary structure of protein, the spectralregions where the amide I and amide II bands appear may be studiedand it is not necessary to analyze the entire spectrum. On the otherhand, when we want to identify a certain material, we must analyze aconsiderable portion of the spectrum.
Although there is no absolute procedure for assignments of infraredbands, the following methods are often found effective:
1. Find group frequencies from comparison of observed frequencieswith a table of group frequencies. During the comparison, intens-ities as well as frequencies must be noted.
2. Compare an obtained infrared spectrum with those of similarmolecules. The similar molecules do not always need to be similar intheir entirety, but rather, may be only partially similar.
3. Measure an infrared spectrum of an isotope-substituted materialwhich contains deuterium, 15N, 13C, etc., and compare the infraredspectrum with an original spectrum. This method is very effectivefor the identification of a band due to a particular functional group,a particular bond, etc.
4. Measure spectra while varying a condition of a material, such as atemperature, pH and a solvent, and compare them with an originalspectrum. For example, since amino acid residues within protein,respectively, have unique pK values, as pH is changed around thepKvalues, it is possible that only bands due to particular amino acidresidues will change.
5. Measure anisotropy of infrared absorption resulting from polarizedlight. This method is convenient to distinguish in-plane and out-of-plane vibrations of a planar molecule from each other.
6. Calculate normal vibrations. Although this is a traditional method,if not combined with another scheme, it does not allow us to com-pletely assign an infrared spectrum of a complicated molecule. Thisis because of a general lack of knowledge regarding three-dimensional structures and force constants of molecules.
7. Try chemometrics and two-dimensional correlation analysis (seeChapter 9)
There are unique marker bands known, some unique to proteins, someunique to nucleus acids, etc., with which we can study structures of
101
materials (amides I and II are typical examples of marker bands forproteins). Hence, for actual analysis of an infrared spectrum of amolecule, it is often important to first identify marker bands. Markerbands for organic thin films, polymers, and biological molecules and thelike will be described in Chapter 8. A library search alone is oftensufficient if the objective is merely identification of a material based onmeasurement of infrared spectra.
It is very convenient to know which bands appear intense in aninfrared spectrum for its analysis. The well-known principles regard-ing intensities of infrared bands are as follows:1. A band due to a functional group with a strong polarity appears
strongly, e.g., OH and C=O stretching vibrations. Conversely, vibra-tions due to a bond with a weak polarity, such as C-C and S-Sstretching vibrations, appear very weakly or do not appear in aninfrared spectrum.
2. Antisymmetric stretching vibrations are stronger thancorresponding symmetric stretching vibrations. For example, COO-antisymmetric stretching vibrations appear more strongly thanCOO- symmetric stretching vibrations.
3. As a general tendency, local vibrations are strong and vibrations ofa molecule as a whole are weak. For instance, in an infraredspectrum of polyethylene, while CH 2 rocking vibrations appearstrongly, vibrations in which a molecule as a whole stretches andcontracts (e.g. accordion vibrations) appear weakly.
4. Among bands arising from an aromatic group, those which givestrong infrared bands are ring stretching vibrations in the1600-1450 cm 1 region and out-of-plane bending vibrations in the900-700 cm 1 region.
REFERENCES
1. T. Miyazawa and E.R. Blout, J. Am. Chem. Soc., 83 (1961) 712.2. Y. Sugawara, A.Y. Hirakawa and M. Tsuboi, J. Mol. Spectrosc., 108 (1984)
206.3. H. Susi and D.M. Byler, Arch. Biochem. Biophys., 258 (1987) 465.4. S. Krimm, in: T.G. Spiro (ed.), Biological Applications of Raman Spectro-
scopy, Vol. 1. Wiley, New York, 1987, p.l.5. M. Jackson and H.H. Mantsch, CRC Crit. Rev. Biochem. Mol. Biol., 30
(1995) 95.6. H.H. Mantsch and D. Chapman (eds.), Infrared Spectroscopy of Bio-
molecules. Wiley-Liss, New York, 1996.
102
GENERAL BIBLIOGRAPHY
L.J. Bellamy, The Infrared Spectra of Complex Molecules, Vol. 1, 3rd edn.Chapman and Hall, London, 1975; Vol. 2, 2nd edn. Chapman and Hall,London, 1980.
N.B. Colthup, L.H. Daly and S.E. Wiberley, Introduction to Infrared andRaman Spectroscopy, 3rd edn. Academic Press, San Diego, CA, 1990.
E. Maslowsky, Jr., Vibrational Spectra of Organometallic Compounds. Wiley,New York, 1976.
K. Nakamoto, Infrared and Raman Spectra of Inorganic and CoordinationCompounds, 5th edn. Wiley, New York, 1997.
N.B. Nyquist, The Interpretation of Vapor-Phase Infrared Spectra GroupFrequency Data. Sadtler Research Laboratories, Philadelphia, 1984.
G. Socrates, Infrared Characteristics Group Frequencies. Wiley, New York,1980.
103
Chapter 6
Instrumentation
6.1 HISTORY OF INFRARED INSTRUMENTATION
Since the discovery of infrared radiation by Sir William Herschel in1800 [1], a variety of methods have been used to improve the experi-mental techniques for measuring infrared spectra. In particular,Herschel used a prism and a mercury thermometer to record hisobservations of heat-based radiation beyond the range of the solarspectrum. Melloni is credited with the construction of the first mid-infrared spectrometer in 1833, after his discovery of the transparencyof NaCl in the infrared. Excellent references on the early history ofvibrational spectroscopy and the minds that shaped the field can befound elsewhere. This chapter will deal in detail with the interfero-metric methods of capturing infrared radiation. Older monographstreat non-interferometric methods in great detail [2].
6.1.1 History of FT-IR instrumentation
The construction of the first interferometers dates back to 1880. LordRayleigh may have constructed an interferometer at that period, but itis Michelson who is credited with the construction of the first operableinstrument at that time. The interferometer was used in the measure-ment of the speed of light in diverse directions. Measurements thattook place at was is now Case Western Reserve University showed thatthere was no detectable difference in the speed of light in eitherdirection. The lack of adequate computing power was the main reasonthat it took approximately eighty years for the instrument to utilize itsfull potential as an analytical tool. Ferraro has recently published avery informative account of the history of FT-IR spectroscopy [3].
105
The first attempts to use interferometric means to measure infraredradiation concentrated in the far infrared region of the spectrum. Theoperational needs for mechanical precision and computational load arelower in the far-infrared compared to the mid-infrared. Therefore, a lotof the early applications and advancements took place in the field ofastronomy where far-infrared spectroscopy is used extensively.
One very important recent development that led to the widespreaduse of infrared spectroscopy as a characterization tool was the intro-duction of the first Fourier transform infrared spectrometer, the FTS14, by the Biorad Company of Cambridge, Massachusetts in 1969.Several developments in the 1950s and 1960s contributed to the intro-duction of this first commercially available instrument. The work of L.Mertz in interferometer design during 1954-56 and the development ofdata reduction algorithms in 1960-65 are probably the most significantcontributors. One historical aspect that should not be overlooked wasthe role of the NASA contract to Block Engineering for an instrumentwith ten times the available resolution. The model 1500 (296 in thecommercial version) had 0.5 cm-l resolution and a better signal-to-noise (S/N) ratio than the dispersive instruments of the time.
Other notable developments were the discovery of the HeNe laseralong with the introduction of better infrared detectors, analog-to-digital (A/D) converters and minicomputers. In 1966 a one-foot laserwith a built-in power supply was available to be used in the first FT-IRspectrometer. In addition, pyroelectric bolometers in the form of thedeuterated triglycine sulphate (DTGS) detector also became available.Their major advantage was that their bandwidth was compatible withthe rapid-scan frequencies. With respect to computing power there wasa remarkable development from the PDP-1 in 1960 to the DG Nova in1969.
After the introduction of this instrument many new instrumentsfrom various manufacturers have appeared and tremendous progresshas been achieved in the years following 1969. A list of the advance-ments will undoubtedly include the very small footprint of the moderninstruments, quadrature detection with forward and backward scan-ning, digital signal processing, diagnostic features, low powered air-cooled sources, the flexible design of the research-grade instruments, themultiple spectral ranges, the very high spectral resolution, and thetremendous progress in FT-IR software. In addition, one of the mostimportant developments was the 'rediscovery' of step-scan interfero-metry, a subject that will be extensively dealt with in this book.
106
What is the future of infrared instrumentation? Without a doubt,any technological breakthrough will eventually find its way to a com-mercial design with time. Improvements in performance, new featuresand capabilities, usability and (hopefully!) a reduction in cost should allbe expected.
6.2 COMPONENTS OF AN FT-IR SPECTROMETER
The components of an FT-IR spectrometer primarily include the sourceinterferometer, the source of radiation, the detector and other opticalelements (beamsplitters, mirrors, etc.). In addition, data manipulationalso takes place in the adjacent computer station. It is beyond the scopeof this book to give a detailed account of all the elements involved;instead, an attempt will be made to cover in more detail importantcomponents of these designs.
6.2.1 Sources
The source of infrared energy in an infrared instrument does notdepend on the type of instrumentation used to detect the radiation.Both dispersive instruments and Fourier transformed instruments canuse the same types of infrared sources. Therefore, a general overview ofthe available technology will be reviewed here. The more typicalsources are the Globar source and the Nernst glower, even thoughnichrome coils have also been used in the past. Nichrome coils operateat lower temperatures and therefore have a lower emissivity. Finally,mercury arc lamps are used most frequently for experiments dealingwith the far-infrared region of the spectrum. The first two types will bediscussed in more detail here.
Globar SourceThis source is made out of silicon carbide (SiC) and it has metallic leadsat the ends which serve as electrodes. The application of electriccurrent results in the generation of heat, which yields radiation attemperatures higher than 1000°C. Water cooling is required for thistype of source because the electrodes need to be cooled [4]. This extralevel of complexity makes this source less convenient to use and moreexpensive. Figure 6.1 shows the ratio of the globar source to a 900°Cblackbody.
107
Prisms:4.2. 0 NaCI. 4.2. Ramsey and Alishouse & KBr
Q CsI3 .4
s Calculated after Silverman1.8
1.0
0.2 I I i2.l 6.0 10.0 14.0 18.0 22.0 26.0 30.0 34.0 38.0
Wavelength (m)
Fig. 6.1. Globar versus a 900°C blackbody. (Reproduced from Ref. [7] with permission.Copyright 1968, Pergamon.)
I.o
0.9
W 0.8
E0.7K
0.60.
n_ 1 3 5 7 9 11 13 15
Wavelength (im)
Fig. 6.2. Spectral emissivity of the globar source. (Reproduced from Ref. [7] withpermission. Copyright 1968, Pergamon.)
One other advantage of this source is its high emissivity down to 80cm- ', making it useful in the far-infrared region of the spectrum. Figure6.2 shows the spectral emissivity of a typical globar source [5]. Thesevalues are only representative and are expected to change considerablywith use. Recently, a new low power air-cooled ceramic source has beenintroduced into the modern FT-IR instruments [6]. This source has theadvantage that no watering cooling is necessary, making their instru-ments portable and easier to maintain.
Nernst glowersThis infrared source's element is a mixture of yttrium and zirconiumoxides and has an emission spectrum that resembles that of a black
108
-255 K Stewart and Richmond
I I I I I I I I I I I I
z
}
3W
Wavelengt (m)
Fig. 6.3. Ratio of a Nernst glower to a 900°C blackbody. (Reproduced from Ref. [8] withpermission. Copyright 1978, Office of Naval Research.)
body at 1800 K. It is an insulator at room temperature and becomes aconductor after it is preheated. It used to be popular but it has anumber of disadvantages, the biggest being its short lifetime andmechanical instability. The spectral characteristics of a Nernst glowerversus a 900°C blackbody can be found in Fig. 6.3 [7].
6.2.2 Infrared detectors
One of the most important elements of an infrared spectrometer is thecomponent responsible for the detection of infrared energy. Typically,the description of a detector is not limited to the responsive elementwhich changes the incoming radiation into an electrical signal, but italso includes the physical mounting of the element, like the windows,the apertures, the Dewar flasks, etc. Together, they form what is calleda detector [8].
There are two general classes of infrared detectors. One class com-prises the thermal detectors and the other class the photon detectors. Asthe name suggests, thermal detectors operate by sensing fluctuationsin the temperature of an absorbing material as a result of exposure tothe incoming radiation. The other category, the photon or as oftencalled quantum detectors are sensitive to changes in the quantity offree-charged carriers in the solid, brought by the interaction with theexternal radiation.
109
Thermal detectorsThermal detectors rely on four different processes to achieve detectionof infrared radiation:1. The bolometric effect. This effect relies on the change in the elect-
rical resistance of the responsive element due to temperaturechanges produced by the absorbed infrared radiation. This changein resistance is detected by conventional techniques.
2. The thermovoltaic effect. In this case, the heating of the junctionbetween two dissimilar materials produces a measurable voltageacross the leads.
3. The thermopneumatic effect. A very common thermal detector, theGolay detector, relies on this phenomenon [9]. In the case of thermo-pneumatic detectors, a gas-filled chamber that contains an infraredabsorbing element is exposed to infrared light. Absorption of energyby the element generates heat, which heats up the gas in thechamber. The consequent increase in the pressure of the gas resultsin the distortion of a thin flexible mirror on the other end of thesealed gas chamber. This distortion is sensed by an independentoptical system. Golay detectors have been extensively used as far-infrared detectors, even though they had problems with their mech-anical integrity at one point. Figure 6.4 shows a cross-section of atypical Golay cell [10].
4. The pyroelectric effect. In this process the radiation increases thetemperature of a crystalline material. The result is a change in theelectrical polarization of the crystal surface and the generation of anelectric field.
TARGET:THIN
IRTRANSMITTIN
WINDOW
BSORBINGFILM
ELASTICMEMBRANE
GAS FILLEDCHAMBER
Fig. 6.4. Cross-section of the Golay cell. (Reproduced from Ref. [10] with permission.Copyright 1976, Institute of Optics.)
110
Photon detectorsThe other category of infrared detectors is the quantum or photondetectors. In photon detectors, incident infrared photons result in theproduction of free charge carriers in the responsive element. No serioustemperature change in the element takes place during this process.The above category can be further divided in four underlying processes:1. Photoconductive effect. The principle behind this effect is that a
change in the number of incident photons reaching a semicond-ucting material changes the number of the free charge carrier in thematerials. Since electrical conductivity is directly proportional tothe number of these charge carriers, it can be used to deduce thenumber of incident photons on the semiconductor.
2. Photovoltaic effect. In this case, a change in the number of incidentphotons on a semiconductor p-n junction results in a change in thevoltage generated by the junction. Figures 6.5 and 6.6 show theenergy band models for unilluminated and illuminated p-njunctions.
3. Photoelectromagnetic effect. In this case, the separation of thecharge takes place via the use of a magnetic field. The chargeseparation produces a voltage that is directly proportional to thenumber of incident infrared photons.
4. Photoemissive effect. In this case, an incident photon is absorbed bythe surface and gives up its energy to a free electron. This electroncan escape the surface and in the case that the surface is in anevacuated chamber equipped with an anode and an eternal circuit,electric current is detected.
Band
_.-----------Fermi Level
P-l n-Region
Unilluminated p-n junction
Fig. 6.5. Energy band model for an unilluminatedp-n junction. (Reproduced from Ref. [4]with permission. Copyright 1978, Office of Naval Research.)
111
Conduction Band
h -' h
Illuminated p-n junction
Fig. 6.6. Energy band model for an illuminated p-n junction. (Reproduced from Ref. [4]with permission. Copyright 1978, Office of Naval Research.)
6.3 DETECTOR NOISE
There are several contributors to the noise (the fluctuation in signalintensity for a steady radiation field) of an infrared detector. In infra-red spectroscopy, the detector noise is most often much higher than anyother noise source. In addition, it has usually a thermal origin.Therefore, the majority of infrared detectors do not operate at roomtemperature.
Johnson noise: this type of noise is generated in resistors due to therandom thermal motion of the charge carriers. As the temperature ofthe element increases there is a concurrent increase in the averagekinetic energy of the carriers, which results in an increased electricnoise voltage. This is the reason this type of noise is also called thermalnoise.
Shot or Schottky noise: this is random noise that has to do with thestatistical fluctuations of the photon fluxes. It has its origin in thediscreteness of electrical charge.
Both of the above types of noise are 'white' types of noises. Thismeans that they are independent of the frequency all the way out to thecut-off frequency. Other types of noise exist that are dependent on thefrequency of the incoming radiation. The most important of these typesis the 1/f noise. Its mechanism is not well understood but, as the nameimplies, its magnitude is reversibly proportional to the frequency of theradiation.
112
f
In addition, electronic components associated with the detectorcontribute to the noise. Pre-amplification is always required for anytype of detection system.
6.4 PERFORMANCE OF AN INFRARED DETECTOR
The performance of an infrared detector is measured by a set of figuresof merit. The responsivity of the detector is the output of the electricalsignal to the incident radiation power. The noise equivalent power(NEP) is the level of incident infrared signal that produces a signal-to-noise ratio of one. Detectivity is defined as the reciprocal of the noiseequivalent power (NEP). The normalized detectivity D* is a widely usedfigure-of-merit and it includes the area of the detector and frequencybandwidth of the measurement.
Thermal detectors show a 'flat' detectivity response throughout theentire spectral region. In contrast, photon detectors have higherdetectivity but over a limited spectral range. Figure 6.7 shows the
10
lA
E
in 8
2 4 6 8 10 12 14 16 18Wavelength (rim)
9109 i
10 3 X 10 10
210 10
10 Chopping Frequency (cps)
Fig. 6.7. Plots of D* versus wavelength for (a) thermocouple versus (b) an InSb detector.
(Reproduced from Ref. [4] with permission. Copyright 1978, Office of Naval Research.)
113
I I I I1_1_~~~' N~-
i.. 1~~,___
10'
1011
1010
1 09
1081
Wavelength (m)
Fig. 6.8. D*(X) values for a number of commercially available quantum detectors.(Reproduced from Ref. [4] with permission. Copyright 1978, Office of Naval Research.)
response for a thermocouple detector as compared with the spectralresponse for an InSb photon detector. In addition, Figure 6.8 shows theplots of the normalized detectivity D* for a collection of commerciallyavailable detectors.
6.4.1 MCT detector
One of the most widely used infrared detectors is the mercury cadmiumtelluride (MCT) detector. This is a photon detector which needs tooperate at liquid nitrogen temperatures of 77 K. Figure 6.9 shows thespectral response of the commercially available detectors as a functionof wavelength. On the other hand, Fig. 6.10 depicts the frequencyresponse of this detector's D*. Essentially, the response is 'flat' fromabout 103 Hz to 106 Hz. Furthermore, the alloy composition deter-
114
l
10M 10
2
M0 9- 10
,t I I I I '
4 6 8 10 12 14 1(Wavelength (m)
6
Fig. 6.9. Plot of detectivity versus wavelength for MCT detectors. (Reproduced from Ref.[4] with permission. Copyright 1978, Office of Naval Research.)
1 10
2 10RF
109
2 -82
103 104 105 106 107
Frequency (Hz)
Fig. 6.10. Plot of D* versus frequency for an MCT detector. (Reproduced from Ref. [4]with permission. Copyright 1978, Office of Naval Research.)
WWC
.0.
a:
tO
C:
10
6 8 10 12 14 16 18Wavelength (. m)
Fig. 6.11. MCT detector. Effect of alloy composition to the spectral responsivitycharacteristics. (Reproduced from Ref. [4] with permission. Copyright 1978, Office of
Naval Research.)
115
I I
i. IB\ C
. i
- Spectral Responseis a Function of x
i l l I , i l
Z -
1
. _
........ I ~{J· I I~~ I{ { I~ I
..
.. ... . . ..' I .. . 1 . .
- In�
I
x
Fig. 6.12. Wavelength cut-off for an MCT detector versus alloy composition at 77 K(Reproduced from Ref. [4] with permission. Copyright 1978, Office of Naval Research.).
mines the spectral response of the detector element. Figure 6.11 showsthe spectral responsivity for three different alloy compositions(Hg,,CdxTe).
It is evident that manipulation of the alloy composition results in adetector which is tailored to particular needs for wavelength sensi-tivity. The spectral response of the material is determined by theenergy gaps between the various energy levels in the material. There-fore, the energy gap in an MCT alloy is related to the ratio of HgTe toCdTe. Figure 6.12 shows the wavelength cut-off for this ternary alloysystem.
6.5 OTHER COMPONENTS
6.5.1 Beamsplitters and mirrors
The typical kind of beamsplitters in the mid-infrared region on com-mercially available instruments is of the germanium (Ge) on potassiumbromide (KBr) substrate type. Recently, semiconductor film beam-
116
Wavelength (m)
Fig. 6.13. Reflectance of some common metallic films used as mirrors. (Reproduced fromRef. [12] with permission. Copyright 1957, Wissenschaftliche Verlagsgesellschaft mbh.)
splitters for infrared spectrometers have been described which areformed from self-supporting semiconductors, including carbon films.Preferably, the beamsplitters are formed from silicon, germanium, ordiamond films [11]. In addition, Figure 6.13 shows the reflectance forsome commonly used mirror surfaces in the infrared region [12].
6.6 DISPERSIVE INSTRUMENTS
Nowadays, dispersive instruments are used only in selected applica-tions due to the fact that interferometric instruments offer distinctadvantages for most applications. However, there are places wheredispersive instrumentation is still used when the response at onewavelength or a short range of wavelengths is sought [13].
The basic components of a dispersive spectrometer are the same asin a Fourier transform instrument with the exception of the inter-ferometer. Any differences are within the elements and are the result ofthe different ways that the source radiation is detected. For instance,sensitive thermocouple detectors are commonplace in dispersiveinstruments, whereas they are not appropriate for rapid-scanning
117
t5
D
instruments [14]. In a dispersive instrument a monochromator is usedin the place of the interferometer. Before 1950, the monochromator wasa rock salt prism for use in the mid-IR region of the electromagneticspectrum and later was replaced by a diffraction grating. Older mono-graphs provide excellent background information on the operation andmaintenance of dispersive infrared instruments and the reader isrecommended to consult them [15,16].
6.7 MICHELSON INTERFEROMETER
Most commercial interferometers are based on the original Michelsondesign of 1891 [17]. Interferometers record intensity as a function ofoptical path difference and the produced interferogram is related to thefrequency of the incoming radiation by a Fourier transformation. Theprinciple of a Michelson interferometer is illustrated in Fig. 6.14. Thedevice consists of two flat mirrors, one fixed and one free to move, and abeamsplitter. The radiation from the infrared source strikes the beam-splitter at 45°. The characteristic property of the beamsplitter is that ittransmits and reflects equal parts of the radiation. One classic type ofbeamsplitter, useful in the mid infrared spectral region, consists of athin layer of germanium (refractive index, n = 4.01) on an infraredtransparent substrate (e.g., KBr). The transmitted and reflected beamsstrike the above described mirrors and are reflected back to the beam-splitter where, again, equal parts are transmitted and reflected. As aconsequence, interference occurs at the beamsplitter where the
RADIATIOFROM SOt
BE
TO DETECTOR
Fig. 6.14. Block diagram of a Michelson interferometer.
118
MOVING MIRROR
I
M
Un
UI
C
Z lMUI
I . ._
Z '
U '
0X
oQc
I
"o00 SZS9 s=a -at i2 s sea s 5 7Z'- 750 TA POINTS
Fig. 6.15. Typical interferogram showing centre-burst region.
radiation from the two mirrors combine. As shown in Fig. 6.14 whenthe two mirrors are equidistant from the beamsplitter constructiveinterference occurs for the beam going to the detector for all wave-lengths. In this case, the path length of the two beams in the inter-ferometer are equal and their path difference, called the retardation(6), is zero.
The plot of detector response as a function of retardation produces apattern of light intensity versus retardation, commonly referred to asthe interferogram. The interferogram of a monochromatic source is acosine function. Equation (6.1) describes the above relationship:
1(6) = B(v) cos(27v6) (6.1)
where v is the wavenumber in cm-l and 6 is the optical path difference,or retardation. The Fourier transform of the above expression is a peakat the frequency of the monochromatic radiation. I is the intensity inthe output beam as a function of retardation (6), and B is the intensityas a function of radiation frequency (v). In contrast, the interferogramof a polychromatic source can be considered as the sum of all cosinewaves that are produced from monochromatic sources. The polychrom-atic interferogram has a strong maximum intensity at the zero
119
I~
$---------
retardation point where all the cosine components are in phase, as canbe seen in Fig. 6.15. This point is also known as the centreburst point[18]. The expression for the intensity of the interferogram of a poly-chromatic source as a function of retardation is described by Eq. (6.2):
1(6) = [[B(v)[1+ cos(2cv6)]] /2]dv (6.2)
Thus, in Fourier transform interferometry the data are "encoded" bythe interference produced by the retardation and then "decoded" by theFourier transform to yield the desired intensity signal as a function offrequency (or wavelength).
6.8 ADVANTAGES OF INTERFEROMETRY
Two kinds of multichannel advantages exist in Fourier transforminterferometry, compared with a dispersive instrument in which only avery narrow band of frequencies is observed at a time. The first-andbiggest practical advantage of Fourier transform spectroscopy-is thesimultaneous detection of the whole spectrum at once; it is called theFellgett or multiplex advantage [19,20]. Even though a factor of ca. 2 insignal strength is lost because half of the beam is reflected back to thesource, the multichannel advantage is nevertheless 10 4 or higher. Thatis, theoretically an interferometer can achieve comparable signal-to-noise to a dispersive monochromator 104 faster.
In addition, the so-called Jacquinot or 'etendue' advantage exists.This advantage is associated with the increase in source throughput[21]. During dispersive detection the throughput is severely limited bythe area of the entrance slit. Even though the interferometer has anentrance aperture of its own, its throughput advantage ranges from 10to 250 over the infrared frequency range. This was the reason that FT-IR spectra of astronomical sources, where very weak astronomicalemission sources are present, were produced even before the FastFourier Transform (FFT) was invented [22].
A third practical advantage of interferometry is the so-calledConnes or registration advantage. Connes advantage stems from theability of interferometry using a monochromatic source (e.g. a helium-neon (HeNe) laser in today's spectrometers) to accurately and preciselyindex the retardation, resulting in a superior determination of the
120
retardation sampling position. For example, if the above mentionedHeNe laser ( = 632.8 nm) is used, zero crossings in the visible inter-ferogram occur at intervals of 632.8/2 nm = 0.3164 mm. Because theNyquist theorem demands at least two sampling points per cycle, thehighest infrared frequency that would satisfy the Nyquist criterion is15,804 cm-l. For mid-IR use, sampling at every other zero-crossing (1kHeNe intervals) produces a maximum Nyquist frequency of 7902 cm- l.Connes advantage allows tremendous reproducibility of interferogramsampling and data storage. This results in full realization of signal-to-noise problems from repeated scans and it is particularly useful for thedynamic experiments that will be discussed later in this book [23,24].
6.9 APODIZATION
The amplitude of the side lobes which appear adjacent to absorptionbands in the Fourier transform of an interferogram can be drasticallyreduced if a mathematical manipulation is performed. This treatmentis called apodization, from the Greek word ano6os (without feet). Thismathematical treatment is necessary because the Fourier trans-formation is performed over finite limits, even though the theoreticalexpression for the interferogram's intensity involves infinite limits.Therefore, when the interferogram is truncated, this sudden cut-offresults in the appearance of oscillations around the sharp spectralfeatures (absorption bands) in the transform.
When the interferogram is multiplied by the apodization function,the transform is essentially free of side lobes. Two of the most popularand effective apodization functions are the triangular and the Happ-Genzel functions. The amplitude of the first side lobe using triangularapodization is larger than that of the Happ-Genzel function, but theopposite is observed for the subsequent lobes. In general, it can bestated that Happ-Genzel apodization is quite similar to triangularapodization and for most situations they give comparable results [25].Both types of apodization were used at different times in the workreported in this dissertation.
Overall, it can be stated that the biggest drawback of apodization isthe worsening of the spectral resolution, since the contributions of theextremes of the interferogram wings are reduced. Therefore, a trade offexists between the reduction in spectral distortion and the worsening ofresolution.
121
6.10 RESOLUTION
Resolution is defined as the minimum distinguishable spectralinterval. The maximum retardation determines the resolution of thescan. The maximum optical resolution achievable by a particular FT-IRspectrometer is given by (Dma)- cm l, where D.ma is the maximumoptical path difference attainable by the interferometer. Figure 6.16shows the effect of different resolution on the appearance of singlebeam spectra. The spectra shown in this figure have been offset forclarity. Figure 6.16a shows the open-beam background spectrum of theunpurged spectrometer recorded with a resolution of 2 cm - l (Dm~ = 0.5cm). It is clear that the rotational lines of vapour water are wellresolved. In contrast, Fig. 6.16b shows the open-beam spectrumacquired with 16 cm- l resolution (Dm, = 0.0625 cm). Vapour waterabsorptions are not resolved due to the lower resolution.
Dynamic methods have the potential to increase spectral resolutionbeyond the above limit due to the existence of the possibility of differentresponses of the components of highly overlapped bands. This possi-
EM
e
Mt
U=
.'A
3600 '100 2600 2100 1600 1'0O 600
Wavenumbers
Fig. 6.16. (a) Open-beam background, 2 cm-l; (b) open-beam background, 16 cm1.
122
a) Ca
b)
bility will be further discussed when dynamic infrared experimentswill be presented.
6.11 PHASE CORRECTION
The non-ideality of the beamsplitter in a real interferometer results inthe introduction of sine components to an interferogram which, inprinciple, should consist only of cosine components. Equation 6.3 showsthe modified relation for the intensity of the interferogram:
+o
1(5) = [[B(v)[l + cos(2gv6 + DBS(v))]] / 2]dv (6.3)
where FBs(V) is the wavelength dependent phase shift introduced by thebeamsplitter.
Phase correction is the mathematical procedure to remove the sinecomponents from the interferogram. The Fourier transform of a com-plete double-sided interferogram provides the correct power spectrum,without any phase correction, since the ambiguity does not affect themagnitude. However, when a single-sided interferogram is computed,some knowledge of the phase is required in order to compute the truespectrum [26]. Two of the most popular phase correction routines usedin single-sided interferograms are the Mertz algorithm and theForman algorithm. In the Mertz routine, the largest data point in theinterferogram is assigned as the zero retardation point and theamplitude spectrum is calculated with respect to this point. A shortdouble-sided interferogram is measured and its corresponding phasearray is used to phase correct the entire single-sided spectrum. TheForman correction is essentially equivalent to the Mertz routine but itis performed in the retardation space [27,28]. Modifications to theMertz phase correction have appeared in the literature and wereoriginally applied to the vibrational circular dichroism (VCD) spectra[29]. The result of these modifications is that the phase spectrum doesnot change sign if a quadrant boundary is crossed.
As an alternative, a "stored" phase array can be used to produceproper phase correction for the transformed interferograms. Thisphase array is calculated from a double-sided reference interferogram.The procedure relies on the fact that the beamsplitter phase does notchange from scan to scan.
123
6.13 EFFECTS OF MIRROR MISALIGNMENT
Mirror misalignment in an interferometer produces a lowering in theenergy on the higher energy end of the spectrum (transform). This canbe seen in Fig. 6.17 which illustrates three single beam intensities. Thedegree of alignment varies in these three scans, and this is evident onthe high energy portion of the spectrum. These continuous-scan resultscan be compared to step-scan phase modulation results obtained bydithering the moving mirror with piezoelectric transducers.
Continuous-scan FT-IRMost commercially available FT-IR spectrometers use the continuous-scan mode of operation, where the moving mirror is scanning atconstant velocity. This type of scanning works very well for routinemeasurements. In the continuous-scan mode of interferometry thelaser fringe counter is used to sense the accuracy of the scanningvelocity. If a deviation is sensed, correction signals are generated that
Wavenumbers
Fig. 6.17. Effect of mirror misalignment on the appearance of single-beam transmissionspectra.
124
assure the proper operation (constant velocity). The consequence of thismode of operation is that each infrared wavelength (), is modulated atits own particular Fourier frequency, given by Eq. (6.4):
f(k) = 2v/ (6.4)
where v is the mirror velocity.Continuous-scan FT-IR is the technique of choice when static
spectral properties are determined. Co-addition of successive scansincreases the signal-to-noise ratio (S/N) by a factor proportional to t,where t is the time that the signal is averaged at each collection point.
Step-Scan FT-IRIn step-scan FT-IR data are collected while the retardation is heldconstant or is oscillated about a fixed value. Therefore, in order to applythe technique to mid-infrared and shorter wavelength measurements,a method for controlling the retardation and implementing a specialsampling rate comparable to that achieved in modern continuous-scaninstruments is required. In recent years several different controlmethods have been reported. However, all of these basically rely on theuse of the HeNe laser fringe pattern to generate the control signal andto determine the step size [30]. The biggest advantage of the step-scanmode is the separation of the time of the experiment from the time ofthe data collection.
Two types of experiment are possible with step-scan interferometry.One type is the time-domain or time resolved experiments where dataare collected as a function of time at each mirror position. Sorting of thedata results in interferograms that contain spectral responses at differ-ent times. The event under study must be a repeatable process in orderfor the experiment to work.
The other type of experiment capable with step-scan is the so-calledfrequency domain or synchronous modulation experiments. In theseexperiments, there are two ways to modulate the intensity of theinfrared radiation in order to generate step-scan interferograms. Oneway is to use amplitude modulation (AM) which can be achieved bymeans of a chopper. When a chopper is used for intensity modulation, alock-in amplifier is used to detect the signal before digitization occurs.The technique has the drawback that the signal is riding on top of alarge DC offset, which has to be subtracted before any meaningful datacan be obtained. This can be done by either calculating the average
125
value of the interferogram and subtracting it from each sample pointbefore the Fourier transform takes place or by setting the lock-inamplifier offset to zero, far from the interferogram. Even though thelatter technique eliminates the problem of reduced dynamic range, thetechnique is still susceptible to DC drift.
Another way to achieve modulation of the radiation is by phasemodulation (PM). Phase modulation is achieved in some step-scaninstruments by a low amplitude oscillation of the moving mirror alongthe light path, but any other way of producing phase-differencemodulation is acceptable. PM results are superior to AM results by atleast a factor of 2 in S/N, when the experiment is detector-noise limited.This improvement stems from the fact that the PM interferogram isessentially the first derivative of the AM interferogram, thereforesource intensity fluctuations and other variations of the beam intensitywill cancel out [31]. Another parameter associated with PM modulationexperiments is the so-called 'phase modulation characteristic' [32].This refers to the connection between the amplitude of the phasemodulation and the wavelength region of maximum modulationefficiency. For the mid-IR region, a PM modulation amplitude of 2 XHeNe
(zero-to-peak) is appropriate (maximum modulation at 2300 cm-l).In contrast to the continuous-scan method, the advantages of step-
scan operation include the ability, as mentioned above, to applyvirtually any modulation frequency to the infrared radiation and tocarry out multiple modulation experiments. Since the frequency ofmodulation is not a function of any retardation velocity (e.g., mirrorscan speed), they have no dependence on radiation wavelength. Inaddition, the use of lock-in amplifier detection or digital signal pro-cessors (DSP), provides a high degree of noise rejection, analogous tothe Fourier filtering effective in the continuous scan mode. Anotheradvantage of lock-in amplifier or DSP detection is the easy retrieval ofthe signal phase. This is possible due to the fact that the beamsplitter(instrumental) phase is identical for the in-phase and quadrature (900out of phase) components of the signal. These components are easilyobtained as outputs of a two-phase lock-in amplifier. As a result, notonly the magnitude M, but also the phase D can be easily obtained byfollowing Eqs. (6.5) to (6.8):
M = (2 + Q2)1/2 (6.5)
D = arctan(Q/I) (6.6)
126
Q = M sine (6.8)
The signal-to-noise (S/N) ratio is increased by staying longer at eachdata collection point. The two modes of operation, step-scan andcontinuous-scan, should produce identical results under conditions ofdetector-limited noise. The time resolution of the step-scan technique islimited only by the rise-time of the detector, by the electronics(especially by the A/D converter), and by the signal strength. Therefore,it is capable of measuring various relaxation processes that occur in thesub-microsecond regime and are closely associated with molecular-scale phenomena.
6.14 FOURIER TRANSFORMATION AND ITS USE IN FT-IRINSTRUMENTATION
The breakthrough in the application of interferometry to spectroscopycame with the discovery by Cooley and Tukey of the fast Fouriertransform (FFT) algorithm in 1964 [33]. The FFT procedure takesadvantage of several properties of the discrete FT, which is somehowredundant in nature [34]. The FT case can be represented as an n-vector (n points interferogram) which must be multiplied by an nxnmatrix, each row of which is a discrete representation of a complexsinusoid. The result of the multiplication is an n-vector, which is thetransformed spectrum. A straightforward approach requires n2
operations, where operations are complex multiplications followed bycomplex additions. Since the nxn matrix is highly ordered and cyclicalit can be readily factored. If Nis chosen such that it is an integral powerof two, then extra advantage may be realized by calculating the FT on adigital computer [35].
As an example, the Fourier transform of a 2048 point vectorrequires (2048)2, or 4.2 million multiplications. The FFT algorithmreduces this amount to (2048) x log(2048), for a total of 24233 multi-plications. Obviously, the great advantage of FFT can be appreciated asthe number of data points gets larger and larger. Today's personalcomputers can calculate an array similar to the one described above ina fraction of one second.
127
I=Mcos¢ (6.7)
REFERENCES
1. W.F. Herschel, Phil. Transact. Roy. Soc., 90 (1800) 284.2. C.N.R. Rao, Chemical Applications of Infrared Spectroscopy. Academic
Press, New York, 1963.3. J.F. Ferraro, Spectroscopy, 14(2), 1999.4. W.L. Wolfe and G.J. Zissis, The Infrared Handbook. Office of Naval
Research, Department of the Navy, Washington, DC, 1978.5. J.C. Morris, Comments on the measurement of the emmitance of the
globar radiation source. J. Optical Soc. Am. (Washington, DC), 51 (1961)758.
6. Nicolet Instruments, private communication.7. W.Y. Ramsey and J.C, Alishouse, A comparison of infrared sources. Infra-
red Physics (Pergamon, Elmsford, NY), 8 (1968) 143.8. W.L. Wolfe and G.J. Zissis, The Infrared Handbook. Office of Naval
Research, Department of the Navy, Washington, DC, 1978, Chapter 11.9. M.J.E. Golay, Rev. Scient. Instrum., 18 (1949) 347.
10. M. Hercher, Detectors and Lasers, in: Contemporary Optical Engineering.The Institute of Optics, Rochester, NY. 1976
11. A. Simon, J. Gast (Bruker Analytische Messtechnik GmbH, Germany.Patent written in German. Application: DE 92-4242440 921216
12. G. Hass and A.F. Turner, in: M. Auwarter (Ed.), Coatings for InfraredOptics. Wissenschaftliche Verlagsgesellschaft mbh, Stuttgart, 1957.
13. I. Noda, A.E. Dowrey and C. Marcott, Appl. Spectrosc., 42 (1988) 203.14. R. White, Chromatography l/Fourier Transform Infrared Spectroscopy and
its Applications. Marcel Dekker, New York, 1990.15. C.N.R. Rao, Chemical Applications of Infrared Spectroscopy. Academic
Press, New York, 1963.16. A.L. Smith, Applied Infrared Spectroscopy, Fundamentals, Techniques,
and Analytical Problem-Solving. Wiley-Interscience, New York, 1979.17. A.A. Michelson, Phil. Mag., Ser. 5, 31 (1891) 256.18. P.R. Griffiths and J.A. de Haseth, Fourier Transform Infrared Spectro-
scopy. Wiley, New York, NY, pp. 407-425, 1986.19. P. Fellgett, Thesis, Cambridge University, Cambridge, UK, 1951.20. P. Fellgett, J. Phys. (Radium), 19 (1958) 187.21. P. Jacquinot, J. Opt. Soc. Am., 44 (1954) 761.22. J. Connes and P. Connes, J. Opt. Soc. Am., 56 (1966) 896.23. J. Connes, Optical Instruments and Techniques. Oriel Press, Paris, 1970.24. R.A. Palmer, Spectroscopy, 8(2) (1993) 26.25. A.G. Marshall and F.R. Verdun, Fourier Transforms in NMR, Optical, and
Mass Spectrometry. Elsevier, Amsterdam, 1990.26. L. Mertz, Infrared Phys., 7, (1967) 17.27. M.L. Forman, J. Opt. Soc. Am., 56 (1966) 978.
128
28. M.L. Forman, W.H. Steel and G.A. Vanasse, J. Opt. Soc. Am., 56 (1966) 59.29. C.A. McCoy and J.A. de Haseth, Appl. Spectrosc., 42 (1988) 336.30. R.A. Palmer, Spectroscopy, 8(2) (1993) 26.31. J. Chamberlain, Infrared Phys., 11 (1971) 25.32. J. Chamberlain and H.A. Gebbie, Infrared Phys., 11 (1971) 57.33. J.W. Cooley and J.W. Tukey, Math. Comput., 19 (1965) 297.34. C.J. Manning, Ph.D. Thesis, Duke University, 1991.35. M.L. Forman, J. Opt. Soc. Am., 56 (1966) 978.
129
Chapter 7
Sampling techniques and applications
PART A. DIRECT TECHNIQUES
In recent years there have been remarkable theoretical andexperimental advances in a variety of measuring methods for infraredspectroscopy, which have made it possible for anyone to try variousinfrared measurement methods relatively easily [1-6]. While trans-mission methods are most often used for measurements of infraredspectra of general samples, the attenuated total reflection (ATR)method, diffuse reflectance (DR) method, reflection-absorption (RA)method, photoacoustic spectroscopy (PAS), infrared microspectroscopy,and emission spectroscopy, etc., are also often employed.
7.1 TRANSMISSION SPECTROSCOPY
Transmission methods are suitable for infrared measurements ofliquid (solutions) samples, powder samples and gases. Practicalmeasures for the intensities of infrared bands in a transmissionspectrum are given by Lambert-Beer's law. Before we explain the law,let us define transmittance, T, and absorptivity, A, When a parallellight beam enters transparent material with the length of d cm (asshown in Fig. 7.1), transmittance, T, is defined as follows:
T=ItIIo (7.1)
where It and Io are the intensities of the parallel beam at the positionsof incidence and exit, respectively. Transmittance, T, is the proportionof the intensity of transmitted light to that of incident light. On the
131
x x+dx
Io It >
Fig. 7.1. Absorption of light by a transparent material.
other hand, absorptivity, A is the proportion of the intensity ofabsorbed light (a) to that of incident light; namely
A = I/Io (7.2)
If one assumes that the transparent material does not scatter light andis non-fluorescent, the following equation holds:
It+a =Io
Therefore
A+T=I
(7.3)
(7.4)
Now we will develop Lambert-Beer's law which explains the degree ofdecrease in the intensity of incident light. If the intensity of incidentlight decreases from i to i + di when the light proceeds from x to x + dx inthe transparent material, the degree of decrease in the intensity (di) isconsidered to be proportional to the intensity of the incident light (i),the concentration of a sample, c (mol dm-3 ), and the thickness of thesample (dx):
-di = c*ic dx (7.5)
where e* is a proportional constant. If we make definite integral of Eq.(7.5) from 0 to d
132
! - /::
- i =d c|cf dx (7.6)
Thus
I t = Io exp(-cdc*) (7.7)
Equation (7.7) is a mathematical representation of Lambert-Beer'slaw, which means that the intensity of incident light decreases expo-nentially. Lambert-Beer's law is usually used in the form of a commonlogarithm. Equation (7.7) can be expressed as follows in terms of acommon logarithm:
It = Io. lO0 d (7.8)
where
8 = 0.434£* (7.9)
If we take the common logarithm of Eq. (7.8)
log(IJIt) = log(l/T) = cds (7.10)
log(IJI t) is defined as absorbance, which is proportional to theconcentration, c, of the sample and the path length, d, of a cell. Theproportional constant is a measure of the strength of absorption at aparticular frequency and is called molar absorption coefficient. Theunit of 8 is (mol dm- cm)-l, namely, M-l cm-l (in SI units, it is m2 mol-).
c is specific for each sample (the values of £ usually range from 10 to105). One can calculate the concentration from the measurement of theabsorbance of a sample, if one knows e and d (usually, d is taken as 1cm). In contrast, one can determine from known d and c.
When we use a transmission method on a liquid sample, the selec-tion of window materials (which transmit infrared light) and the lengthof a cell are important. During selection of window materials, we mustnote a usable wavenumber range, a refractive index, and solubility inwater. Table 7.1 summarizes the usable wavenumber range, therefractive index, and the solubility in water of representative windowmaterials. Among the window materials for non-aqueous solutions,KBr is most often used. KBr has a wide usable wavenumber range
133
TABLE 7.1
The usable wavenumber range, the refractive index, and the solubility in water ofrepresentative window materials for infrared transmission spectroscopy
Window Usable wavenumber Refractive Propertiesmaterial range/cm- 1 index
CaF 2 75000-1000 1,40 insoluble in water
BaF 2 67000-800 1,45 insoluble in water
KBr 43000-400 1,52 soluble in water and alcohol
CsBr 42000-250 1,65 soluble in water
CsI 42000-200 1,72 soluble in water
NaCl 40000-600 1,50 soluble in water
KC1 33000-400 1,47 soluble in water
ZnSe 20000-500 2,42 insoluble in water
KRS-5 12000-350 2,35 insoluble in water, poisonous
Si 10000-100 3,42 insoluble in water
Ge 5000-400 4,00 insoluble in water
(4000-340 cm-l) and is inexpensive; furthermore, the refractive indexof KBr (n = 1.52) is close to that of a solution. Although we can use onlyabove 1000 cm-1, insoluble CaF2 (n = 1.39) is proper for an aqueoussolution (n = 1.33). KRS-5 (n = 2.37) is often used for infrared measure-ments in lower wavenumber regions. However, KRS-5 is poisonous andrequires an attention.
7.1.1 Liquid (solution) samples
Infrared spectra of liquid samples are measured using a fixed cell forliquid or an assembled cell. Fixed cells and assembled cells arebasically the same in that a spacer having a certain thickness isdisposed between two window materials. While a fixed cell isadvantageous in that the cell has a clearly defined thickness and isairtight, it is not easy to clean this type of cell. Conversely, although anassembled cell is easy to clean, this type of cell is not airtight in general.When our sample is a solution sample with high viscosity and a lowvapour pressure, it is also possible to measure a spectrum only with thesolution sample held between two window materials.
134
Since water exhibits strong infrared bands, a path length of a cellmust be 10 upm or shorter to measure an infrared spectrum of anaqueous solution by a transmission method. If we use heavy water(D2 0) instead of light water (H2 0), strong water bands (-3500 cm-l ,-1650 cm- ) show a downward shift. Therefore, it is effective to usedeuterium water; one measures spectral regions in the vicinity of 3500cm -1 and 1650 cm-l. The ATR method is often also used to measureinfrared spectra of aqueous solutions. A variety of liquid transmissioncells are commercially available. Figures 7.2a and b show expandedviews of the micro demountable flow-thru cell and heated demountablecell kit, respectively.
(a)
(hi
Fig. 7.2. Expanded views of the micro demountable flow-thru cell (a) and heateddemountable cell kit (b). (From catalogue of Nicolet.)
135
7.1.2 Powder samples
To measure an infrared spectrum of a powder sample by a transmissionmethod, the KBr disc method is usually used. Since a particle diameteris too large when we use a powder sample as it is, incident light isirregularly reflected and, as a result, we cannot obtain a good spec-trum. Therefore, it is necessary to crush the sample into pieces eachhaving a diameter of 1-2 pm in advance.
7.1.3 KBr method
When using the KBr method, crush and mix 1-2 mg of a sample andapproximately 100 mg of KBr powder in an agate mortar, introduce themixture into a tabletting equipment, and tablet. With this method, thefollowing three points should be noted:1. Since it is impossible to obtain good tablets if KBr or a sample
contains moisture (i.e., resultant tablets become opaque), removethe moisture as much as possible.
2. If the sample is not sufficiently crushed, the tablets produced willbecome opaque or the quantity of transmitted light will decrease(due to light scattering). Hence, the crushing must be sufficient.
3. K+ or Br and cations or anions contained in the sample sometimesexchange with each other. Further, crushing, pressurization, etc.sometimes causes denaturation of the sample.
To confirm that a situation like (3) has not occurred, it is desirable tomeasure infrared spectra of the same sample by other methods (e.g.,the nujor method) in parallel with the KBr method. When the amountof the sample is small, use micro-tabletting which allows one to make atablet having a diameter of 1 mm.
7.2 INTERNAL AND EXTERNAL REFLECTION SPECTROSCOPY
7.2.1 Attenuated total reflection (ATR) method
As its name suggests, the ATR method is a type of reflectance methodand has been used mainly for surface analysis and analysis of bulkmaterials and aqueous solutions [1-6]. In the ATR method, a sample isplaced on a prism which has a larger refractive index than that of thesample, as shown in Fig. 7.3, and infrared light is introduced to the
136
anterior capsuleepithelium
nucleus ncex - posterior capsule
cortex
ATR prism (ZnSe)
Fig. 7.3. An ATR prism and an eye lens on it. (Reproduced from Ref. [7] with permission.Copyright (1998) Society for Applied Spectroscopy.)
prism such that the infrared light is reflected totally at an interfacebetween the prism and the sample [7]. At this stage, to develop totalreflection, the incident angle 0 must be larger than the critical angle Oc.Where the refractive indices of the prism and the sample are nI and n2,respectively, the critical angle is defined as:
Oc = sin-l(n2 /nl) (7.11)
Total reflection discussed here is not reflection whereby the incidentlight is totally reflected at the interface, but reflection whereby theincident light penetrates inside the sample once to a certain extentbefore being reflected. That is, although the incident light is reflected100% in a wavelength range in which the sample does not absorb light,in a wavelength range in which the sample absorbs it the reflectance isdecreased depending on the strength of the absorption. Hence, if wemeasure the intensity of reflected light in a certain wavelength range,we can obtain a spectrum that resembles a transmission spectrum.
In the ATR method, the penetration depth c is important. The depthdp is expressed as follows:
dK (7.12)
2x in 2 0 _ )2)
where kl denotes the wavelength of the light within an ATR crystal. Asis clear from the Eq. (7.12), the depth dp is determined by the incidentangle, the wavelength, and further, by a ratio of the refractive index of
137
a sample to the refractive index of the ATR crystal. Since the depth dp isat most a few gm in the infrared region, an ATR spectrum providesinformation regarding a surface and around the same. In the ATRmethod, the contact between a sample and an ATR prism must be verysmooth. Figure 7.3 shows an example of non-destructive analysis of aneye lens by the ATR method [7].
The ATR method is very suitable to obtain infrared spectra ofaqueous solutions. Figures 7.4a and b show infrared spectra of watermeasured with the transmittance method and ATR method, respect-ively [8]. A strong feature which appears in the range of 3600 to 3200cm-l is due to the OH stretching vibrations, while a band in the vicinityof 1640 cm-l is assigned to the HOH bending vibration. A majorproblem in studying aqueous solutions comes from these two bands.Although the spectrum (Fig. 7.4a) is obtained using a very thin liquidcell (whose thickness is 10 lpm), we can find a strong band withabsorbance of 1.5 or higher. The ATR method considerably weakens theband due to the OH stretching vibrations. This is because the shorterthe wavelength, the smaller the penetration depth dp (Eq. (7.12)). Inthis manner, with the ATR method, we can suppress the intensity ofthe strongest band of water, and therefore, data processing for sub-tracting the infrared spectrum of water is relatively easy.
Figure 7.5a shows an ATR infrared spectrum of oxidized cyto-chrome c (pH 9.3, 10wt%) in a phosphate buffer. In Fig. 7.5b, a
0cd
0
E:
4000 3600 3200 2800 2400 2000 1600 1200 800
Wavenumber/cm -'
Fig. 7.4. Infrared spectra of water measured with the transmittance method (a) and ATRmethod (b). (Reproduced from Ref. [8] with permission. Copyright (1994) Tokyo Kagaku
Dojin.)
138
ZC3
C
EX
Wavenumber/cm -'
Fig. 7.5. (a) An ATR/infrared spectrum of oxidized cytochrome c (pH 9.3, lOwt%) in aphosphate buffer. (b) An ATR/infrared spectrum of the phosphate buffer solution.
(c) Difference spectrum obttained by subtracting spectrum (b) from spectra (a).
spectrum of the phosphate buffer solution is presented. Note that thespectrum of the protein solution is close to that. Hence, in order toextract useful information from the spectrum shown in Fig. 7.5a, wehave to subtract the spectrum of buffer (Fig. 7.5b). Figure 7.5c shows aresulting spectrum that is obtained by subtracting the spectrum ofbuffer. A simple guideline for determining if the water spectrum issuccessfully subtracted is to see whether the range of 2400 to 1700 cm- 'is flat.
7.2.2 Prisms and accessories for ATR spectroscopy
ATR spectroscopy has long been used for various samples from aqueoussolutions to bulk materials [1-6]. A variety of prisms and accessoriesfor ATR spectroscopy have been developed and are commercially avail-able. They are divided into two groups: single reflection type with ahemicylinder crystal and multiple-reflection type with a trapezoidalcrystal. Figure 7.6 depicts optical schematics of several commerciallyavailable ATR accessories. In FT-IR spectroscopy, the multiple-reflec-
139
tion setups are more popular than single reflection setups because inthe former one can control the ATR signal intensity easily by adheringsamples on both sides of an ATR prism or by changing the size ofsamples. The energy loss by the multiple-reflection can be compensatedby the increase in the number of acquisition or the use of a MCT
(b)
(c)
Fig. 7.6. Various accessories for ATR spectroscopy: (a) single-reflection variable-anglehemicylinder; (b) multiple-reflection single-pass crystal; (c) circle ATR cell for liquid
samples.
TABLE 7.2
The usable wavenumber range, the refractive index, and the properties of representativewindow materials for ATR spectroscopy
Window Usable wavenumber Refractive Propertiesmaterial range/cm I index
suitable for aqueous solutionpoisonoussuitable for aqueous solution,fairly fragilefragilehigh refractive index, suitablefor aqueous solution, fragile
ZnSeKRS-5
AS2 Se3
20000-40020000-30012500-800
SiGe
2,42,402,80
3,404,00
5000-16005000-900
140
--
(a) (b)
Fig. 7.7. (a) Accessory for micro ATR; (b) in situ ATR accessory.
detector. The ATR cell shown in Fig. 7.6b is very suitable for films,solids, and liquids, while the cell shown in Fig. 7.6c is designed forliquid samples. Table 7.2 summarizes properties of selected opticalmaterials used for ATR spectroscopy. Recently, micro ATR cells and insitu ATR accessories have made marked progress; Figs. 7.7a and bshow their examples, respectively.
7.2.3 Examples of ATR infrared studies
Two examples of ATR infrared studies are introduced here. Anotherexample will be described in Section 9.7.3. Figure 7.8a-c show ATRspectra of water and the anterior and posterior portions of the lenscapsule of a 3-month-old albino rabbit lens on an ATR prism [7]. Thespectra of the capsules are very close to that of water, but one can seeweak features in the 1600-1000 cm-l region that are not assigned towater. Figures 7.9a and b present difference spectra that were obtainedby subtracting the spectrum of water from the spectra of the lenscapsule [7]. The thickness of the capsules of the rabbit lens is about2-20 pm, while the penetration depth of the ATR prism in the1700-1000 cm-l region is less than 1 pm. Therefore, all the ATR signals
141
i
Ii
II
I
I
0031
w0z
o0(,
WAVENUMBER /cm- 1
Fig. 7.8. ATR/infrared spectra of water (a) and the anterior (b) and posterior (c) portionsof the lens capsule of a 3-month-old albino rabbit. (Reproduced from Ref. [7] with
permission. Copyright (1989) Society for Applied Spectroscopy.)
in Fig. 7.9a and b may be due to type IV collagen, a major component ofthe capsule that envelops the lens. Figure 7.9c shows an ATR spectrumof purified type IV collagen in an aqueous solution. It is noted that theATR spectra of the rabbit lens (Figs. 7.9a and b) are very close to that oftype IV collagen in the aqueous solution (Fig. 7.9c). Bands at 1638 and1553 cm-l are due to amide I and amide II of type IV collagen, respect-ively. Medium features at 1080 and 1033 cm-l are assigned to C-Ostretching modes of collagen [7]. The frequencies of amide I and IIsuggest that type IV collagen in the capsules assumes a secondarystructure that is very close to 3 helix [7]. This ATR study is a goodexample demonstrating the potential of ATR spectroscopy in investi-gating the structure of biological molecules in situ.
ATR/IR spectroscopy has considerable promise in on-line monitor-ing [9,10]. In general, an ATR immersion probe is used as a sendinghead, which allows one to monitor reaction occurring within about 1 ipmof the surface of an ATR prism. The ATR method has two advantages inchemical process analysis. One is that the immersion probes have littleeffect from bubbles and suspensions in reaction mixture. Another isthat the ATR method is applicable to samples that do not transmitenough light. Figure 7.10a shows the results of on-line monitoring of
142
WAVENMMBR /cm-1
Fig. 7.9. (a) The difference spectrum between spectrum (a) and spectrum (b) in Fig. 7.8.(b) The difference spectrum between spectrum (a) and spectrum (c) in Fig. 7.8. (c) ATR/infrared spectrum of Type IV collagen from human placenta in aqueous solution (Repro-duced from Ref. [7] with permission. Copyright (1989) Society for Applied Spectroscopy.)
the esterification of acid anhydride and diol measured by an ATR insitu setup [10]. The esterification is one of the most basic reactions inchemical industries. In the esterification by measuring the acid valueand hydroxyl group value at any time the terminal point of the reactionmust be predicted. It can be seen from Fig. 7.10a that as the reactionproceeds, a broad feature near 3400 cm l due to the OH stretchingmode of alcohol decreases and a sharp band at 1700 cm-l assigned tothe C=O stretching mode of ester increases. Figure 7.10b illustratescorrelation for the acid value between the laboratory data and the ATR/IR data [10].
7.2.4 Reflection-absorption spectroscopy
Reflection-absorption spectroscopy (RAS) is a powerful technique formeasuring IR spectra of thin films on metal [1,2,8,11,12]. Figure 7.11illustrates the principle of RAS. Let us consider the behaviour ofpolarized light impinging on a metal surface. When light impinges on
143
(a)
0.5
-0.010Q
aC
0.5
-0.01046
0.5
--(0 fi
4000
initiation of reaction
N.3600 3200 2800 2400
in the middle of reaction
200oo 160 1200 725
,i Xjl)00 3600 3200 2800 2400 2000 16 200 1 725
termination of reaction
0003600 200 2800 200 2000 16t0 _ ,
Wavenumber cm '
(b)
Fig. 7.10. (a) The results of on-line monitoring of the esterification of acid anhydride anddiol measured by an ATR in situ setup. (b) Correlation for the acid value between thelaboratory data and infrared data. (Reproduced from Ref. [10] with permission.
Copyright (1995) Kogyo Gijutsu Co.)
the metal surface, an electric field is generated near the surface. Theintensity of the electric field depends upon the incident angle and thedirection of polarized light. When perpendicular-polarized light is used,the electric vector of the incident light and that of the reflection lightcancel each other out because the phase of the incident wave is shiftedby 180 ° due to the effect of free electrons in metal. As a result, there is
144
120 Regression Statisticso00 RSO.=0.99
80 Std. Err.=3.4
40 61 67.0~~40l ~~~~37 36.1
- 20 29 26.6cJ P~~~~~26 25.9
0 20 40 60 80 100 120
acid value iAoraor4 data)
41 1 fA" � �! --rd_
---- O WO 320 280 240 200 160 12-0 72
_
Fig. 7.11. Behaviour of two kinds of polarized light which is incident onto a metal surface:(a) perpendicular polarization; (b) parallel polarization.
almost no standing wave. In contrast, when parallel-polarized light isapplied, the electric vector of the incident light and that of thereflection light strengthen each other, generating an electric fieldperpendicular to the metal surface. The strength of this standing waveincreases as the incident angle approaches 90 ° .
Figure 7.12 shows the dependence of the absorption factors for theparallel (Ap) and perpendicular (As) polarization at the wavenumber ofmaximum adsorbed layer [12]. An optimal incident angle that gives thehighest sensitivity changes with metals and the wavenumber of incid-ent light. Usually the optimal incident angle is 85-89° . The higher thereflectivity of the metal, the larger the optimal incident angle.
When parallel-polarized light impinges on a thin film absorbed on ametal surface, the standing wave interacts with the molecules in thefilm and the light is absorbed. The change in reflectance in the spectralregion where the light is absorbed can be represented by the followingequation [8]:
-1 ) - 1 cs(7.13)n Cos0
Here, AR and Ro are a change in reflectance induced by the presence ofthe thin film and reflectance in the absence of the film, respectively. n1and n2 are refractive indices of medium (such as atmosphere) and that
145
x
0 20 40 60 80
Angle of incidence, degrees
Fig. 7.12. Dependence of the absorption factors for the parallel (Ap) and perpendicular(As) polarization at the wavenumber of maximum adsorbed layer. (Reproduced from Ref.
[12] with permission. Copyright (1993) John Wiley & Sons.)
thin film, respectively. 0, a, and d represent an incident angle, anabsorption coefficient, and a thickness of the thin film, respectively. Inthe case of transmission spectroscopy, the ratio of a change in theintensity of transmitted light in the presence of the sample (A) and theintensity of the incident light (Io) can be represented by the followingequation:
rlIo = -ad (7.14)
Comparison of Eqs. (7.13) and (7.14) reveals that the sensitivity of RASis higher by (4n1
3 sin20)/(n2 3 cosO) than that of transmissionspectroscopy [8]. The term 4nl3 sin2 0 represents the dependence of theintensity of standing wave appearing on the metal surface upon theincident angle, while the term 1/cosO is concerned with a sample areairradiated by the incident light.
RAS has been widely used for studies of thin films such asLangmuir-Blodgett films, thin polymer films, coating films andepitaxial layers on silicon wafers [12]. RAS is very useful not only forinvestigating chemical composition and molecular structures but also
146
for molecular orientations. Good examples of applications of RAS aregiven in Section 8.6.
7.3 DIFFUSE REFLECTANCE SPECTROSCOPY
A diffuse reflectance method is a measurement method for measuringreflected light (diffuse-reflected light) which exits a sample surfaceafter impinging upon the sample surface and thereafter gettingreflected, transmitted while refracted, and scattered repeatedly (Fig.7.13) [1,2]. When we irradiate a powder sample with light, while aportion of the light is regularly reflected at a powder surface, theremaining majority enters the powder and diffuses. During the processof diffusion, since light having particular wavelengths is absorbed bythe sample, if we measure the intensity of the diffuse-reflected light atvarious wavelengths, we obtain a spectrum that is similar to a trans-mission spectrum.
The intensity of a diffuse-reflectance spectrum is generallyexpressed by a Kubelka-Munk equation such as:
K (1-R )2f(R ) (7.15)
S 2R
where K, S, and R, are an absorption coefficient, a scattering coefficientand an absolute diffuse reflectance, respectively. Further, f(R.) iscalled an K-M (Kubelka-Munk) function. Since K is in proportion to a
I I
I: incident lightD; diffuse reflection lightS: regular refrection light
Fig. 7.13. Schematic representation of regular reflection and diffuse reflectance for apowder sample.
147
YA
dy
0
incident light diffuse reflectancelight
t
1I t J+dJ
I+dI t/
Fig. 7.14. Incident light and diffuse-reflected light in a powder layer (Kubelka-Munktheory).
molar absorption coefficient, , and a concentration of a sample c (K =yc where y is a proportional constant), if the scattering coefficient is aconstant value, the K-M function should be in proportion to the sampleconcentration. To measure the absolute diffuse reflectance is notrealistic; we therefore measure a relative diffuse reflectance R instead(which is a ratio of the intensity of reflection from the sample to theintensity of reflection from a standard substance).
Let us yield a Kubelka-Munk equation. Assuming that monochro-matic light is incident upon a powder layer which has a thickness d, asthat shown in Fig. 7.14, from the top along they-axis, the incident lightpropagates in the sample in the negative direction along the y-axis anddiffuse-reflected light propagates in the positive direction along thesame axis. A decrease, dI, in the intensity I of the light which propa-gates within a thin layer portion dy in the negative direction and adecrease, dJ, in the intensity J of the light which propagates in thepositive direction are expressed as follows:
-dI = (K + S) Idy - SJdy (7.16a)
dJ = - (K + S) Jdy + SIdy (7.16b)
The first term on the right-hand side of Eq. (7.16a) denotes an intensitydecrease due to absorption and scattering of the incident light, whilethe second term on the same side denotes a contribution from back
148
d
t
'1F
o
scattering light. Equation (7.16b) can be interpreted in a similarmanner. Now, if(S + K)/S = 1 + K/S = a, Eqs. (7.16a) and (7.16b) can bere-written as follows:
-dl/Sdy = aI- J (7.17a)
dJSdy = -aJ + I (7.17b)
Diving Eq. (7.17a) by I and Eq. (7.17b) by J and adding the twoequations, we obtain
dr/Sdy = r2 - 2ar + 1 (7.18)
Integrating this equation, we obtain
(r2 -2ar +1)-ldr =Sldy (7.19)
In this equation, the values of r when y = 0 and y = d hold are Rg (abackground reflectance) and R (the reflectance of the sample),respectively. If an integral of Eq. (7.19) is expressed by the relationshipas below
dr 1dr ~dr (7.20)(r2 - 2ar + 1) r + (2ar - 1)2 }{r -(2ar - 1) 2})
the integral is solved simply as:
{R, -a -(a 2 1)V2 {Rg -a +(a 2 _ 1)21 =2sd(a2 1)2 (7.21)In12 2sd(a _ 1)"" (7.21)
{Rg -a -(a 2 -1)2 ){Rs -a +(a2 -1)1/ 2
Since we can ignore Rg for an extremely thick sample (i.e., Rg = 0 when d= ~), Eq. (7.21) is simplified as follows:
{-a -(a 2 _ 1)'2){R -a +(a2 _ 1)l/2 =0 (7.22)
If we solve Eq. (7.22) with respect to R,
149
R = 1 1 (7.23)a+(a2 -1)/ 2
1+K + (KlS) 2+ 2 K s}.3
We can obtain the Kubelka-Munk equation (7.15), if we solve thisequation above with respect to KIS.
To carry out qualitative and quantitative analysis using the diffusereflectance method, we need to use an equation which links theintensity of diffuse-reflected light and an absorption characteristic of asample. An equation that is often used is the following equation whichis yielded from the Kubelka-Munk equation.
K = cosh(log(R)) -1 (7.24)
Equation (7.24) is illustrated in Fig. 7.15. Although K/S (which isrelated to the absorption characteristic of the sample) and log(l/R)(which is related to the intensity of diffuse-reflected light) are not in alinear relationship with each other, in a narrow KIS range we canregard that the two are approximately in a linear relationship witheach other. When we analyze an infrared diffuse-reflectance spectrum,log(1/R) is usually indicated along the vertical axis.
Problems with the diffuse-reflectance method are an influence byregular reflection and a scattering coefficient. The former is influencedby the size, the shape and an absorption coefficient of powder. Ingeneral, the smaller a powder diameter is, the weaker the regular
4
2
0
log (l/R)
Fig. 7.15. Relationship between log (1/R) and K/S derived from Kubelka-Munk equation.
150
s
reflection light becomes. The latter is influenced by the diameter, theshape, a filling density, etc., of power. Hence, infrared diffuse-reflect-ance spectra are usually measured for samples mixed with KCl or KBrpowder to reduce the influence of regular reflection. For a sample thatinteracts with KCl or KBr, diamond powder and silicon powder are alsoemployed as a diluent.
The Kubelka-Munk theory is based on a continuum model. It doesnot consider the particle nature of the powdered samples. The scatter-ing coefficients is affected by packing density and particle size andhence affects the resulting infrared spectrum. Studies have beenundertaken to investigate the effect of particle size, size distribution,packing density and the orientation of the sample cup [13-15].Generally, the spectra of the same sample vary 15-30% (in absolute K-M units) when run by several people [16]. Griffiths and co-workersdemonstrated the effect of pressure on the diffuse reflectance infraredspectrum of powdered samples. They concluded that the duration ofpressure applied is also an important factor for spectral reproduc-ibility. They obtained a spectral reproducibility of 3% relative standarddeviation after subjecting the sample to high pressure (order of tons persquare inch) over a period of 15 min.
The problem arising from the factors adherent to the physicalnature of the sample was approached by Christy et al. [15,17] in twodifferent ways.
1. For a sample with a narrow range of particle size distribution, thepacking was carried out by an automatic packing machine toeliminate variations arising from packing pressure and time.
2. The sample cup was rotated slowly during the spectral measure-ments to eliminate the inhomogeneity of the sample arising fromthe different shapes and sizes of the sample particles.
However, these techniques are not widely used because of practicalproblems. Attempts have also been made to modify the Kubelka-Munkfunction to include particle size. The Kubelka-Munk function wasshown to possess an excellent inverse relationship with particle size(see Fig. 7.16) of the samples [18]:
f(R) oc lid (7.25a)
where d is particle diameter.
151
0.37
0.30
0.23
; 0.16
i
.00.09
0.02
3280 3120 2952 2784
Wavenumber cm'
Fig. 7.16. Diffuse reflectance spectra of 4%(w/w) samples of mono-disperse polystyrenespheres in KBr in the region 3300-2700 cm- 1.
By introducing particle size in the Kubelka-Munk function (Eq.(7.25b)), quantitative determinations could be made using the diffusereflectance technique [18].
f(R) = (KISd (7.25b)
However, the above equation must be taken strictly as an empiricalrelationship because there is no theoretical justification for theinclusion of the particle size in the Kubelka-Munk function.
The diffuse reflectance spectrometry is applied to a wide variety ofsolid samples. The samples that can be ground can be easily mixed withground KBr powder for spectral measurement. Furthermore, samplesthat are dark like coal and kerogen are comfortably measured using thediffuse reflectance technique (see Fig. 7.17). Samples that are difficultto grind, for example asphaltenes can be measured using a techniqueused by Christy et al. [19].
In this technique the asphaltene sample is dissolved in a low boilingliquid such as dichloromethane. A background spectrum is measured
152
aE
eI0
2
4Ua0
WU
Wavenumber cm-I
Fig. 7.17. Diffuse reflectance spectra of three different coke samples with their volatilematter content (VMC) values.
with firmly packed KBr powder. Then the asphaltene solution can becarefully dropped onto the surface of the KBr powder. The samplepenetrates the particles and settles on the surface of the particles.Since the diffuse reflectance technique is a near surface technique, asmall amount of the sample from a few drops of the solution is more
153
2000 1600
WAVE NUMBER1000 600 1/cm
Fig. 7.18. Diffuse reflectance spectrum of asphaltene (obtained by deposition technique)and absorption spectrum of the same amount of sample in KBr using the transmission
technique.
than enough to acquire a good quality diffuse reflectance spectrum(Fig. 7.18).
The sampling technique in diffuse reflectance spectrometry has alsobeen modified to suit high temperature and high-pressure studies.Thermal dehydration and decomposition reactions have been carried
154
. .TRANSMITTANCE SPECTRUM I i I i
TRANSMITTANCE SPECTRUM
U)
zZ
v
id
I I i I I 200 I i I 1 In Do 3000 2000 1600 1000 6
DIFFUSE REFLECTANCE SPECTRUM
A, _~~~~~~~~~~~~~~4000 3000
40 To
out [2--23]. An example using high temperature in diffuse reflectanceinfrared spectrometry is given in Chapter 9.
7.4 PHOTOACOUSTIC SPECTROSCOPY
When a sample is irradiated by monochromatic light it is absorbed andconverted into heat. This heat is propagated into the gas surroundingthe solid and causes a variation in pressure. If the gas is contained tosurround the sample, then the pressure variation can be detected as anacoustic signal. The photoacoustic spectroscopy is based on this signal.
In photoacoustic spectroscopy, the sample is placed in a cell con-taining a gas. A microphone is attached to the cell for the detection ofthe photoacoustic signal. A sketch is shown in Fig. 7.19.
Rosencwaig and Gersho [23] have discussed the theory of the photo-acoustic effect with solids. The theory was developed considering thediffusion of heat generated by the absorption of electromagneticradiation by a solid sample.
When infrared radiation strikes the surface of a sample that has anabsorption coefficient cm-l, the radiation intensity decaysexponentially as
I=I e (7.26)
where I is the incident energy and I is the energy at depth x. Theoptical absorption depth of the sample is p = 1/P cm. If the radiation is
Zig
Microphone
F=-o+lb)
Fig. 7.19. Sketch of the setup used in photoacoustic measurements.
155
CGas
/ / I' / zzr //
modulated sinusoidally at o rad s-l, then the intensity of radiation at adepth x is
I = Io (1 + cosot) e- (7.27)
Absorption of infrared radiation at a depth x produces heat energy PIper unit volume (heat density).
PI = X PIo (1 + cosot) e- > (7.28)
The heat generated then decays exponentially as
PI e (7.29)
where a is the thermal diffusion coefficient. The heat decay can then bewritten as
4 1Io (1 + cost) e e e- = X pIo (1 + cosot) e- (P+"' X (7.30)
The diffusion depth of the heat generated is p, = 1/a cm. The diffusiondepth can be related to the physical parameters Ks, p,, Cs as
Ps = (2KJpsCsco) (7.31)
where Ks is the thermal conductivity, p, is the density, and Cs is thespecific heat of the sample.
The oscillating heat is then dissipated to the gas that is in contactwith the solid. Equation (7.31) shows that the heat generated at depth xis oscillating.
By considering the sample thickness from x = 0 to x = -(l + lb) andgas column length from x = 0 to x = +lg, Rosencwaig and Gersho [23]have solved the thermal diffusion equation for the system, temperaturedistribution in the cell, the periodic heat variation in the gas and theacoustic pressure wave produced in the cell. The equations are toocomplex to deal with here. However, the solution for the incrementalchange in pressure in the cell that is responsible for the production ofacoustic signal is shown in Eq. (7.32). The term Q varies with theopaqueness of the solid sample and the gas in the cell.
6P(t) = Q e- [ (wt -h/4)] (7.32)
156
Rosencwaig and Gersho [23] have divided the solids into six differentcategories depending on their optical opaqueness to explain thedependency of Q and the signal: three cases for optically transparentand three cases for optically opaque solids according to their relativemagnitude of the thermal diffusion length (p,), as compared to thethickness of the solid () and optical absorption length (p).
(a) For optically transparent solids where pa > 1, the cases are
1. Thermally thin solids where p, >> 1 and p, > p.2. Thermally thin solids where ps >> 1 and p < pp.3. Thermally thick solids where p. < 1 and yp << pp.
For thermally thin solids the signal is proportional to Pl and varies asco- 1 and depends on the properties of the backing material. For thicksolids the signal depends on Pp,. It means the acoustic signal dependsonly on the light absorbed within the thermal diffusion length ps.
(b) For optically opaque solids where 1<< 1, the cases are
1. Thermally thin solids where p >> 1 and p, >> pp.2. Thermally thick solids where ps < 1 and pi > pp.3. Thermally thick solids where p, << 1 and p, < pp.
For thermally thin solids, the signal is independent of P and depends onthe thermal properties of the backing material and varies as m-1. Forthermally thick solids in case 2 the signal is independent of anddepends on the thermal properties of the solid and varies as o-l. Forthermally thick solids in case 3 the signal is proportional to 1ps anddependent on the thermal properties of the solid and varies as -3/2.
When a photoacoustic signal is plotted against wavelength (wave-number) it gives a spectrum that is similar to the absorption spectrumof the material.
This is because the photoacoustic signal approximates Beers law[24]. The theory proposed for the photoacoustic effect of solid materialshas been reviewed by Monahan and Nolle for particulate solid material[25]. This and several other investigations into the photoacoustic effectof particulate solid materials show that the effect is dependent on theparticle size of the bulk [26-28]. The photoacoustic signal was shown tobe inversely proportional to the particle size when the samples arediluted in non-absorbers [24,26-28]. The similarity in the signaldependency on the particle size of the photoacoustic spectra and
157
reflectance spectra led to the Kubelka-Munk type treatment of thephotoacoustic signal [24,26-28].
Most of the samples are susceptible to photoacoustic detection in theinfrared region [24]. The photoacoustic infrared measurements aremade using carbon black as reference sample. The technique needsalmost no sample preparation and can be used in measuring thespectra of samples in solid, liquid and gaseous phases. The techniqueprovides an alternative means of acquiring optical spectra of opaquesolid materials.
The applications of photoacoustic spectroscopy in the infraredregion has increased significantly since the late 1970s. With the highthroughput and multiplexing advantages of modern FT-IR spectro-meters, photoacoustic spectroscopy can be used as a routine analyticaltechnique in the mid-IR region. Vidrine [24] has applied the techniquein the mid-infrared region to a wide variety of solid and liquid samples(Fig. 7.20).
PART B. HYPHENATED TECHNIQUES
The combination of different analytical techniques to tackle a problemyields the so-called hyphenated techniques. Obviously, the desiredresult is the coupling of two or more techniques without sacrificing theperformance of either one. In recent years, coupled or hyphenatedtechniques have become popular and have been successfully applied tothe solution of many analytical problems [29,30]. HPLC-MS, tandemMS-MS, GC-FTIR, TLC-FID, GC-MS, etc. are some of the morecommon hyphenated techniques. An overview of the most widely usedcombinations that involve FT-IR spectroscopy in polymer analysistoday will be discussed here.
7.5 TGA/FT-IR
The coupling of thermogravimetric analysis (TGA) and Fourier trans-form IR spectroscopy (FT-IR) is a good practical example of such aninstrumental approach for solving specific analytical problems. Thishyphenated technique, TGA/FT-IR, provides a quantitative assess-ment of the decomposition process via the thermogram, and an identifi-cation of the decomposition products from the infrared signatures of
158
n
-
L t-mooI l, .E
CJ) '-W __. r,
0o
m-
LLJ D
-', U.......
-me o zzz>sIJ
z
0
I=
,I
1
Ia
NT
V
Xi: r
iL r-
r wII I
- 0I
~nr(uN-O nOO rO
YV w_- NN-
j. tO0;,-a,,aT'. .- ~. ntr .N stU)....
LilI
uI
C
Co
'-S:
ow-wa
C-E
.5 0
0-
Owi0 ,
c'1
i:-
159
r,
0o0. OO 00·
the evolved gases. The gases are transferred from the TGA instrumentby means of a heated transfer line to avoid the possibility of conden-sation. With such a combination, the sample is introduced into the TGAinstrument without any form of chemical or physical modification. Theapplication of the sequential infrared analysis adds a new dimension tothermogravimetric analysis by adding specificity, which it otherwiselacks. An alternative way of looking at the combination is to considerthe TGA instrument as a sample handling or sample treatment front-end to the FTIR spectrometer, where one can make full use of theinterpretive and diagnostic characteristics of infrared spectralanalyses [31].
There are many examples in the literature where the combinationof TGA-FTIR has been used successfully to study a variety of materials.In one such study, the effect of aliphatic amines on the mechanism ofthe thermal decomposition of polybenzoxazines was investigated [32].Figures 7.21 and 7.22 show the TGA thermograms of the methyl-dimerand the amyl dimer, and Fig. 7.23 shows the corresponding FT-IRspectra of the evolved gases. In this work it was also proposed that theMannich base in polybenzoxazines plays a significant role in the ther-mal degradation of polybenzoxazines. Figure 7.24 shows the proposedmechanism of Mannich base cleavage in the benzoxazine dinner. Thecontribution of hydrogen bonding to the degradation mechanism of theMannich base was also examined.
Another example involved the characterization of weathered seal-ants [33]. In that study, TGA/FT-IR results were compared for siliconeand polyurethane unweathered and weathered sealants (6000 h ex-posure time). The results indicated that the TGA/FT-IR combination isuseful in the determination of the degradation changes occurring in thesealants due to weathering. In another study, the characterization ofamine-activated epoxies as a function of cure took place using TGA/FT-IR [34]. It is known that the physical and chemical properties of cureddiglycidyl ether of bisphenol A (DGEBA) are greatly affected by theinitial and final cure temperatures and cure schedule. These propertiesare also affected by the deviation from the stoichiometric ratio of curingagent used. Analysis of a previously cured epoxy for these parametershas usually involved large samples and a greater amount of time. Inthe experiment described here, a cured epoxy was studied as itdecomposed. During the TGA/FT-IR experiment, evolution profiles forspecific gases were obtained, as well as the normal TGA weight lossprofiles. Using this information, both the cure schedule and epoxy/
160
12U
100
Z 80
;60
40
20
0
6
5{
3 al
1 '
0-
-I0 50 100 150 200 250 300 350 400
Temperature (C)
Fig. 7.21. TGA thermograms of methyl-dimer (solid symbols) and amyl dimmer (opensymbols). (Reproduced from Ref. [32] with permission. Copyright (1998) J. Wiley & Sons.)
8
D51
Wavenumber (cm'1)
Fig. 7.22. Infrared spectra of evolved gases from degrading amyl-dimer. (Reproducedfrom Ref. [32] with permission. Copyright (1998) J. Wiley & Sons.)
activator cure ratios could be established from the analysis of the curedpolymer. The particular material studied, a DGEBA polymer curedusing a primary cycloaliphatic diamine, showed a curing mechanismsimilar to that obtained using an aromatic diamine. However, thedecomposition behaviour was more reminiscent of an epoxy cured byusing an aliphatic diamine system. This work demonstrated that acured polymer could therefore be characterized in terms of both therm-al history and activator-resin ratio in a single TGA/FT-IR experiment.
161
.-A
0
<4
4( D0Wavenumber (cm'l)
Fig. 7.23. Infrared spectra of evolved gases from degrading methyl-dimer. (Reproducedfrom Ref. [32] with permission. Copyright (1998) J. Wiley & Sons.)
OH OH
CH3 CH, CH,
CCH CI H
IH~
·CH3 6 cHCj-IN-CH
CH, CH,
Fig. 7.24. Mechanism of Mannich base cleavage in benzoaxazine dimmer. R is the aminesubstituent. (Reproduced from Ref. [32] with permission. Copyright (1998) J. Wiley &
Sons.)
162
In another study, the identification of the decomposition products ofcarbon fibre-reinforced phenylethynyl-terminated polyimide compo-sites (PETI/IM7) resulted in a proposed three-step mechanism for thedecomposition [35]. The assigned glass-transition temperature and themechanism for the thermal decomposition of PETI/IM7 were obtainedusing DSC, DMA and TGA/FTIR/MS techniques. The assigned glass-transition temperature was shifted to a much higher temperature afterthe sample was cured. TG/MS/FTIR results indicated that water andNMP were released from the fresh sample during the staging step.Furthermore, NMP and CO2 were the two major products released fromthe sample during the curing step.
TGA/FTIR and isothermal TGA (IGA) was used in a study of poly-imide thermal oxidative stability to obtain simultaneous identificationand relative quantification of the materials evolved during decompo-sition in either air or nitrogen [36]. Two high-temperature stableaddition-cured polyimides and two aromatic condensation polyimides,all four containing fluorinated connecting linkages in the dianhydridemonomers were compared. Figure 7.25 shows the structure of the 3Fand 6F thermoplastics and the PMR-II-50 and VCAP-75 uncrosslinkedthermosets. The TGA-FTIR technique allowed for the simultaneous
3FDA/PPDANPA n=115 {3F)
6FDAIPPDA/PA n-113 (6F)
PMR-II-50 n-9
VCAP-75 n-14
Fig. 7.25. Structures of the 3F and 6F thermoplastics and the PMR-II-50 and VCAP-75uncrosslinked thermosets. (Reproduced from Ref. [36] with permission. Copyright (1999)
J. Wiley & Sons.)
163
Temperature,'C
Fig. 7.26. TGA curves for the 3F and 6F polyimides. (Reproduced from Ref. [36] withpermission. Copyright (1999) J. Wiley & Sons.)
Air __ Nitroaen0.8
Eo 0.6o
8 0.4Ma
o 0.2'
0
U.
0.6
0.4
0.2
0
350 450 550 650 750 350 450 550 650 750
Temperature, C Temperature, °C
F 3 F -6F PMR-11-50 - VCAP-75
Fig. 7.27. Evolution profiles of carbon dioxide in air and nitrogen. (Reproduced from Ref.[36] with permission. Copyright (1999) J. Wiley & Sons.)
identification and relative quantification of evolved decompositionproducts (CO,, CO, ArNCO, and CHF3 ) of the four polyimides degradedin air or nitrogen. Isothermal TGA-FTIR (IGA-FTIR) was also done inair to determine the relative rate of product evolution at a constanttemperature. Figures 7.26 and 7.27 show the thermograms and theevolution of carbon dioxide in air and nitrogen. Similar profiles wereobtained for all the evolved gases. As a result, the probable initial
164
I
i----L-,
0 X . 3
I 1 1Carbon Monoxide Trifluoromethane and a = Carbon Monoxideand Carbon Dioxide some Hydrogen Fluoride b + c = p Phenylene Diisocyanate
b + d = Phenyl Isocyanate
Fig. 7.28. Probable initial decomposition events and identified evolved degradationproducts. (Reproduced from Ref. [36] with permission. Copyright (1999) J. Wiley & Sons.)
decomposition events and identified evolved degradation products aredepicted in Figure 7.28.
Other authors were able to exactly assign the volatile componentsmeasured by IR spectroscopy to the decomposition stages detected inTGA. The thermal decomposition of elastomer sealing rings and of thethermal behaviour of vinyl flooring material were the two systemsstudied [37]. In another study, the thermal degradation of styrene-sulphonic acid blends and copolymers of styrene was studied [38]. Theblends had enhanced thermal stability relative to virgin polystyrenebut there was no enhancement in thermal stability for the copolymers.Therefore, it was concluded that it was necessary to have adjacentsulphonic acid groups to permit the formation of a graphite-like char-acter which can provide thermal protection to the polymer. It wastherefore necessary to have a good match in degradation temperaturesof the two components if one is to have significantly enhanced thermalstability.
The utility of TGA/FTIR was demonstrated in an investigation ofseveral polymeric systems including graft co-polymers of acrylonitrile-butadiene-styrene (ABS), poly(methylmethacrylate), and styrene-buta-
165
*ffe_ _
diene block copolymer blends [39]. One of the findings of this work wasthat additives may interact with poly(methylmethacrylate) by co-ordination to the carbonyl oxygen to a Lewis acid and the subsequenttransfer of an electron from the polymer chain to the metal atom or bythe formation of a radical which can trap the degrading radicals beforethey can undergo further degradation. When an inorganic char-formeris grafted onto a polymer, there is a good correlation between TGAbehaviour in an inert atmosphere and thermal stability in air. How-ever, the same cannot be said when the char is largely carbonific.
The effect of two novel epoxypropanecarbazole-based dyes on thethermal stability of PVC has also been reported [40]. TGA/FTIR wasused to study the effect of the metal on the thermal decomposition ofmetal clusters doped poly(acrylic acid) (PAA) and poly(methacrylicacid) (PMAA) which were prepared by radical decomposition. Thecolloids were obtained by condensation of the metals and acrylic acid at77 K using several metals such as Au, Ag, Pd, Cu, Bi, Sn, Sb, Ge, Ga, In,Cd and Zn. The presence of the metal clusters avoided the formation oflarger molecular weight polymers. A complete study of the thermaldegradation between 50 and 550°C was performed, and the decompo-sition temperatures were obtained from the second derivatives. InPAA, the highest decomposition temperature corresponds to the un-doped polymer, 546°C, but in PMMA, the Pd-doped polymer increasesthe decomposition temperature from 467 to 469°C for the lowest molec-ular weight. Infrared spectra of the evolved gases indicated that thedecomposition products are mainly MAA and alkenes [41].
A study on thermal degradation of polymeric sulphonic and phos-phonic acids and their sodium salts was reported in which theidentification of the volatile products and decomposition residues waskey to proposing a mechanism for the degradation [42]. TGA/FTIRstudies used to confirm the thermal degradation mechanism for co-polymers based on long-chained diol dimethacrylates and BIS-GMA/TEGDMA 2,2-bis [4-(2-hydroxy-3-methylacrylolyl-oxypropoxy)phenyl]propane/triethyleneglycol dimethacrylatel [43]. Thermal degradationstudies of polyacrylonitrile [441, poly(styrene-g-acrylonitrile) [45],poly(N-isopropylacrylamide) [46] and poly(methyl methacrylate)blended with propyl ester phosphazene [47] were also reported. In thecase ofpolyacrylonitrile, cyclization of the polymer proceeds before anymass is lost and the driving force for cyclization is the formation ofaromatic rings. The extent of cyclization was controlled by the presenceof head-to-head linkages within the polymer. Ammonia and hydrogen
166
cyanide are the first gases lost and schemes are proposed to account fortheir formation. Oligomers are lost from the uncyclized portion of thepolymer lying between the cyclized portions and the amount of non-volatile fraction is largely determined by the extent of oligomer loss. Adetailed mechanism is presented to account for the observed formationof the volatile products and the structural changes that occur in theresidue.
TGA-FTIR was also used to identify possible mechanisms ofthermal degradation of Nafion H and Nafion/PMMA blends [48]. Astudy of the phase transition and thermal stability of Xydar and Zeniteliquid crystalline polymers was reported [49]. The mechanism of thethermal decomposition of liquid crystal polymer Vectra B950, a randomliquid crystalline copolymer of ester amide, in both air and in nitrogenwas also studied by the same group [50]. A single-stage decompositionprocess was found when heating in nitrogen atmosphere and thedecomposition is due to the ester-linkage rupture. However, a double-stage decomposition process was found when heating in air, and thatthe decompositions are mainly due to the ester linkage rupture for thefirst decomposition step and the oxidative reaction for the seconddecomposition step. Annealing slightly changes the decompositioncomponents occurring in the early stage of thermal degradation.
TGA/FTIR has also found application in studies of flammability andfire-retarding properties of polymeric materials. The effect of variousflame retardants on a PP/PE copolymer was studied using TGA/FTIR[51]. Specifically, a PP/PE copolymer was successively flame retardedusing Mg(OH)2 , then using brominated trimethylphenyl indaneassociated with Sb203 (Br/Sb), and finally using blends of equal weightsof this last combination with Mg(OH)2 or talc-containing, non-hydratedfillers. The decompositions of the pure and the additive-containingcopolymer were studied by TGA/FTIR. It was found that a goodcorrelation existed between the maxima of Gram-Schmidt curves andthe derivatives of TGA curves. The coupling of techniques shows thatthe incorporation of the Br/Sb flame retardant limits strong exothermicphenomena due to sample ignition. In the case of Mg(OH)2 associatedwith Br/Sb, the decomposition of the hydrated mineral occurs at a lowertemperature than the reaction between brominated trimethylphenylindane and Sb2 O3. This delays the action of Br/Sb flame retardanttowards higher temperatures improving the thermal stability of thepolymer. A good agreement is also found between TGA-FTIR con-clusions and fire resistance tests carried out on standardized samples.
167
0
-20e
.t -60.J
-80
-100
0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 5500 6000 6500
Time (s)
Fig. 7.29. TGA curves of PP/PE copolymer containing flame retardants. (Reproducedfrom Ref. [51] with permission. Copyright (2000) Elsevier.)
3 T25-
2
1.5
W 1
o 0.50
-0.52000 2500 30010 3500 4000 4500 5000 5500 6000 6500 7000
Time (s)
- ComnbuStes -COZ -- H20
Fig. 7.30. Gram-Schmidt curves of PP/PE with Mg(OH) 2 evolving gases in air. (Repro-duced from Ref. [51] with permission. Copyright (2000) Elsevier.)
Figure 7.29 shows the TGA curves of PP/PE copolymer containingflame retardants and Figure 7.30 shows the Gram-Schmidt curves ofPP/PE with Mg(OH)2 evolving gases in air.
The flammability of a series of polyurethanes based on 2,4-toluenediisocyanate (TDI), with different amounts of 3-chloro-1,2-propanediol(CPDO), has been reported [52]. Flammability of the polymers wasdetermined using the oxygen index (OI) method. The influence ofCPDO on the thermal decomposition parameters (e.g., initial decompo-sition temperature (IDT), char residue at 500°C, and DTG maximum
168
Fig. 7.31. FT-IR spectra of a characteristic sample after 3.0 min. (Reproduced from Ref.[52] with permission. Copyright (1998) J. Wiley & Sons.)
99.0
00.0
T 0.
%T 95.0
94.0
910
92.0
91.0
Fv-( -
00O 2 000 1000 7'0CW1
Fig. 7.32. FT-IR spectra of a characteristic sample after 5.3 min. (Reproduced from Ref.[52] with permission. Copyright (1998) J. Wiley & Sons.)
temperature) and on the (OI) values were all discussed. Figures 7.31and 7.32 show the FT-IR spectra of a characteristic sample after 3.0min and after 5.3 min, respectively. Figure 7.33 shows the correlationbetween the OI and IDT and T30%. Some correlations between the
169
io., ..__fv,~
drA_
I
- A _
Il-ijr~-
200
IDT[9C1106 -
192 -
188 -
184 -
I I I I I -
-L
T,[°C
- 275
- 270
- 265
- 260
-266
- 250
20 21 22 23 24 26 2601
Fig. 7.33. Correlation between the OI and IDT and T30 %. (Reproduced from Ref. [52] withpermission. Copyright (1998) J. Wiley & Sons.)
thermogravimetric data and OI values were found, thus making itpossible to apply the TGA method for certain flammability predictionsof modified polyurethanes.
TGA/FTIR has been applied to the study of the solid-phase transi-tions of the anti-tumour agent, AG337 [53]. Loss of water was observedin the range of 20-150° and HC1 was lost in the range of 200-250 °. Thishyphenated technique has also been applied to studies of supportedsolid acid catalysts. The deactivation and regeneration of sulphatedzirconia was probed in an effort to improve catalytic properties [54].The deactivation of sulphated zirconia catalysts in the isomerization ofn-butane was also studied [55]. Nafion and Nafion/(silicon oxide)-basednanocomposites were investigated [56]. The decomposition processes ofCoMgAl-hydrotalcite (CoaMgbAl(OH)c(TA)dnH 2 O) clays intercalatedwith terephthalate anions ([C6H4(COO)2]2 - or TA2-) was studied by avariety of methods including TGA/FTIR [57]. It was found that the as-prepared samples undergo different decomposition pathways whenthey were heated in air and in nitrogen atmospheres respectively;particularly the collapse of the layered structure, i.e., dehydroxylationand the thermal decomposition of TA2 - were overlapped within a
170
.o
i_. ·
---
ran
U)
r--1
r
0 200 400 600Temperature (C)
800
Fig. 7.34. Integrated absorbance of the evolved gases with air as the carrier gas.(Reproduced from Ref. [53] with permission. Copyright (2000) American Chemical
Society.)
narrow temperature range (20-30°C) in air, showing a vigorouslyexothermic effect. However, the two thermal processes were distinctlyseparated in N2. Each thermal process lasted over a rather widetemperature range (100-200°C). Figure 7.34 shows the integratedabsorbance of the evolved gases with air as the carrier gas, and Fig.7.35 shows the integrated absorbance of the evolved gases with N2 asthe carrier gas.
Carbon nanoparticles and short tubules were also produced in thesolid state from the intercalated TA2 - anions during the decompositionof the hydrotalcite-like compounds in N2. These carbon nanomaterialsare multiwalled and close-ended with a diameter of 10-35 nm and alength of 20-200 nm. Pathways of the nanocarbon formation as well as
171
(a)
_-- C.Hyv
H20
C02
(b)
G.Hy
B 3
H20
C02
Zjj
CraC
0 300 600 900
Fig. 7.35. Integrated absorbance of the evolved gases with N2 as the carrier gas.(Reproduced from Ref. [53] with permission. Copyright (2000) American Chemical
Society.)
catalytic function of cobalt oxides generated from the above thermalprocesses were further investigated with various instrumentalmethods. Finally, the characterization of poly(ureidosilazanes) andtheir pyrolytic conversion to ceramic materials was also reported [58].
7.6 LC/FT-IR
The combination of liquid chromatography with infrared spectroscopyhas found extensive use primarily in polymer characterization. Theadvantage of combining liquid chromatography with FTIR spectro-metry is the specific detection or identification of materials.
172
(a)
CxHy
H20A
C02
(b) la C
CxHy
H20
C02II
GiTlmMk (IR tspwanQ
Twit
.rnMnuu "In rnevyv)
Opt ad c5e on dlac
Fig. 7.36. LC/FT-IR technique.
There are two main approaches: one is to use a flow cell arrange-ment and continuously record the infrared spectra; the other is toeliminate the solvent by deposition of the eluent on a substrate andevaporating the solvent. A recent review [59] focused mainly on theflow cell method. This review states that flow-cell LC-FTIR methodshave rather poor detection limits but can be useful for the specific andquantitative detection of major constituents of mixtures. On the otherhand, solvent-elimination techniques provide much better sensitivityand enhanced spectral quality which is essential when unambiguousidentification of low-level constituents is required. The LC-transform®(Lab Connections) is one of the most common methods for solventelimination [60]. It consists of two modules, a sample collection moduleand a scanning module accessory. The fist module collects the eluentfrom the column as a thin trail around the perimeter of the samplecollection disk. The solvent is removed by using a nozzle with a heatednebulizer. At the same time, the sample is deposited on the collectiondisk [61]. The collection disk is made out of germanium and is placed ona rotating stage inside the scanning module. This module consists of ascanning controller and of the necessary optics that couple the infraredlight back to the FT-IR spectrometer. Figure 7.36 shows such aninstrument.
173
The first demonstration of identifiable infrared spectra obtainedfrom buffered (volatile and nonvolatile buffers) mobile phases using themonodisperse aerosol generator interface for combining liquidchromatography with FT-IIR (MAGIC-LC/FT-IR) spectrometry wasdescribed in 1990 [62]. Ammonium acetate, a volatile buffer, was usedto buffer an 80:20 acetonitrile:water mobile phase to pH 5.0. Caffeinewas deposited from this buffered mobile phase, and the spectrum wasused as a reference to compare with caffeine spectra obtained fromnonvolatile buffered mobile phases. The two nonvolatile buffers usedwere potassium hydrogen phthalate (KHP) and potassium dihydrogenphosphate (KH2PO4 ). The KH2PO4 was used to buffer an aceto-nitrile:water mobile phase and a methanol:water mobile phase, where-as the KHP buffer was used only in a methanol:water mobile phase.Samples of caffeine were deposited from each of the above buffersystems along with the nonvolatile buffer. IR spectra of caffeine wereobtained by spectral subtraction of previously stored buffer spectrafrom the caffeine:buffer spectra. The resulting spectra were identical toa caffeine reference spectrum.
Various examples in the literature show the power of the combina-tion of liquid chromatography with infrared spectroscopy. Useful solu-tions to problems of determining polymer composition as a function ofmolecular weight for a range of polymers have been illustrated by thetechnique. One study focused on the use of a solvent-evaporativeinterface in conjunction with a GPC-viscometer chromatograph and aFTIR spectrometer in order to provide functional-group information asa function of molecular weight [63]. The GPC-viscometer/solvent evap-orative interface/FTIR system was applied to a variety of polymer andcoatings systems as a tool for product problem solving and elucidationwas presented. In addition, examples of the use of the solvent evapora-tive interface to elucidate compositional heterogeneity of copolymersare illustrated. The potential use of the solvent evaporative interface inGPC/LC cross fractionation studies for very fine elucidation of polymercompositional heterogeneity was also explored.
This hyphenated technique has also been used in the character-ization of asphalt binders based on chemical and physical properties[64]. The chemical composition and physical properties of unmodifiedand polymer modified asphalts were studied using a variety of tech-niques including GPC \ FT-IR. Two viscosity-based asphalt grades andtwo polymers (styrene-butadiene-styrene and styrene-ethylene-butylene-styrene) that were used to modify asphalt were studied. The
174
combination of GPC and FTIR was an excellent approach for finger-printing and quality control of polymers and asphalt binders. Inaddition, the theological properties of asphalt binders were goodcharacteristics for determining the optimum polymer concentrationsfor effective modification.
A thermospray was modified and used to couple HPLC to FTIRspectrometry, which was applicable to both normal- and reversed-phase HPLC [65]. Column effluents from the HPLC system weredesolvated by thermospray and solutes were deposited as individualspots on a moving stainless steel belt substrate, which continuouslytransferred the analytes into the diffuse reflectance (DRIFT) accessoryof the FTIR, enabling identification of deposited solutes by measure-ment of the IR spectrum. The thermospray temperature and thermo-spray height were shown to influence the deposition of solutes. By useof a heated external nitrogen gas flow, desolvation of the reversed-phase HPLC eluents was improved.
A coupled GPC/FT-IR system was also developed to measure shortchain branching as a function of molecular weight in polyethylenes andethylene copolymers in relatively short time scales. Careful selection ofthe IR detector, use of a low volume flow-through cell with a largeoptical path length and selecting GPC conditions to maximize thepolymer concentration in the cell enabled the characterization of poly-mers with very low average comonomer concentrations. A method forcalibration of the infrared detector was presented and results for aseries of polyethylenes of known average co-monomer content, VLDPE,LLDPE, MDPE and broad molecular weight polyethylenes were alsopresented to illustrate the capability of the system. The quality of thedata from the GPC/FTIR can be assessed with results on the samepolymers obtained using other fractionation techniques. It was foundthat reliable results could be obtained above MW of approximately10,000. However, at low molecular weights where chain end correctionsbecome large for infrared measurements, values were confirmed withmeasurements obtained using NMR spectroscopy.
In another study, where this time solvent elimination did not takeplace, infrared spectroscopy was proposed as a molecular specificdetection system for HPLC in an aqueous phase, focusing on thechromatographic separation of sugars in beverages. The separationwas achieved with an isocratic HPLC setup using an ion exchangecolumn with Ca 2 ' serving as the counterion. The FT-IR detection of theC-O bands in the mid-IR between 1000 and 1200 cm-1 was performed
175
re
0.03
8 0.02C
0.01
1400
LUCOSE
OSE
1300 1200 1100 1000 900
wavenumber cm"
Fig. 7.37. Three-dimensional plot of a standard solution containing 10 mg/ml each ofsucrose, glucose and fructose. (Reproduced from Ref. [65] with permission. Copyright
(1997) American Chemical Society.)
0.006
0.005
0.004
; 0.003
f 0.002
0
1400 1300 1200 1100 1000 900
wavenumrnber cm'
Fig. 7.38. FT-IR spectra extracted from the peak maxima of HPLC peaks. (Reproducedfrom Ref. [65] with permission. Copyright (1997) American Chemical Society.)
in real time with a 25 pm flow cell without elimination of the solvent.Characteristic FT-IR spectra of the common sugars sucrose, glucose,and fructose in concentrations of 1 mg/ml were recorded during theseparation process. The calibration of these compounds in the 5-100mg/ml range resulted in a linear correlation with a standard deviationof 0.11, 0.07, and 0.11 mg/ml for sucrose, glucose, and fructose, respect-
176
0
0 5 10 15retention time Imin
20 25 30
Fig. 7.39. HPLC-FTIR traces of a taurine-containing soft drink. (Reproduced from Ref.[65] with permission. Copyright (1997) American Chemical Society.)
0.010
0.008
0.006
0.004
0.002
0
-0.0011400 1300 1200 1100 1000 900
wavenumber /cmn
Fig. 7.40. Taurine (A) and ethanol (B) spectra extracted from the HPLC-FTIR run of ataurine containing soft drink. (Reproduced from Ref. [65] with permission. Copyright
(1997) American Chemical Society.)
ively. Figure 7.37 shows a three dimensional plot of a standard solutioncontaining 10 mg/ml each of sucrose, glucose and fructose, whereas Fig.7.38 shows the FT-IR spectra extracted from the peak maxima of HPLCpeaks.
The method was, furthermore, applied to the analysis of nine softdrinks and fruit juices containing between 6 and 97 mg/ml of eachcarbohydrate. The accuracy of the method was confirmed by standard
177
<lale
Analysis time
Fig. 7.41. Average baseline-corrected chromatogram. (Reproduced from Ref. [66] withpermission. Copyright (1997) American Chemical Society.)
ion exchange HPLC with refractive index detection. The averagedeviation from the reference method was in the range of 0.5-0.9 mg/ml.Furthermore, the method was able to identify and quantify minorcomponents in beverages, such as taurine (4 mg/ml) and ethanol (0.4mg/ml). Figure 7.39 shows the HPLC-FTIR traces of a taurine-con-taining soft drink whereas Figure 7.40 the taurine and ethanol spectraextracted from the HPLC-FTIR run of a taurine containing soft drink.
For many situations, chemometric methods are used to enhance thedata analysis. In one such study, the analysis of a reaction product byHPLC coupled with Fourier transform spectroscopy LC/FTIR origin-ates a series of overlapping peaks [66]. The applicability of theorthogonal projection approach, the fixed size window evolving factoranalysis approach, and the evolving factor analysis approach for theresolution of those overlapping peaks into individual chromatogramsand infrared spectra is discussed. The reaction product under studywas the result of the reaction of a straight-chain alkyl alcohol withcitric anhydride. The results are evaluated by identifying the differentcompounds present using the spectral characteristics of the resolvedpure compound spectra and the chemistry of the system. Figure 7.41shows the average baseline-corrected chromatogram and Fig. 7.42 the
178
Wavenumber (cm-i)
Fig. 7.42. Pure component spectra of one of the clusters. (Reproduced from Ref. [66] withpermission. Copyright (1997) American Chemical Society.)
pure component spectra of one of the clusters. Analysis of the infraredspectra suggested that the main compound of cluster 3 is an ammo-nium salt of dialkyl citrate ester.
179
LC-FTIR was also used to assist in the complete structure eluci-dation of a globular protein, -lactoglobulin [67]. Other efforts in thisarea have focused on improvements in instrumentation. For example, aheated gas flow modified thermospray was developed which facilitatesthe delivery of evaporated eluents for IR analysis using diffusereflectance [68]. Another report discussed the use of a temperatureprogrammed packed capillary liquid chromatograph coupled to an off-line FTIR spectrometer for the analysis of the antioxidant, Irgafos P-EPQ [69].
Liquid chromatography (LC) was coupled semi-online to FTIRspectrometry using a spray-jet assembly interface to eliminate the LCeluent prior to IR detection [70]. The usefulness of the LC-FTIR systemin the identification of closely related compounds in complex mixtureswas demonstrated by the analysis of a chlorinated pyrene samplewhich contains a number of chloropyrene isomers and congeners.Characteristic FTIR transmission spectra of all constituents wererecorded. Since most of these compounds were not analyzed by IRbefore, spectral assignment was mainly based on the empiricalHansen-Berg rules for substituted pyrenes. The identification limitsfor the chloropyrenes typically were 5-10 ng.
7.7 GC/FTIR
This is the most commonly used technique in coupling a chroma-tographic analysis to an FT-IR detection system. The technicaldevelopment that made GC/FTIR so widespread was the introductionof the gold-coated glass 'lightpipe' [71,72]. This design is based on asmall-volume gas cell which is constructed to match the elutionvolumes of the GC peaks. In addition, the fact that the carrier gasesused as a mobile phase do not absorb in the infrared region has helpedthe application of the technique. The detection limits achievable withthis technique are at the nanogram level, thanks to improvements incapillary column technology.
GC/FTIR methods were used to establish identification limits forvolatile organics in blood [73]. These methods were based on the purge-and-trap extraction technique. FTIR identification limits weremeasured for a number of volatile organic compounds. The FTIRidentification limits, ranging from 0.01 mg/l for ethyl acetate, methyl-ethyl ketone, and sevoflurane to 24 mg/I for methanol, generallyallowed the detection of volatile-substance exposure at a lower level
180
than is acutely toxic. Quantitative calibration data were presented forselected substances, based on the FID response, which shows that themethod is also amenable to quantitative analysis. The throughput ofthe method without additional automation is five samples per day, thepurge-and-trap stage being the limiting factor.
In another study, a GC/FTIR/MS technique was utilized for thedetermination of unusual amidine products obtained by the sublima-tion of amino acids in the presence of silica catalyst [74]. Furthermore,the identification of individual naphthenes in a mixed hydrocarbonsample was made using GC/FTIR with neural network and regressionanalysis [75]. Specifically, the goal was to differentiate between cyclo-pentane- and cyclohexane-containing compounds in mixed aliphatichydrocarbon samples. A set of single-ring model compounds was used,with acyclic aliphatic hydrocarbons used as counter-examples. The GC-FTIR method was envisioned as a means of determining individualnaphthenes in a sample.
Mathematical techniques have also been employed to improve GC/FTIR spectra. In one such study, it was found the commonly used co-addition of spectra to a relative intensity level of 40% of the GC peakdoes not lead to the optimal improvement in S/N of the resultingcomposite spectrum for either simulated Gaussian-shaped or experi-mentally obtained asymmetric GC bands. The optimal intensity levelfor co-addition is a function of the shape of the GC band and the ratio ofthe number of background to sample scans used in generating theindividual IR spectra. The authors also introduced the use of classicalleast-squares (CLS) techniques as a superior method to improve the S/N of the composite analyte spectrum. Using CLS methods, spectraincluded in generating the composite spectrum can be a small fractionof the maximum intensity in the GC peak while still resulting in S/Nimprovements. The theoretical S/N of the composite spectrum usingCLS methods is always as good as or better than that achieved with theco-addition method. The improvements achieved in S/N when CLSmethods are used can be more than a factor of 2 greater than results forthe traditional co-addition method for the cases considered. Also,increasing the number of background to sample scans was a veryconvenient method to improve the S/N of the composite spectrumobtained by either method. The results for GC/FTIR are also generallyapplicable to LC/FTIR, SFC/FTIR, and TGA/FTIR for bands thatcontain a single analyte [76]. In addition, a set of the semi-empiricalmethods was tested to find the best auxiliary tool for the GC/FTIR
181
spectroscopy-mass spectrometry identification of cyclic amide-typecompounds [77].
Finally, the pyrolysis of aquatic humic substances was studied bypyrolysis GC/FTIR [78]. The humic substances studied gave similarpyrolysis products, but in varying proportions. Many of the pyrolysisproducts (e.g., methanol, acetone, alkylbenzenes, cyclopentane,aliphatic and aromatic organic acids, acetamide, pyrrole and phenols)were identified by their FTIR spectra using a digital library forautomatic comparison. Some of the compounds were related to ligninfragments, which form a large part of the humic substances investi-gated. Other products gave hints as to the involvement of tetrapyrroles,fatty acids, furanoses, and amino compounds in the structure of humicmacromolecules.
7.8 SFC/FTIR
The use of supercritical fluid chromatography (SFC) is growing veryrapidly and is a very active area of research nowadays. A supercriticalfluid is a material that is held above its critical temperature andpressure. These fluids show a behaviour between a liquid and a gas andthe interest in them comes mainly from environmental reasons. Theiruse resembles the use of organic solvents in extraction methods, there-fore one can imaging the advantages of using a typical supercriticalfluid such as CO2 instead of organic solvents.
Applications of supercritical fluids range from extractions andchromatography to solvents for reaction chemistry. They are also usedin the preparation of new materials. A resent review covered manyaspects of the field in detail [79]. Spectroscopic monitoring is importantin all of the above cases and vibrational spectroscopy is particularlyuseful in this context because the vibrational spectrum of a givenmolecule is usually quite sensitive to the environment of that molecule.Thus, vibrational spectra are excellent probes of conditions within thefluid. The authors showed examples that included the use of super-critical Xe as a spectroscopically transparent solvent for chemistry andfor supercritical fluid chromatography with FTIR detection of analytesas well as the use of supercritical CO2 .
In another study, packed-column supercritical fluid chromato-graphy with a mobile-phase gradient of CO2 and methanol wasperformed on a mixture of 8 sulphonamides [80]. The analytes weredetected and identified with FT-IR. A fixed-integral restrictor afforded
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the decompression zone between the column and germanium diskwhere the analytes were deposited.
The comparison of direct-deposition supercritical fluid and gaschromatography/Fourier transform infrared spectra to condensed-phase library spectra also took place in an attempt to bring attention topotential pitfalls [81]. In particular, comparisons of spectra from direct-deposition (DD) capillary gas chromatography (GC) and supercriticalfluid chromatography (SFC)/FTIR measurements of two quinones withC2 symmetry axes and several barbiturates to spectra from condensed-phase libraries of the corresponding compounds were reported. Thebest spectral search results were obtained when the eluites weredeposited on an amorphous substrate, such as ZnSe. A small number ofpolar, H-bonding compounds align with each other or with a crystallinesubstrate. Different crystalline forms of some polymorphic analytescan also yield ambiguous identifications. These effects produce enoughdifferences in the DD GC/FTIR and SFC/FTIR spectra to causeoccasional incorrect identifications when the spectra are searchedagainst KBr-disk library spectra.
Polydimethylsiloxanes modified by the introduction of ethyleneoxide units were characterized using a variety of SFC coupledtechniques including SFC/FTIR [82]. The aim of this work was to formsufficiently water soluble siloxane compounds. In another studyessential oil constituents of hops (Humulus lupulus) were characterizedusing SFC/FTIR techniques. Infrared spectra of these constituentswere taken as films deposited on AgCl disks and compared with thoseobtained after chromatographic separation in the IR flow-cell withsupercritical carbon dioxide. Spectra from AgCl disks were comparableto those in supercritical CO,, but in supercritical CO2 most of the bandsappeared approx. 8-10 cm-l to higher wavenumbers. Open-tubularSFC-FTIR analysis of the essential oil of four different hop varietieswas performed. The SFC-FTIR chromatograms showed differences inthe location and relative intensity of the peaks depending on thevariety, which was further confirmed by the FTIR spectra.
Also, a supercritical fluid extraction method for the analysis ofnonionic surfactants in a washing powder is presented. By varying theextraction conditions, it is possible to fractionate the extractedmaterials according to their polarity. The subsequent analysis andidentification of the nonionic surfactants by SFC/FTIR or massspectrometry detection did not require any additional samplepreparation. Most nonionic surfactants were extracted by SFE without
183
CO,
integral restricto
gasd)
eratureor
germanium disk
Fig. 7.43. Configuration of the nozzle assembly and the integral restrictor. (Reproducedfrom Ref. [85] with permission. Copyright (1997) Elsevier.)
using a modifier to enhance the polarity of the supercritical CO2 . Othersubstances can then be extracted using supercritical CO2 with 5%MeOH as modifier [83].
Furthermore, SFC/FTIR was used to simultaneously detectaromatic and aliphatic nonvolatile compounds of microwave susceptorpackaging [84]. Microwave susceptor packaging is designed to brownand crisp food in a microwave oven. During microwave cooking, thepackage can reach temperatures above 260°C. Because of these hightemperatures and the multilayer construction of the packages, manytypes of chemicals can potentially migrate into the food. SFC/FTIRspectroscopy in series with flame-ionization detection provided aunique solution to the simultaneous detection of the above compounds.The authors demonstrated the utility of SFC for determining thesepotential migrants in solvent extraction of several microwave sus-ceptor packaging materials. The extraction of one package studiedcontained 2-(2-butoxyethoxy)ethanol and several aliphatic chemicalswhose FTIR and mass spectra are characteristic of aliphatic ketones.
The LC-Transform, routinely used for LC/FTIR analysis, wasshown to perform very well for SFC/FTIR separation of Irganox 1076[85]. In particular, the separation of Irganox 1076 with 5% methanolmodified CO2 was demonstrated. High quality spectral data were
184
I4.S
IR spectrum Jf lrganox 1076
4000 3000 2000 1000Wavenumters (cm-1)
Fig. 7.44. FTIR spectrum of Irganox 1076 collected using the configuration shown in Fig.7.43. (Reproduced from Ref. [85] with permission. Copyright (1997) Elsevier.)
obtained throughout the 4000-700 cm-l range with no interferencefrom methanol. The only modification to the commercially availableinterface for SFC/FTIR was the insertion of a fixed integral restrictorinto the spray nozzle. Figure 7.43 shows the configuration of the nozzleassembly and the integral restrictor. The modified CO2 mobile phase isevaporated during the spray process, and the resulting chromatogramis deposited as a continuous track on an IR transparent (e.g., usuallygermanium) flat surface (e.g., the sample collection disk). This trackcan then be scanned in a spectrometer to obtain spectra of the discretesample components. Figure 7.44 depicts the FTIR spectrum of Irganox1076 collected via this procedure.
A direct deposition system for SFC/FTIR analysis of environmentalanalytes was also evaluated [86]. A direct-deposition FTIR system wasevaluated for applicability to gas chromatography and supercriticalfluid chromatography of environmental analytes. A 100-pjm internaldiameter fused-silica transfer line was used for GC, and a 50-pmtransfer line with an integral restrictor was used for SFC. Minimumidentifiable quantities for GC/FTIR ranged from 0.5 to 2.0 ng. Some ofthis sensitivity improvement can probably be attributed to the smallerinternal diameter GC column used in this work and the ability toprogram the direct-deposition sample plate, thereby compensating forchanges in analyte elution volume across the GC temperature ramp.Figure 7.45 shows the GC/FTIR spectra of DDT, dioctyl phthalate andfluoranthene. In addition, excellent SFC/FTIR chromatograms wasobtained for poly(ethylene glycols) of average molecular weights of 400,600, 1000, and 1500 respectively. Figure 7.46 shows the SCF/FTIRspectra of poly (ethylene glycol) at two different times. The decreasingratio of-OH to -CH stretching modes as the retention time increases is
185
-
0004-
0.002-
to)0.004
CUr_
toA 0.002
0.000
U.uu -
0.004-
0.000-
tc)
1I
3000 2600 2200 1600 1400 1000Wavenumber (cmrl)
Fig. 7.45. GC/FTIR spectra of DDT, dioctyl phthalate and fluoranthene. (Reproducedfrom Ref. [86] with permission. Copyright (1994) American Chemical Society.)
consistent with the increasing ration of recurring molecular chainresidue to terminal unit -OH.
Chemometric methods are also commonly used in SCF/FTIRspectroscopy [87]. In one such study principal component analysis wasapplied to the rapid discrimination of extractable compounds that areindigenous to papers and nonindigenous compounds based on their
186
l -
"I\
0.12
(a)
0.00w0z
r
0
0.20
0.00 -
(b)
A lIIII.__ / ~J ~nu LJ U
4000 3000 2000 1000t
WAVENUMBER (cm -')
Fig. 7.46. SCF/FTIR spectra of poly(ethylene glycol) at two different times. (Reproducedfrom Ref. [86] with permission. Copyright (1994) American Chemical Society.)
infrared signatures. This method was applied with online supercriticalfluid extraction and SCF/FTIR to yield a fully automated analysis ofcompounds that can be extracted from very complex matrixes.
Finally, the analysis of subnanogram quantities of analytes wasdemonstrated using 600 pg of caffeine [88]. The minimum identifiablequantity for caffeine (a strong IR absorber) obtained with this interfacewas 600 pg (injected), whereas the level of detection was at 1-10 ng forweaker absorbers. Spectra over the entire mid-infrared region ofcompounds separated with a mobile phase of carbon dioxide modifiedwith two percent methanol were recorded. The interface shows linearbehaviour over two orders of magnitude for both the area under astrong absorption band in the IR spectra vs. injected quantity and forthe area under a peak from the functional group chromatogram versusthe injected quantity.
187
.:
7.9 INFRARED MICROSPECTROSCOPY
7.9.1 FT-IR microscope and redundant aperturing
Infrared microspectroscopy is a technique where microscopic techniqueis used in combination with infrared spectroscopy. It has been revivedafter the introduction of modern FT-IR spectrophotometers andsensitive detectors such as mercury-cadmium-telluride (MCT) and hasbeen proved to be one of the powerful analytical tools both in analyticaland industrial applications [89,90]. Infrared microspectroscopyprovides the analytical chemist not only with the visual viewing of thematerial under the microscope but also with the chemical informationof the part of the material that is being viewed in the form of itsinfrared spectrum.
The instrumentation in infrared microspectroscopy is speciallydesigned to use with infrared radiation. Optics in an ordinary micro-scope do not transmit infrared radiation. To avoid this problem,reflecting type optics are used. Most of the infrared microscopes useCassegrain type reflecting objectives. These objectives can be usedeither as a condensing lens or as an objective lens.
liable aperture
granian Objective
Samnle
Condenser X i .
Variable aperture
Fig. 7.47. Sketch of an FT-IR microscope in transmission and reflectance mode.
188
5amnlD sujrf2ce
a)
b)
ndant Aperture
I I
Fig. 7.48. The redundant aperturing technique: (a) sample surface with two differentchemical compositions; (b) redundant aperture size that is suitable for the analysis of
these materials.
Modern FT-IR microscopes are made to perform the followingfunctions: (a) irradiation of a micro sample with infrared radiation; (b)collection of the radiation emerging from the sample; (c) imaging thecollected radiation on to a detector (usually mercury-cadmium-telluride detectors) that is connected to the microscope and FT-IRinstrument; and (d) allowing the user to select the precise area he/shewants to measure.
Figure 7.47 shows a general lay out of an FT-IR microscope intransmission and reflection mode. The microscope can also be used as avisible microscope. This function allows the user to select the area ofinterest for analysis. The visible and IR optical paths are made to becollinear and parfocal to ensure identical optical paths. This alsoensures the user, the area selected for FT-IR measurement and thearea actually measured are the same. As mentioned above, the FT-IRmicroscopes employ reflecting mirrors (Cassegrainian optics) for theoptical elements instead of lenses in the visible light microscopes. Theaperture placed before the cassegrainian objective gives a bettersample definition. In transmission mode, the infrared radiation istransmitted through the sample and condensed by a cassegrainian
189
condenser and imaged through another aperture. This aperture blockdiffracted light that is strayed from the adjacent sample area. Thistechnique is called redundant aperturing (Fig. 7.48).
Modern infrared microscopes give users the opportunity formeasuring infrared spectrum of a prescribed area of a sample either intransmittance mode or reflection mode. Furthermore, when thin layersof materials are present on completely reflecting bases, reflection-absorption techniques can be used to measure the spectrum. Here, thespecular reflection is minimum and the returning radiation will beattenuated by penetrating the sample twice. The spectrum can be usedin the same way as a transmittance or absorbance spectrum. There areaccessories available that can be connected to infrared microscopes tomeasure infrared spectra using the attenuated total internalreflectance technique. The samples are measured using a suitablereference. For example, when samples are deposited on reflectingbases, the base itself can be used as the background.
Several applications involving infrared microspectroscopy arediscussed in Chapters 8 and 9.
REFERENCES
1. P.R. Griffiths and J.A. deHaseth, Fourier Transform InfraredSpectroscopy. Wiley, Chichester, 1986.
2. H.A. Willis, J.H. van der Maas and R.G.J. Miller (Eds.), LaboratoryMethods in Vibrational Spectroscopy, 3rd edn. Wiley, Chichester, 1987.
3. N.J. Harrick, Internal Reflection Spectroscopy. Interscience, New York,1987.
4. F.M. Mirabella, Jr. (Ed.), Internal Reflection Spectroscopy: Theory andApplication. Marcel Dekker, New York, 1993.
5. M.W. Urban, Attenuated Total Reflectance Spectroscopy of Polymers;Theory and Practice. American Chemical Society, Washington, 1996.
6. M. Claybourn, Infrared Reflectance Spectroscopy of Polymers. GlobalPress, 1998.
7. Y. Ozaki, F. Kaneuchi, T. Iwamoto, M. Yoshiura and Iriyama, Appl.Spectrosc., 43 (1989) 138.
8. M. Tasumi, S. Ochiai, H. Kato, Y. Furukawa and K. Masutani, Principleand Practice of FT/IR Spectroscopy, 2nd edn. Tokyo Kagaku Dojin, Tokyo,1994, p. 105 (in Japanese).
9. D.W. Vidrine, Mid-Infrared Spectroscopy in Chemical Process Analysis,in: J.M. Chalmerr (Ed.), Spectroscopy in Press Analysis. SheffieldAcademic Press, Sheffield, 2000, p.9 6.
190
10. N. Mitsui, H. Higashiyama and M. Watari, Keiso, 38(12) (1995) 46 (inJapanese).
11. W.G. Golden, Fourier Transform Infrared Spectroscopy, J.R. Ferraro andL.J. Basile (Eds.), Vol. 4. Academic Press, New York, 1987, p. 315.
12. M.W. Urban, Vibrational Spectroscopy of Molecules and Macromoleculeson Surfaces. Wiley Interscience, New York, 1993.
13. M.P. Fuller and P.R. Griffiths, Anal. Chem., 50 (1978) 1906.14. I.M. Hamadeh, S.A. Yeboah, K.A. Trumbull and P.R. Griffiths, Appl.
Spectrosc., 38 (1984) 486.15. R.A. Velapoldi, J.E. Tvedt and A.A. Christy, Rev. Sci. Instrum., 58 (1987)
1126.16. S.A. Yeboah, S.H. Wang and P.R. Griffiths, Appl. Spectrosc., 38 (1984)
259.17. A.A. Christy, J.E. Tvedt and R.A. Velapoldi, Rev. Sci. Instrum., 59 (1988) 3.18. A.A. Christy, O.M. Kvalheim and R.A. Velapoldi, Vib. Spectrosc., 9 (1995)
19.19. R.L. White and A. Nair, Appl. Spectrosc., 44 (1990) 69.20. C. Bremard, C. Depecker, H. Des Grousilliers and P. Legrand, Appl.
Spectrosc., 45 (1991) 1278.21. R.L. White and J. Ai, Appl. Spectrosc., 46 (1992) 93.22. A.A. Christy, E. Nodland, A.K. Burnham, O.M. Kvalheim and B. Dahl,
Appl. Spectrosc., 48 (1994), 5.23. A. Rosencwaig and A. Gersho, J. Appl. Phys., 47 (1976) 1.24. D.W. Vidrine, Appl. Spectrosc., 34 (3) (1980) 314.25. E.M. Monahan and A.W. Nolle, J. Appl. Phys., 48 (8) (1977) 3519.26. J.J. Freeman and R.M. Friedman, J. Phys. Chem., 84 (1980) 315.27. R.S. Davidson and D. King, Anal. Chem., 56 (1984) 1409.28. C.Q. Yang and W.G. Fateley, J. Mol. Struct., 146 (1986) 25.29. B.W. Cook, Spectroscopy (Eugene, Oreg.), 6(6) (1991) 22-26.30. K. Norton, A.J. Lange and P.R. Griffiths, J. High Resolut. Chromatogr.
14(4) (1991) 225-259.31. S. Materazzi, Appl. Spectrosc. Rev., 32(4) (1997) 385.32. Hong Yee Low and H. Ishida, J. Polym. Sci., Part B: Polym. Phys., 36(11)
(1998) 1935-1946.33. R.M. Paroli and A.H. Delgado, Can. Polym. Mater. Sci. Eng., 69 (1993)
139.34. J.D. Johnson, D.A. Compton, R.S. Cass and P.L. Canale, Thermochim.
Acta, 230 (1993) 293.35. Y. Tang, Y. Xie, W.-P. Pan and A. Riga, Thermochim. Acta, 357-358 (2000)
239-249.36. M.J. Turk, A.S. Ansari, W.B. Alston, G.S. Gahn, A.A. Frimer and D.A.
Scheiman, J. Polym. Sci., Part A: Polym. Chem., 37(21) (1999) 3943-3956.
191
37. F. Hoffmann, R. Riesen and J. Foreman, Am. Lab. (Shelton, Conn.), 32(1)(2000) 13-14, 16-17.
38. Q. Yao and C.A. Wilkie, Polym. Degrad. Stab., 66(3) (1999) 379-384.39. C.A. Wilkie, Polym. Degrad. Stab., 66(3) (1999) 301-306.40. K. Pielichowski, I. Hamerton, J. Pielichowski and P. Stanczyk, Eur.
Polym. J., 34(5/6) (1998) 653-657.41. G. Cardenas, C. Munoz and H. Carbacho, Eur. Polym. J., 36(6) (2000)
1091-1099.42. D.D. Jiang, Q. Yao, M.A. McKinney and C.A. Wilkie, Polym. Degrad.
Stab., 63(3) (1999) 423-434.43. K. Pielichowski, D. Bogdal, J. Pielichowski and A. Boron, Thermochim.
Acta, 307(2) (1997) 155-165.44. T.J. Xue, M.A. Mckinney and C.A. Wilkie, Polym. Degrad. Stab., 58(1-2)
(1997) 193-202.45. T.J. Xue and C.A. Wilkie, Polym. Degrad. Stab,. 56(1) (1997) 109-113.46. H.G. Schild, J. Polym. Sci., Part A: Polym. Chem., 34(11) (1996) 2259-
2262.47. B-L. Denq, Y-S. Hu, W-Y. Chiu, L-W. Chen and Y-S. Chiu, Degrad. Stab.,
57(3) (1997) 269-278.48. M.L. Mittleman, J.R. Thomsen and C.A. Wilkie, Polym. Mater. Sci. Eng.,
63 (1990) 957-961.49. T-S. Chung and X. Jin, Polym. Eng. Sci., 40(4) (2000) 841-856.50. T-S. Chung, M. Cheng, P.K. Pallathadka and S.H. Goh, Polym. Eng. Sci.,
39(5) (1999) 953-962.51. J.-P. Gibert, J.-M. Lopez Cuesta, A. Bergeret and A. Crespy, Polym.
Degrad. Stab., 67(3) (2000) 437-447.52. K. Pielichowski, J. Pielichowski and A. Prociak, Pol. J. Appl. Polym. Sci.,
67(8) (1998) 1465-1471.53. S. Rastogi, I. Zamansky, S. Roy, P. Tyle and R. Suryanarayanan, Pharm.
Dev. Technol., 4(4) (1999), 623-632.54. B. Li, R. Marcus and R.D. Gonzalez, Prepr. - Am. Chem. Soc., Div. Pet.
Chem., 44(4) (1999) 430-433.55. B. Li and R.D. Gonzalez, Appl. Catal., A, 165(1/2) (1997) 291-300.56. Q. Deng, C.A. Wilkie, R.B. Moore and K.A. Mauritz, Polymer, 39(24)
(1998) 5961-5972.57. Z.P. Xu and H.C. Zeng, J. Phys. Chem. B, 104(44) (2000) 10206-10214.58. D. Seyferth, C. Strohmann, N.R. Dando and A.J. Perrotta, Chem. Mater.,
7(11) (1995) 2058-2066.59. G.W. Somsen, C. Gooijer and U.A.T. Brinkman, J. Chromatogr., A, 856(1/
2) (1999) 213-242.60. J.N. Willis and L. Wheller, Polym. Mater. Sci. Eng., 69 (1993) 120.61. M.X. Liu and J.L. Dwyer, Appl. Spectrosc., 50 (1995) 349.
192
62. R.M. Robertson, J.A. de Haseth and R.F. Browner, Appl. Spectrosc., 44(1)(1990) 8-13.
63. T. Provder, M. Whited, D. Huddleston and C-Y. Kuo. Prog. Org. Coat., 32(1997) 155.
64. J.B. Wei, J.C. Shull, Y.J. Lee and M.C. Hawley, Int. J. Polym. Anal.Charact., 3(1) (1996) 33.
65. M.A. Mottaleb, Anal. Sci., 15(1) (1999) 57-62; R. Vonach, B. Lendl and R.Kellner, Anal. Chem., 69 (1997) 4286-4290..
66. F. Cuesta Sanchez, B.G.M. Vandeginste, T.M. Hancewicz and D.L.Massart, Anal. Chem., 69(8) (1997) 1477-1484.
67. V.E. Turula, R.T. Bishop, R.D. Ricker, J.A. de Haseth, J. Chromatogr., A,763(1-2) (1997) 91-103.
68. M.A. Mottaleb, Anal. Sci., 15(1) (1999) 57-62.69. I. Bruheim, P. Molander, E. Lundanes, T. Greibrokk and E. Ommundsen,
J. High Resolut. Chromatogr., 23(9) (2000) 525-530.70. U.A.Th. Brinkman, N.H. Velthorst and T. Visser, Anal. Chim. Acta, 290(3)
(1994) 269-276.71. L.V. Azarraga, Appl. Spectros., 34 (1980) 224.72. R.P. Griffiths, J.A. deHaseth and L.V. Azarraga, Anal. Chem., 55 (1983)
1361.73. I. Ojanpera, K. Pihlainen and E. Vuori, J. Anal. Toxicol., 22(4) (1998)
290-295.74. V.A. Basiuk, Spectrochim. Acta, Part A, 55A(2) (1999) 289-298.75. J.D. Jegla, P.R. Griffiths and D.P. Klein, Prepr. Am. Chem. Soc., Div. Pet.
Chem., 41(4) (1996) 663-666.76. D.M. Haaland, E.V. Thomas and D.S. Blair, Appl. Spectrosc., 47(10) (1993)
1612-1619.77. V.A. Basiuk, Spectrochim. Acta, Part A, 55A(2) (1999) 289-298.78. R. Kuckuk, W. Hill, P. Burba and A.N. Davies, Fresenius'J. Anal. Chem.,
350(7-9) (1994) 528-532.79. M. Poliakoff, S.M. Howdle and S.G. Kazarian, Angew. Chem., Int. Ed.
Engl., 34(12) (1995) 1275-1295.80. M. Ashraf-Khorassani, M.T. Combs, L.T. Taylor, J. Willis, X. Liu and C.R.
Frey, Appl. Spectrosc., 51(12) (1997) 1791-1795.81. K.L. Norton, A.M. Haefner, H. Makishima, G. Jalsovszky and P.R.
Griffiths, Appl. Spectrosc., 50(9) (1996) 1125-1133.82. U. Just, D. Jones, R.H. Auerbach, G. Davidson and K. Kappler, J. Bio-
chem. Biophys. Methods, 43(1-3) (2000) 209-221.83. R.H. Auerbach, K. Dost and G. Davidson, J. AOAC Int., 83(3) (2000)
621-626.84. E.M. Calvey, T.H. Begley and J.A.G. Roach, J. Chromatogr. Sci., 33(2)
(1995) 61-65.
193
85. S.H. Smith, S.L. Jordan, L.T. Taylor, J. Dwyer and J. Willis, J.Chromatogr., A 764(2) (1997) 295-300.
86. D.F. Gurka, S. Pyle, R. Titus and E. Shafter, Anal. Chem., 66(15) (1994)2521-2528.
87. J. Yang, E.J. Hasenoehrl and P.R. Griffiths, Vib. Spectrosc., 14(1) (1997)1-8.
88. K.L. Norton and P.R. Griffiths, J. Chromatogr., A, 703(1/2) (1995) 503-522.
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Chapter 8
Applications of infrared spectroscopy inbasic and industrial research
For many years now, infrared spectroscopy has enjoyed universalacceptance as a chemical characterization tool across almost all thedisciplines of science. The usefulness of the technique can be attributedto its ease of use, the cost of the instruments, and the plethora ofapplications that come from the use of different sampling techniques. Itshould, however, be pointed out that mass spectroscopy and nuclearmagnetic resonance (NMR) are nowadays the primary identificationtools for structural elucidation of organic compounds, with vibrationalspectroscopy playing a complementary role.
Therefore, the greatest value of infrared characterizations comesfrom technicalities associated with the ease of use of the technique. Dueto the number of different subjects that can be covered in this topic weare forced to concentrate our attention on a few selected examples.These examples deal mainly with the use of FT-IR spectroscopic tech-niques to polymeric materials [1], organic thin films and biologicalmaterials, though applications of other types of materials will also bepresented.
8.1 POLYMER APPLICATIONS
8.1.1 Infrared characterization of polymers and polymericsurfaces
Infrared spectroscopy has been used extensively in polymer character-ization for a long time, providing information on chemical nature,isomerization, conformational order, state of order, and orientation
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[2,3]. The use of vibrational spectroscopy as a characterization tool tomeasure orientation in polymers has been reviewed recently [4].
Some of the most recent examples of the use of infrared spectroscopyin the characterization of polymeric materials will be presented here.In such examples, FT-IR spectroscopy has been applied as a bio-diagnostic tool of polymer implants and tissue surfaces [5]. In thisparticular study, surface analysis allowed the determination of thespecific molecular compounds and structures most appropriate forlong-term compatibility in humans. Important information associatedwith the bioinertness or bioactivity of implants was obtained from thespectral features of the polymer material used, including the level ofpolymerization.
In another study, fluorocarbon compounds based on vinylidenefluoride copolymers and bisphenol AF were prepared to determine thenetwork-forming structures of the cured materials [6]. Sections fromkey stages of processing were taken and their FT-IR spectra wererecorded. These spectra established directly, for the first time, thatbisphenol AF served as the crosslinker during cure. Additionally,persistent unsaturation was formed on the elastomer backbone aftercrosslinking. It was also observed that curing for extended periods oftime produced no observable effect on the network. Furthermore, post-curing reduced residual hydrofluoric acid in the compound andresulted in the appearance of new absorptions at 2851 and 2920 cm l,respectively, which are indicative of amorphous regions of poly(vinyl-idene fluoride). These data served as an indicator in the understandingof the fracture behaviour and long-term performance of this class ofmaterials.
Also the use of segmented polyurethanes as biomedical implantmaterials was studied by vibrational spectroscopic probes combinedwith measurements with angular dependent XPS or ESCA [7]. Thesedata provided a detailed description in the surface composition ofBiomer and Avcothane which are commercially available biomedicalgrade polymers. In addition, the surface composition of the modelsystem polydimethyl siloxane (DMS) was also studied. Both attenuatedtotal reflectance (ATR) and photoacoustic (PA) techniques wereutilized. The authors were successful in elucidating the depth ofsegregation of DMS blocks in Avcothane as well as the presence of DMSin the very top surface of Biomer. It was found that this combination oftechniques worked better in the understanding of these complexpolymer surfaces.
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In another study, the thermal degradation of CO-ethylene-propylene alternating copolymers was followed by FTIR spectroscopy[8]. The infrared spectra of solid samples, performed in inert atmos-phere and under high vacuum, were recorded as a function of time atdifferent temperatures. These data indicated that the reaction processconsisted of intra or intermolecular hydrogen transfer, yielding an enoland a small quantity of unsaturated species. At temperatures abovethe melting point, scission of the polymer chain occurred and theproduct had large number of unsaturated fragments.
In another study, the radical grafting reaction of maleic anhydrideinto poly(propylene oxide) (PPO) was followed by infrared spectroscopy.PPO is widely used in the preparation of thermoplastic elastomers,surfactants, and additives. A protection of -OH end-groups of PPO wasrealized by acetylation in order to prevent side-reactions of thesegroups with anhydride. FT-IR spectroscopic studies were able to followthe extent of the grafting reaction due to the appearance of a character-istic shift in the carbonyl region of cyclic anhydrides to higher wave-numbers [9].
The copolymers of tetrachloroethylacrylate (TeCEA) and penta-fluorophenylacrylate (PFPA) and of TeCEA and pentafluoro-phenylmethacrylate (PFPMA) were examined with regard to theirapplicability as core materials for optical waveguides [10]. Inparticular, their thermal properties as a function of polymerizationconditions were investigated and optimized by addition of crosslinkers.The polymerization reactions were followed by FT-IR spectroscopy,which was able to successfully quantitate the unsaturation level inthese polymers. In addition, optical characteristics such as materialdispersion and attenuation of the polymers were also studied. Thefundamental demands on waveguide polymers are high opticaltransmission at the near-infrared region around 1300 and 1550 nm, theadjustability of the refractive index of the core polymer versus thecladding polymer, and finally sufficient thermal stability of at least70°C. Both the examined copolymers show low absorption at 1300 and1550 nm of 0.2 and 0.7 dB/cm respectively. The refractive index ofTeCEA/PFPA copolymer is tunable between 1.464 and 1.518 at 1300nm. In addition, the TeCEA/PFPMA copolymer is tunable between1.469 and 1.518 at the same wavelength.
In another study, the first attempt to investigate polymer-surfactant interactions in gelling and non-gelling aqueous mixtures ofa nonionic cellulose ether and a surfactant by means of vibrational
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Zw
z
400 600 800 1000 1200 1400
FREQUENCY (cm-1)
Fig. 8.1. IR absorption (dashed line) and Raman (solid line) spectra of solid EHEC atroom temperature. (Reproduced from Ref. [11] with permission. Copyright (1999)
American Chemical Society.)
spectroscopy was recorded [11]. In particular, a series of aqueoussolutions of ethyl hydroxyethyl cellulose (EHEC) with addition ofanionic surfactant sodium dodecyl sulphate (SDS) of different con-centrations was investigated by FTIR absorption techniques. Figure8.1 shows the IR absorption and Raman spectra of solid EHEC at roomtemperature. The data showed that, even in the solid state, i.e., belowthe gel point, interactions between the polymer and the surfactantwere present. Figure 8.2 shows the IR absorption spectra of EHECaqueous solutions (4 wt%) with different SDS concentrations at roomtemperature. In addition, both bound and free surfactant moleculeswere detected. This interaction, which cannot be characterized aschemical, occurred mainly between the side chains of the polymer andthe sulphonic acid groups of SDS. Figure 8.3 shows the infrared spectraof several EHEC/SDS/water systems in sol and gel states. Above the gelpoint, a new type of interaction appears, which mainly involves theS03 - groups and water molecules. The intermolecular interactionswere studied versus the changes of both temperature and polymer-surfactant compositions and a possible model for the gelation processwas discussed.
This study found that there was an interaction between EHEC andSDS even at temperatures below the gel point, i.e., in the solution state,though the effect was weak and can hardly be characterized as achemical interaction. However, when the temperature rose, a new typeof interaction appeared in the system that could be associated with
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wCW
Z
o
zcf
0O0co
1000 1050 1100 1150 1200 1250 1300 1350 1400 1450
WAVENUMBER (cm-')
Fig. 8.2. IR absorption spectra of EHEC aqueous solutions (4 wt%) with different SDSconcentrations (at room temperature). (Reproduced from Ref. [11] with permission.
Copyright (1999) American Chemical Society.)
enhanced chain mobility. The most prominent one was the interactionbetween the SO, groups of SDS and the glucose rings, which led to anessential decrease of the mobility of the rings and also to theirdeformations. Finally, clear changes in the state of water occurred withgelation. In the gel state the hydrogen bonds between water moleculesbecome stronger. Moreover, the degree of H-bond strengtheningincreased with the level of SDS addition, which suggested that thiseffect was inspired by the S03 groups.
Furthermore, the effect of interelectrode spacing on the propertiesof hydrogenated amorphous Si (a-Si:H) films grown by RF plasmaenhanced CVD method with control of dusty plasma conditions byheating both the electrodes was studied [12]. The formation of pre-cursors responsible for gas phase polymerization itself was thought tobe controlled by preheating of the source gas mixtures. Optimization ofthe interelectrode spacing for film characteristics was carried out forthis novel deposition technique that combined cathode heating andpreheating of the source gases. The films were characterized by infra-red spectroscopy along with absorption and reflection measurements inthe visible and near-infrared regions, and ESR spectroscopy.
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I
UC
arCCG0
O0
Wavenumber (cm-1)
Fig. 8.3. IR absorption spectra of several EHEC/SDS/water systems in sol (solid line) andgel (dashed line) states. Letters denote the sample type (see Table 8_1). (Reproduced from
Ref. [11] with permission. Copyright (1999) American Chemical Society.)
In another study, poly(8-quinolyl acrylate) and the polymers of thecomplexes of 8-quinolyl acrylate with CuBr, NiBr2, CoBr 2 and uranylacetate were prepared and characterized by elemental analyses,electronic and vibrational spectroscopic studies and magnetic moments[13]. Furthermore, by measuring the shift of satellite infrared peaks itwas possible to determine the value of interactive bond elongation indilatons [14]. Measurement of the satellite intensity permitteddetermination of the concentration of regularly formed sequences inpolymers. Investigation of the dependence of this concentration ontemperature, time, and load permitted study of the regularities of
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formation kinetics of dilatons. These spectroscopic data indicated thatdilatons generally originated in the surface layers of polymer solids.
8.1.2 Phase behaviour of polymer blends [15]
In one representative study, poly(ethylene oxide) (PEO) and poly(vinyl-phenol) (PVP) interacted quite strongly in the solid state via theformation of hydrogen bonds [16]. The interaction is specific at themolecular level and centres around the hydroxyl group of PVP. High-resolution FTIR and 13C NMR spectroscopy provided convincing evi-dence that the infrared absorption of the -OH group and the phenoliccarbon resonance of PVP are sensitive to the presence of the semi-crystalline PEO. It was postulated that the free electron pairs of theether O of PEO provided the complementary site for H bonding with theOH proton of PVP. Melting, crystallization, and single glass transitionbehaviour were all discussed from a phase-diagram viewpoint andrepresent macroscopic responses that are driven by molecular levelassociations. Flory-Huggins analysis of the melting point depressionphenomenon suggested that the thermodynamic interaction para-meter, X2, per monomer unit of PEO is -1.5 in the vicinity of themelting temperature. This implied that the energetics of mixing areexothermic and contribute favourably to concentration dependentmiscibility in the amorphous phase. Thermodynamic analysis of melt-ing point depression via the X12 parameter was consistent with theinfrared results, which revealed that the interaction between the twodissimilar polymers is stronger than the self-association of hydroxylgroups in PVP.
The blending between poly(methyl methacrylate) (PMMA) andferroelectric (vinylidene fluoride-trifluorethylene) [P(VDF-TrFE)]copolymer chains was investigated by FTIR spectroscopy over the fullrange of composition, for the copolymer with 50 mol% of trifluor-ethylene (TrFE) [17]. The FTIR spectra revealed an absorption band at1643 cm l, characteristic of the blend and absent in the individualconstituents. This band was attributed to the interaction of thecarbonyl group of the PMMA side chains with the disordered helicalchains present in the amorphous region of the P(VDF-TrFE). Theconsequences of adding PMMA onto the formation of the all transconformation of the copolymer chains was also investigated and theeffects of thermal heating on the spectra were relevant only for thesamples where the ferroelectric semicrystalline phase was present.
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8.1.3 Deuteration studies
Isotopic exchange and direct deuteration in particular, are commontechniques in IR spectroscopic studies directed at elucidation of poly-meric structure [18,19]. Frequency shifts upon isotopic substitution areexpected due to the mass dependence of the vibrational frequency inthe simple harmonic oscillator model. These frequency shifts can bepredicted with reasonable accuracy from the changes in the atomicmasses alone, since the force constants will remain essentiallyunchanged.
Krimm's rule [20,21] is an approximation rule that applies tohydrogen-deuterium substitution
VJVk = [1-(ATi/pT)]- /2 (8.1)
where k and vk, are the zero order frequencies of the kth vibrations for-H and -D groups, respectively; T is the total kinetic energy; ZAT isthe change in kinetic energy upon isotope exchange' and E is the ratio ofisotopic to normal mass, respectively.
For the case of polyethylene, Table 8.1 shows the predicted versusthe actual frequency for deuterated polyethylene (PE). The FT-IRspectrum of low density/perdeuterated high density (LDPE/d*-HDPE)is shown in Figure 8.4. These values compare very well with thosecalculated by the application of Krimm's rule.
8.1.4 Orientation measurements
Orientation in polymers can be measured by a variety of techniques,such as x-ray diffraction, NMR, birefringence, polarized fluorescence,
TABLE 8.1
Predicted versus actual frequencies for deuterated PE
Wavenumber ratio observed (CH2/CD2) predicted Vibrational assignments
1.342 1.349 asymmetric stretching1.372 1.379 symmetric bending1.341 1.349 bending1.384 1.379 rocking
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WUZ
CVI
--t
WAVENUMBERS
Fig. 8.4. LDPE/d*-HDPE FT-IR spectrum; 2 cm-l resolution.
Raman depolarization, sonic techniques and infrared dichroism. Thelatter technique is one of the most frequently applied tools for thecharacterization of anisotropy in polymers. Most polymer systems aresubjected to the application of stress during manufacturing. The stressis either applied in one direction (uniaxial stretching), or it can beapplied along two perpendicular directions (biaxial stretching). Theelucidation of the molecular mechanisms that take place duringelongation is of great importance to the polymer industry [22].
Classic rheo-optical studies emphasize the direct relationshipbetween the perturbation and the spectral response. In addition,dynamic FT-IR spectroscopy provides the element of time in theindividual spectral responses of different parts of the molecules withrespect to the external perturbation. Before the discussion of the rheo-optical studies in polymeric systems, a brief introduction to the theoryof infrared linear dichroism will take place.
8.1.5 Infrared linear dichroism
In general, maximum absorption takes place when the electric vector isparallel to the transition moment of the specific normal mode
203
(functional group) and no absorption will take place when the electricvector is perpendicular to the transition moment. The absorption ofeach mode is proportional to the square of the dot product of the electricE and transition moment M vectors, according to the equation
I = (EM)2 cos2 O (8.2)
where k is a proportionality constant and 0 is the angle between the twovectors.
In the case of a polymer macromolecule, the finally observedabsorbance A is the sum of the intensity contributions from all thestructural units of the polymer (n)
A = k '(EM) 2 dn (8.3)n
The effect of the anisotropic distribution of the transition momentswith respect to the direction of the electric vector E of the polarizedradiation is characterized by the dichroic ratio R
R =All/A1 (8.4)
where Al and A are the absorbances measured with radiationpolarized parallel and perpendicular to the stretching direction. Thevalue of R can range from zero (where there is no absorption in theperpendicular direction) to infinity (no absorption in the paralleldirection). For random orientation, R = 1. If R is greater than 1 theband is called a parallel band; if R is smaller than 1 it is called aperpendicular band. Therefore, several kinds of information can beacquired from the knowledge of R, namely, the elucidation of themolecular geometry by the determination of the transition momentdirections of particular functional groups with respect to the molecularaxis and unambiguous assignment of various modes to specificsymmetry types of the normal modes.
An important parameter for every absorption band is the so-calledstructural absorbance Ao
A o = (A +Ay +Az)3 (8.5)
which represents the absorbance of the band without the contributionsdue to the orientation of the polymer. For uniaxially oriented sample,
204
preferred orientation
Z
tent vector
X
Fig. 8.5. A schematic representation of the distribution of the molecular chains and theircorresponding dipoles with respect to the draw axis.
produced by stretching in one direction, the structural absorbancebecomes
Ao = (A + 2A)/3 (8.6)
In practice, the orientation is never perfect and this effect can besimulated by supposing that, on average, all the molecular chains aredisplaced by the same angle from the preferred orientation (stretchingaxis). Figure 8.5 is a schematic representation of the distribution of themolecular chains and their corresponding dipoles with respect to thedraw axis. The Herman orientation function F is expressed by Eq. (8.7):
F= [3 < cos20 > - 1]/2 (8.7)
where 0 is the angle between the draw direction and the local molecularaxis chain. This orientation function can be related to experimentallymeasured quantities, such as the dichroic ratio R of the absorptionband according to Eq. (8.8):
F = (R - 1)(R + 2)/(R - 1)(R + 2) (8.8)
where Ro = 2 cot2a is the dichroic ratio for perfect uniaxial order. As avaries from 0 to /2, Ro varies from infinity to zero. No dichroism isobserved at the so-called magic angle (for a = 54°44', Ro becomes unity).
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Some examples of the application of linear dichroism techniques topolymers will be presented here. In one such study, linear dichroismspectra in the mid-infrared region of fluorene aligned in stretchedpolymers and nematic liquid crystals were compared with earlierexperimental and theoretical investigations [23]. Linear dichroismspectra of molecules aligned in such anisotropic solvents were simple toobtain, especially for small and medium-sized molecules. Mostmolecules obtain a satisfactory alignment by these methods and thespectra were simple to interpret. The information obtained from thesespectra about vibrational transition moment directions was oftencrucial for vibrational assignments in molecules like fluorene. Evenhigh quality calculations are still unable to provide safe assignmentsfor all the fundamental vibrations in fluorine, as long as they are onlycompared with traditional spectra. Linear dichroism spectra provideda separation of the experimental information according to symmetryclasses. This procedure reduced the assignment puzzle drastically. Inthe present case the result was an almost complete and safe assign-ment of all symmetry-allowed fundamentals of fluorene. In a similarstudy, samples of aligned molecules may be produced by using stretch-ed polymers as anisotropic solvents [24]. Although the molecularalignment is rarely perfect and the orientation distribution function isnot known, an exact, simple, and useful mathematical description ofthe partial alignment was possible. The aligned samples could bestudied by optical spectroscopy with linearly polarized light in order togain information on the properties of the molecular alignment, on thestructure of the solute molecules and their interaction with the solvent,or on spectral assignments of electronic and vibrational transitions inthe solute molecules. It is usually assumed that the alignment of solutemolecules in stretched polymer sheets is uniaxial around the stretchingdirection, even in thin polyethylene sheets. The validity of this assump-tion was investigated and confirmed through a series of measurements,using different angles between the direction of the linearly polarizedlight beam and the plane of the stretched sheet. The degree of align-ment of solutes in stretched polyethylene is known to increase whenthe temperature is lowered. A systematical study was carried out of thealignment of a solute molecules in stretched polyethylene as a functionof temperature. This study showed that the main change in alignmenttakes place at temperatures around -10° . The change was associatedwith large improvements in alignment within the crystalline regions ofpolyethylene. As a practical consequence, the improved alignment,
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which was previously obtained by cooling to LN 2 temperatures, may beeasily available at more convenient temperatures.
8.1.6 Dynamic FT-IR procedures
The majority of the dynamic and time resolved experiments withmodern FT-IR instruments take place with the use of step-scan inter-ferometry. Since a lot of the examples that will be presented laterinvolved the use of dynamic FT-IR techniques, a short description ofthese techniques will take place here.
For the purposes of this book, dynamic infrared spectroscopy isdefined as the use of infrared spectroscopy to monitor a time-dependentprocess. The study of the dynamics of the vibrational excitation/de-excitation process itself is outside the scope of this work. However,since the time-scale of this process is of the order of 10-13 s or less,changes in the IR spectrum can be used to monitor the dynamics ofslower processes, within the practical limits of the speed of the detectorand electronics and the strength of the signal.
Operationally, dynamic spectroscopy can be divided into experi-ments which use the impulse-response technique ("time-resolved"spectroscopy) and those which use synchronous modulation techniques("phase-resolved" spectroscopy) [25]. In the first case the dynamicresponse to a perturbation is monitored as an explicit function of time;in the second case the phase and magnitude of the response withrespect to that of the perturbation are measured. It has been previouslystated that these two types of experiment are actually closely related(by the Fourier transform) and may be considered as limiting cases of ageneral modulation experiment which uses n frequencies [26]. For theimpulse-response experiment n - c, while for the synchronouslymodulated experiment, n = 1.
Until recently, dynamic infrared spectroscopy has been restricted tothe study of either relatively slow processes or limited wavelengthranges. Dispersive spectrometers with point by point data collection orvery slow scanning offer access to broad wavelength range but requirevery long data collection times to achieve this and are seriously limitedby low throughput. However, for synchronous modulation experiments,over limited wavelength ranges, quite good results for time-resolutionin the us range have been achieved in reasonable times by use ofdispersive IR [27-30]. Tunable laser radiation using either a gas phaselaser (such as CO) or a diode laser is another possible approach to
207
dynamic IR spectroscopy. The high intensity per spectral bandwidth ofthe laser make such techniques excellent from the point of view of bothspectral and temporal resolution, but the requirement to makemeasurements essentially point by point (i.e., without any multiplexadvantage) and the limited tuning ranges available, restrict thegeneral utility of such techniques.
The synchronous modulation step-scan FT-IR spectra are acquiredmost of the time through a double demodulation experiment. In theseexperiments, the phase modulation of the IR beam, produced by the"jitter" of the moving mirror is used as a carrier frequency for theintensity modulation induced by the electric field reorientation of theliquid crystal sample, or at the mechanical stress modulationfrequency.
The amplitude of the phase modulation can be varied between a fewnm and several pm, in order to maximize the efficiency of modulation inthe spectral range of interest [31]. For example, an amplitude of 2 XHeNe
(1.26 pm) is used for full mid-IR spectroscopy. The infrared beam isinitially passed through optical filters that remove optical frequenciesoutside the useful range, thus reducing the level of noise in theacquired spectra. Undersampling may be used in order to reduceacquisition time. In this technique, the correct combination of opticalfilters and sample spacing eliminates the unwanted effect of aliasing(folding) [32], while at the same time producing the desired spectralrange. The infrared beam also passes through a gold wire-grid polari-zer which allows only light polarized parallel to the initial orientationof the liquid crystal director to reach the sample. The dynamic spectrathus show only changes in the infrared absorption which are associatedwith the reorientation of the transition dipoles in response to themechanical perturbation [33]. The acquisition time used to be sub-stantial for this kind of experiment, due to the fact that the changesunder investigation are very small (on the order of 10 4 absorptionunits). Modern research-grade FT-IR spectrometers equipped with thestep-scan option and DSP collection electronics reduce the acquisitiontime considerably.
8.1.7 Fourier transform dynamic infrared spectroscopy
The use of Fourier transform interferometric techniques for dynamicvibrational spectroscopy offers the combination of broad free spectralrange with relatively high spectral resolution and fast data acquisition
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times. However, again, until recently, harnessing the multiplex andthroughput advantage of FT-IR to dynamic measurements has been oflimited success except for low resolution measurements and/ormonitoring relatively slow processes.
There are, in fact, several ways to perform dynamic FT-IR measure-ments. First, if the lifetime of the event under investigation is > 10x theshortest scan period of the conventional continuous-scan interfero-meter, each interferogram can be considered to be instantaneous.However, even though scan rates of > 50 Hz have recently beenachieved on commercial instruments (using bi-directional scanning),this is always at the expense of resolution and, in any event, can only beapplied for a minimum of -20 ms time resolution. In addition, this is atechnique limited strictly to the impulse/response mode.
Another continuous scan approach, which is applicable to synchro-nous modulation experiments is to scan the mirror slowly enough thatthe highest Fourier frequency generated in the spectral bandwidth ofinterest is more than 10x lower than the external modulation appliedto the sample. This method has been successful, but it requires aninterferometer of exceptional stability [34]. Even so, it is not practicalfor external modulation frequencies of < 400 Hz, except in the far-IR.
8.1.8 Step-scan dynamic FT-IR
As an alternative to the continuous scan mode of interferometry, thedata may be collected in the step-scan mode, in which the retardation ischanged incrementally and data are collected while the retardation isheld constant. As previously stated, step-scan interferometry is moreuniversal in its application than is the continuous-scan method since itcan be applied without fundamental restrictions, to either synchronousmodulation or impulse/response experiments. Since the retardation isconstant while data are collected (or, as in some cases, the retardationis modulated about a fixed valve), the spectral multiplexing is un-coupled from the time-domain. Furthermore, step-scan FT-IR offersboth conceptual and practical simplicity since the experimental para-meters can generally be changed independently and with ease.
Although the step-scan mode of interferometry predates thecontinuous-scan mode by decades, until recently it has not been widelyavailable to experimenters in a form suitable for routine use outsidethe far-IR [28]. Both types of time-resolved experiment, either impulse-response or synchronous modulation experiments, can be performed
209
using the step-scan mode of operation. For impulse/response experi-ments data are collected as an explicit function of time at the desiredintervals after each impulse. The perturbation/impulse is repeated ateach step as many times as necessary to achieve the desired signal tonoise. Data from all times are sorted by time and transformed toproduce the time-resolved spectra.
8.1.9 Step-scan impulse-response experiments
The development during the last decade of modern step-scan interfero-metry instrumentation has allowed FT-IR to be applied to the study oftime-dependent phenomena in ways not previously possible, because ofthe problems of uncoupling the spectral multiplexing from the temp-oral domain in the continuous-scan FT-IR mode [35]. Specifically, thetime regime from tens of nanoseconds to tens of milliseconds has beenaccessible to time-domain measurements to only a very limited degreewith continuous-scan instrumentation and not at all for modulation-demodulation (frequency-domain) experiments in this time range. Thestep-scan technique not only works very well in this time regime andfor slower phenomena, but is only prevented from application to fasterprocesses by the signal strength, the speed of available detectors, theintensity of sources, and the speed and sophistication of the electronics.
As in the synchronous modulation experiments, it is necessary thatthe response of the system to the perturbation in the impulse-responsetime-resolved, or "time-domain" mode should be perfectly reversible, sothat any desired number of repetitive pulses can be used to achieve thenecessary signal averaging. In these experiments a signal from thespectrometer externally triggers the pulse generator, which thenproduces a voltage step across the cell and maintains this voltage for atime along with respect to the response time of the sample. As statedabove, repetitive pulses (separated by a suitable recovery interval) ateach interferometer position are used for signal averaging. The result-ing data are then sorted by time to produce individual interferogramsfor each time t, which are then transformed to give the time-resolvedspectra.
Figure 8.6 shows the data collection scheme for the simplified caseof one excitation pulse for each retardation step. The data are sortedvertically to produce the time-resolved interferograms. The time inter-vals are usually equal, but this is only an experimental convenience,not a fundamental requirement.
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Retardation Time Intervals
60 to*, tl, t2, . ..... tn
1 to*, t, t 2 , . . ., tn
$n to*, tl, t2, ·. . ., tn
Fig. 8.6. Data collection scheme for step-scan impulse-response experiment.
An example of the application of a infrared time resolved techniquewill briefly take place here. In this study, a time-resolved infraredspectrometer in the spectral region of 700-4000 cm-l was constructedwith a resolving power of 50 ns and detection limit of 10-6 [36]. Iso-merization of retinal by light irradiation was examined to suggest anisomerization mechanism from trans form to 3:1 mixture of 13-cis and9-cis forms within < 50 ns. The time-resolved IR spectra of N,N-dimethylamino-4-benzonitrile in polar BuOH and nonpolar hexa-decane with and without oxygen bubbling gave conclusions that the2096 cm-l band appearing only in polar solvent with a life of several nsand no oxygen effect was due to CN stretching vibration of the excitedsinglet state of twisted intramolecular charge transfer structure. A2040 cm-l band appearing also in polar solvents with longer life in theorder of 100 ns and disappearing by oxygen bubbling was due to CNstretching vibration of the excited triplet state.
8.2 APPLICATIONS TO LIQUID CRYSTALS AND LIQUID CRYSTALPOLYMERS
Thermotropic liquid crystal polymers have awakened a great deal ofinterest in the past decade from both technological and scientific pointsof view. Great emphasis was placed on the modification of physical andthermal properties, and analysis of the corresponding structure-property relations [37]. Vibrational spectroscopy is a useful tool in thecharacterization of these materials, and the type of informationavailable through infrared spectroscopy relates to crystallinity andpolymorphism, phase transitions and orientational behaviour.
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Efforts to investigate the responses of liquid crystals to appliedelectric field using vibrational spectroscopy started in 1981, usingattenuated total internal reflectance (ATR) spectroscopy [38]. Inaddition, the time course of the reorientation is most suitably studiedby the use of dynamic vibrational spectroscopy. Both time-resolvedRaman spectroscopy [391 and dynamic infrared spectroscopy [40] havebeen applied to the electric-field induced reorientation of nematicliquid crystals. Coles and Tipping used microsecond time-resolvedRaman spectra of a nematic liquid crystal as a function of the appliedelectric field [41]. Kaito et al. used fast FT-IR scanning with milli-second time resolution to study the time-dependent polarized infraredabsorption of a nematic liquid crystal [42]. Toriumi et al. published thefirst stroboscopic FT-IR data with sub-millisecond time resolution in1988 [43]. In 1991, Gregoriou et al. published the first synchronousmodulation data on the reorientational behaviour of a nematic liquidcrystal in response to an AC electric field [44].
8.2.1 Dynamic IR spectroscopy of polymers
Excellent reviews of the relevant instrumental and theoretical back-ground of polymer deformation and relaxation studies by simultaneousFourier-transform IR spectroscopic and mechanical measurementsexist in the literature [45,461. In the first review, the vibrationalspectroscopy of stressed polymers, orientational measurements usinginfrared dichroism, deuteration, and experimental results for thermo-plastics and elastomers are discussed.
Dynamic rheo-optical IR techniques promise an exiting future forvibrational spectroscopy as a tool on polymer research [47]. The earlierwork by Noda et al. [48] has been successfully adapted to interfero-metric measurements using step-scan FT-IR techniques [49]. Noda etal. [50] performed a dynamic infrared linear dichroism study of highdensity and low-density polyethylene films near the -transitiontemperature. It was found that a different deformation mechanismoperates above and below T. Specifically, a negative dynamicdichroism at 1473 cm7l and a positive dynamic dichroism at 1463 cm -lwere observed at 32°C. This observation was interpreted to mean thatabove T, the orthorhombic crystallographic b axis reorients parallel tothe direction of applied strain, while the crystallographic a axisreorients perpendicular to the strain direction for both HDPE and
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LDPE. The dynamic dichroism of both bands changes sign at -50°C(below Tp), indicating that the dynamic reorientation directions for thecrystalline a and b axes are shifted below To. In this earlier work withdispersive instrumentation switching between spectral regions was adifficult task, requiring a substantial investment in time.
Lefebre et al. have performed infrared measurements on the PS/PPO compatible blend in terms of static uniaxial strain above the glasstransition temperature [51]. Evidences that the PPO and PS chainsorient in a different way were found, in spite of the compatible nature ofthe blend. The PPO orientational behaviour does not depend on PPOconcentration in the concentration range that was studied (0-35%)while PS orientation regularly increased up to 25% PPO and thenremained constant. The authors suggested two explanations for thisbehaviour. Either the increase of the PPO concentration results in anincrease of the knots of the physical network, or the relaxation of the PSchains is hindered by PPO chains. The first explanation is notsupported by their experimental results, since the PPO orientationremained constant as the concentration increased.
In a similar study, side chain liquid crystalline polyurethanes are anew class of materials that show promise for mechano-optic applica-tions. The rich morphology afforded by these materials also provided achance to understand the interplay between polyurethane morphologyand liquid crystalline ordering. In this study, the response of a poly-urethane with liquid crystals pendant to the soft segments to anapplied strain using Fourier Transform Infrared (FT-IR) lineardichroism was detected. It was found that this complex materialfollowed trends established in the literature for both side chain liquidcrystalline homopolymers and segmented polyurethanes. At lowstrains, the soft segments aligned with strain inducing an orientationin 'lone' hard segments. Up to strains of 40%, the LC mesogens alignwith the strain field and the hard segments in hydrogen bondeddomains align perpendicular to the field. At strains above 40%, arearrangement of the ordering was found that resulted in the smecticlayers and the hard segments aligning parallel to the field. In addition,dynamic FT-IR experiments showed that the viscoelastic reorientationof various segments of the macromolecule could be monitored as afunction of the applied strain. For the polyurethane under study, thecyano band was used to follow mesogen movements, and the urethanecarbonyl to track the hard segment. Evidence were presented for twotypes of hard segments: those involved in hydrogen bonding within
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hard domains, and those found in 'lone' hard segments in the softmatrix. Evidence were also found for two types of mesogens: thosefound in smectic layers, and those not involved in smectic ordering atthe hard domain interface. The hard domains and the smectic layershad strong viscous components to their mechanical response. The 'free'mesogens and the 'lone' hard segments, on the other hand, exhibited amore elastic response. A model was proposed to represent thesefindings, and reflections on the cooperative movement of the differentmacromolecular components of the polyurethane were offered [52,53].
8.3 APPLICATIONS TO OPTICALLY ACTIVE MATERIALS
8.3.1 Organic light emitting diodes (OLEDs)
Electroluminescent devices based on organic low molecular weight (e.g.,Alq3) and polymeric materials (e.g., PPV) are recently attracting muchattention mainly due to applications as large area light-emittingdevices (OLEDs). Generally, these devices are thin-film single-layer ormultilayer structures composed of a hole transport and an emitting andan electron transport material sandwiched between two electrodes.OLED devices are generally fabricated utilizing vapour depositiontechniques or film-casting techniques from solution.
The structure and the correlation between intermolecular inter-actions and optical properties in various such systems have beeninvestigated with infrared spectroscopy among other methods. Someselected examples will be presented here.
In one such study, the authors reported the presence of carbonylmoieties as defects, formed during the thermal conversion of aprecursor to poly(p-phenylenevinylene) (PPV) [54]. The increase incarbonyl groups was correlated with a dramatic reduction of PPVphotoluminescence. If the conversion is carried out in a reducingatmosphere, e.g., 15% hydrogen in nitrogen, and the amount ofcarbonyl moiety was substantially reduced and the photoluminescenceintensity of the polymer increased as much as five-fold.
In another study, thin films of a cross-linkable hole-conductingmonomeric triarylamine for use in organic light emitting diodes wereexamined [55]. The rate of photo-crosslinking and the overall polymeri-zation yields were measured using real-time FTIR spectroscopy. Theelectronic properties were characterized in a typical diode configura-
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OC.H, OCH,,
OC,H, _0 CH,
H,C, O, H,,Co OOo
H,C,O H,,C,O O
"'v" r0
CH, 2 o cOC,H, 0 OC OH,,
0
H'C•ka---o OC,H,,
OH"CO 'a i' NC
OC,H, , XCH,,H,,C,O. 2b
H,C, o-" "O- ' o
3 ON C H, ' OC,H,,
OCH,, HC /0 "0
_0
0
H~C'-o 0CM *CO-' M-~
O - c
H'C-O H,,CCO 0
OCH,0 OC,H ,,
Fig. 8.7. Chemical structure of the mono-1, bis-2a-c and tris acrylate 3,4 derivatives ofhexaalkoxytriphenylenes. (Reproduced from Ref. [56] with permission. Copyright (1999)
American Chemical Society.)
tion using InSn oxide and Al as the contacts. The current passedthrough the devices was limited by the injection of holes into the semi-conducting polymer layer by tunnelling. Cross-linked layers withstoodapproximately 20 times higher currents than non-cross-linked layersbefore dielectric breakdown occurred.
In a similar study, new hexaalkoxytriphenylenes having one, two, oreven three lateral attached acrylate moieties as polymerizable groupswere synthesized and characterized for use as novel insoluble holetransport materials in organic LEDs [56]. Figure 8.7 shows the chemi-cal structure of the mono-1, bis-2a-c and tris acrylate 3,4 derivatives ofhexaalkoxytriphenylenes. The conditions for the photopolymerizationof these monomers in thin film were evaluated and tested. Thebisacrylates and trisacrylates were used to build insoluble networks.When a mask was used during the irradiation, patterned films wereprepared. The polymeric reaction was controlled by GPC and FTIRspectroscopy. Figure 8.8 shows the spectroscopic data that verify the
215
co0
oal
1C
wave numbers [cm']
Fig. 8.8. Spectroscopic verification of the photo-cross-linking reaction in thin films by FT-IR (16 scans; 4 cm- ' resolution, films on KBr): (a) trisacrylate 4 before polymerization;(b)photopolymerized film of 4; (c) reference spectrum of a polymer derived from solutionpolymerization of 1. (Reproduced from Ref. [56] with permission. Copyright (1999)
American Chemical Society.)
photo-cross-linking reaction in thin films. The networks and patternedstructure were also confirmed by UV spectroscopy, surface profiles, andSEM photographs. Since hexaalkoxytriphenylenes are known as excel-lent photoconductors, the photopolymerized films were used as holetransport layers in two layered OLED with Alq3 . Finally, Figure 8.9illustrates the OLED characteristic of a two-layer device with Alq3 asemitting/electron transport layer and a cross-linked film as a hole-transport layer.
Polymer light-emitting diodes, based for example on MEH-PPV, areknown to be susceptible to oxidative degradation [571. This leads to lossof conjugation, i.e. lower carrier mobility and higher operating voltage,and to the formation of carbonyl species, i.e. to luminescence quench-ing. In-situ FTIR revealed that ITO can act as the source of O. Toexplore further the mechanism of oxidation and to provide guidance forits elimination, the authors have studied the behaviour of MEH-PPVLEDs prepared with a variety of conducting polymer anodes includingpolyaniline and polythiophene derivatives cast from various solventsand with various molecular and polymeric dopants. In all the casesexamined, polymer anodes led to significant improvement in lifetimeover devices with ITO as the anode contact. Also, in contrast to thevariability observed for ITO anodes, conducting polymers with
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voltage [V]
10'
OTo
E
' 10'
C lo"
L ,2 10
-15 -10 -5 0 5 10 15 20 25
electric field [10 e V/cm]
Fig. 8.9. LED characteristic of a two-layer device with Alq3 as emitting/electron transportlayer and a cross-linked film of 3 as hole-transport layer ITO/3 (35 nm)/Alq3 (35 nm)/Al(200 nm). (Reproduced from Ref. [56] with permission. Copyright (1999) American
Chemical Society.)
polymeric dopants yield consistently good devices with powerefficiencies of approximately 0.5% at 5 V and brightness >1000 cd/m2.Anodes prepared with small molecular dopants are more variable andexhibit short-term behaviour which suggested interfacial electro-chemistry. The authors described the device characteristics in thecontext of a model of hole-dominated bipolar charge injection withLangevin recombination.
In another study, poly(p-phenylenevinylene) (PPV) was derivedfrom a sulphonium salt precursor by ion beam irradiation [58]. Aquadrupole mass spectrometry analysis of the evolved species showedrapid loss of HC1 and tetrahydrothiophene groups during irradiationwith 100 keV Ne+, indicating precursor degradation. Rutherford back-scattering spectrometry confirmed the reduction of the sulphur andchlorine content in the PPV film, whereas infrared spectroscopyshowed that the vibration mode at 2940 cm - l for the sulphonium grouphas vanished for a 2 x 1016 ion effluence. The appearance of the trans-vinylene peaks, at 3024 and 965 cm-l in PPV indicated the full con-version of the precursor into the conjugated polymer for this effluence.The correlation between a narrower optical band gap and the by oneorder of magnitude higher conduction of a film implanted with Na + ionswith respect to a Ne+ irradiation showed the doping effect induced by animplantation with electronically active species.
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8.3.2 Conducting polymers
In the area of the application of FT-IR techniques to study conductingpolymers, excellent reviews on the theory of polarons, bipolarons, andsolitons and use of vibrational spectroscopy in the studies of self-localized excitations and charge transfer in conducting polymers exist[59]. Geometry of polymer chains and changes induced by doping;electronic states of polarons, bipolarons, and solitons; electronicabsorption spectra of poly(p-phenylene) and detection of radical anionsin p-oligophenyls were some of the issues addressed.
In addition, the first vibrational spectroscopic investigation of anovel non-aqueous proton conducting polymer gel electrolyte consist-ing of a PMMA matrix and a solvent mixture (ethylene carbonate (EC)/propylene carbonate (PC) or EC/PC/N,N-dimethylformamide (DMF))with a dissolved organic acid (benzoic or salicylic acid) took place [60].The protonic conductivity of the gels was of the order 10-4-10 - 5 S/cm atroom temperature. It was found that the conductivity was proportionalto the degree of dissociation of the acid, the latter determined fromRaman spectroscopic data, and that the degree of dissociationdepended on the properties of the solvent mixture. Finally, therelationship between the proton conductivity and the solvent-diffusiondynamics was also studied.
Electronic absorption and vibrational spectroscopies of dopedconjugated polymers, whose ground states are nondegenerate werealso studied [61]. These studies have concluded that polarons are themajor species generated by doping in most nondegenerate conjugatedpolymers such as polythiophene, poly(p-phenylene), and poly(p-phenyl-enevinylene), in contrast with the previous view that bipolarons are themajor species.
8.3.3 Composites and nanocomposites
FT-IR spectroscopy has also been used in the study of compositematerials and nanocomposite films. In one such example, infraredspectroscopy was used to monitor the formation of thin films of photo-sensitive hybrid organic-inorganic glass on silicon via the solutionsol-gel method [62]. Glasses consisted of photoinitiator, methacryloxy-propyltrimethoxysilane, methacrylic acid, and zirconium oxide. Clear,low optical loss films were obtained, indicating nanophase homo-geneity in the samples. The nanocomposite films were suitable for
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fabricating optical components such as ridge waveguides and Braggdiffraction gratings. The increase in the refractive index of the glassrelative to the surrounding material during photolithographicprocessing was identified as a key material parameter in devicefabrication. Accordingly, electronic and vibrational spectroscopy wereused to provide insight into the structural changes that occur whenglasses were irradiated with continuous narrow band 4.9 eV and pulsed6.4 eV light. Arguments were advanced, linking the changes in refract-ive index to collateral densification leading to volume compaction of thesilicate network during organic free-radical polymerization. This wasshown by following the time evolution of relevant infrared absorptionbands. Free silanol and unreacted methoxysilane were consumed in theprocess. Matrix densification was indicated by shifts to lower wave-numbers in the transverse optical phonon mode associated withdecreasing Si-O-Si bond angles of the asymmetric stretchingvibration. Growth in the Si-O-Si framework was observed throughincreased intensity in this infrared absorption. Similar behaviour wasobserved for films irradiated with 6.4 eV light from an excimer laser. Aphase mask in combination with pulsed 6.4 eV light was used toinscribe a 1.5 mm, high-reflectivity polarization-independent Bragggrating into a ridge waveguide. The high reflectivity is thought to arisefrom a periodic modulation of the volume compaction of the matrix.Overall, the organic component of the glass confers unique propertieson the material that allows it to be densified even with 4.9 eV light. Bycomparison, sol-gel silica with no organic component must be densifiedat nearly twice the photon energy.
Di(carboxystyryl)benzene was self-assembled with a Zn complex inTHF on SiO2 and Si substrates to form thin films that exhibited blue-green luminescence [63]. FT-IR spectroscopy of a 56 nm film on Sishowed characteristic absorption bands at 1600 cm-l, 1543 cm-l, and1412 cm-l consistent with a powder sample. The refractive index (n)was 1.66 at 633 nm. Multilayer growth proceeded by a 15 Angstromincrease after initial surface coverage. These films were pursued for thepreparation of self-assembled films for electroluminescenceapplications.
In a similar study, high-energy milling provided an effective andenvironmentally conscious method for nanosizing Si [64]. Colloidalsuspensions of nano-sized Si were demonstrated and used for thefabrication of high refractive index nanocomposites. Si nanoparticleswith average sizes of 20-40 nm and size distributions of approximately
219
25% were separated from milled powder via sonication and centri-fugation. These nanoparticles were analyzed using TEM, dynamic lightscattering, x-ray diffraction and UV-visible/FTIR spectroscopy.Formation of stable colloids was in part attributed to a thin surface-oxide layer. The decrease in the average particle size caused a blue shiftin their absorption spectrum, thus increased the transparency in thered part of the visible region. These Si nanoparticles were used tofabricate high refractive index nanocomposites, with refractive indexes<3.2, when dispersed in gelatin.
Langmuir-Blodgett (LB) films composed of the mixture of anamphiphilic polymer containing azobenzene (Az) side chain (6Az10-PVA) and 4'-pentyl-4-cyanobiphenyl (5CB) were prepared to mimic the2-dimensional contacting region of the LC/Az interface of the commandsurface which photochemically switches the LC alignment. UV-visibleabsorption and FT-IR spectroscopic measurements were carried outunder illumination [651. These procedures allowed separate and simul-taneous evaluations of the static state and dynamic molecular motionsof both Az and LC molecules which probably reflect the initial trigger-ing step of the domino-mode response of the LC. The spectroscopic dataindicated the induction of reversible perpendicular/tilt orientationalchanges of both the Az side chain and 5CB molecules upon alternativeirradiation of 365 and 436 nm light. Thus, 6Az10-PVA/5CB hybrid LBfilm was regarded as a satisfactory interface model of a commandsurface that promotes the homeotropic/planer alignment switching.From the time courses of the photoisomerization of Az and the orienta-tional change, the molecular tilt was not governed only by the trans/cisratio of Az unit, but was strongly process-dependent (forward or backprocess), indicative of involvement of strong molecular cooperativity.
Photoinduced vibrational bands of poly(3-octylthiophene) werestudied at room temperature by using time-resolved FTIR spectroscopy(TR-FTIRS) in the nanosecond to microsecond time domain [66]. Aphoto-bleach occurred in the deformation band of :C-S-C: at 1463-1419 cm-l, and a few transient absorption bands occurred at lowerfrequency (e.g., approx. 1290 cm-l). The transient absorption band at1290 cm-l showed a signal exponential formation occurring in <200 ns,and a double exponential decay process, with lifetimes of 53 and 788 ps.Adding Fe2 03 nanoparticles into the polymer composite significantlyenhanced the photoinduced signal, indicating the interaction betweenpolymer and nanoparticle. The dynamics of these photoinduced specieson the nanosecond to microsecond time scale were discussed.
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In addition, vibrational spectroscopy was used for assessment ofnew materials for the guided tissue regeneration (GTR) technique [67].Implants applied in the healing of periodontal defects using this tech-nique have to meet stringent requirements concerning their chemicalas well as physical properties. At present the implants prepared fromtwo layers membranes differing in porosity in their outer and innerlayers were studied clinically. Composite plates consisted of threelayers: a poly(lactic acid) film, carbon fibres coated with polylactic acidand carbon fabric. Analysis of the infrared spectral data of samplestreated in Ringer solution allowed the description of the phenomenaresulting from the composite degradation. It was shown that materialbiostability was related to the presence of carbon fibres.
Furthermore, the use of a new cathode material based on a compo-site of an organosulphur compound, 2,5-dimercapto-1,3,4-thiadiazole(DMcT), poly(aniline), and catalytic amounts of copper ion in secondarylithium cells was also reported [68]. After failure of these cells, replace-ment of the lithium anode restored the original capacity. Vibrationalspectroscopy of the copper/DMcT system indicated that addition ofCu(II) oxidized and complexed DMcT and thus allowed more solvent tobe evaporated from the films. Furthermore, it was found that the redoxprocesses in the film were greatly stabilized by copper ion, likely due toa mixture of catalytic and conductive effects.
Pyrrole can be polymerized within montmorillonite clays via chem.means using Fe3+ and Cu2+ as the oxidizing species [69]. The resultantcomposite had properties of both the conducting polymer and the hostmaterial. Vibrational spectroscopy, thermal analysis and conductivitydata all indicate that polypyrrole was present in the interlayer regionof the clays used. Electrochemically the conducting polymer-clay com-posite showed promise for both sensor and electrolysis applications.Cyclic voltammetry was studied for ascorbic acid oxidation at carbonpaste electrode and conducting polymer-clay composites/carbon pasteelectrodes.
Finally, correlations were studied between dielectric, vibrational,spectroscopic and heological parameter variations during cure of athermoset formulation of Araldite MY 0510 and 4,4'-methylenedianiline [70]. Reaction kinetics values obtained from dielectric andfrom spectroscopic results were in excellent agreement. Gelation andvitrification times determined by dielectric and theological measure-ments were also found to agree well, despite the empirical nature ofsuch correlations. A characteristic pattern was noticed in plots of
221
imaginary impedance as a function of reaction time, which can be usedto identify gelation and vitrification during network formation. Therealization of the full potential of dielectric impedance spectroscopy inmonitoring the progress of chemophysical changes in reactive poly-mers, however, hinges upon a development of fundamental scientificcorrelations between dielectric and chemorheological phenomenaduring cure.
8.4 APPLICATIONS OF INFRARED MICROSPECTROSCOPY
Since the introduction of the first FT-IR microscope interface by BrukerInstruments in 1983 the technique has progress to the point that verybeautiful chemical images are nowadays generated from a step-scanFT-IR microscope equipped with a focal plane array detector. Manyreviews exist in the literature that can familiarize the reader with thesubject. In these reviews, applications are discussed in the area offorensic science, materials science, art restoration and the biologicalscience [71,72].
The coupling of imaging modalities with spectroscopic techniquesadds additional dimensions to sample analysis in both the spectro-scopic and spatial domains [73]. The particular ability of infraredimaging to explore the spatial distribution of chemically distinctspecies demonstrates the versatility and diversity of spectroscopicimaging. The particular spectroscopic imaging instrument integratedseveral infrared focal-plane arrays with a Michelson step-scan inter-ferometer, generating high-fidelity and high spectral resolution mid-infrared spectroscopic images. The instrumentation produced multi-dimensional, chemically specific images, while simultaneously obtain-ing high resolution spectra for each detector pixel. The spatialresolution of the images approached the diffraction limit for mid-infrared wavelengths, while the spectral resolution was 4 cm-l. Dataderived from a variety of materials, particularly biological samples,illustrated the capabilities of the technique for readily visualizingchemical complexity and for providing statistical data on sampleheterogeneity.
Another approach utilized the use of the infrared scattering fromthe tip of an atomic force microscope. This technique overcomes theproblem that the spatial resolution is diffraction-limited to a scale ofabout half the wavelength, or about five micrometers in the infrared
222
spectral region [74]. The scanning near-field optical microscope, how-ever, can reveal sub-wavelength detail because it uses near-fieldprobing rather than beam focusing. Therefore, the use of the aperture-less approach to scanning near-field optical microscopy was demon-strated in an attempt to obtain contrast in vibrational absorption on ascale of about 100 nm, about one-hundredth of a wavelength. Infraredscattered light was recorded from the tip of an atomic force microscopescanned over a composite polymer film. At the boundary betweendifferent polymers contrast changes were observed owing to changes invibrational absorption. The contrast was strongly enhanced in the nearfield of the probe tip, which we interpret as evidence of surface-enhanced infrared absorption. When extended to multi-wavelengthoperation, this approach should enable imaging of chemical compoundsat nanometre resolution.
Another different approach toward mid-infrared spectroscopicimaging microscopy was introduced in which instrumentation wasdesigned about an InSb multichannel, focal-plane array detector and avariable-bandpass dielectric filter [75]. The system could be configuredfor either macroscopic or microscopic applications, and high-fidelity,chemically specific images were acquired in real time. With thedielectric filter used in this assembly, continuous tuning was providedfor the 4000-2320 cm-l spectral region with spectral resolution ofapproximately 35-18 cm -l at the extremes of this wavelength interval.The functioning of the imaging microscope was demonstrated withsamples includingpolystyrene microspheres, preparations of lipids andan amino acid embedded in KBr disks, and a tissue sample derivedfrom a coronal slice of a monkey cerebellum.
Another recent study concentrated in reducing the noise of a chemi-cal imaging experiment. Temporal resolution of fast FTI-R imaging islimited by rapid degradation of data quality, due to increased noise,with faster image acquisition [76]. Various coaddition schemes werepresented, meant to reduce noise and improve the quality of imagesacquired from such systems. The application of the proposed schemesallowed for improved signal-to-noise ratio (SNR) characteristics in theresulting data. Figure 8.10 shows the single-beam spectrum from apixel with KBr disks in the beam path and an absorbance spectrum ofthe polymer film. On the other hand, Figure 8.11 shows the collectionand coaddition scheme to obtain absorbance images with a higher SNRusing fastest single-beam image collection and the coaddition schemesto coadd pixels with the same true absorbance values.
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Fig. 8.10. The single-beam spectrum from a pixel with KBr disks in the beam path and anabsorbance spectrum of the polymer film. The profile with lower noise is obtained bycoadding 256 pixels illustrating noise. (Reproduced from Ref. [76] with permission.
Copyright (1999) Society for Applied Spectroscopy.)
These schemes were tested by monitoring the dissolution of a poly-mer film [poly(a-methylstyrene)] by a low-molecular weight solvent[methyl iso-Butyl ketone (MIBK)]. Figure 8.12 shows an image of apolymer/air interface and a comparison of spectra obtained from apixel. Pseudo coaddition improved the SNR by approximately 45%. Atotal acquisition time of about 100 s was achieved, allowing the dis-solution process to be monitored by using image acquisitions separatedby 3 min. Low noise concentration profiles, linear solvent penetrationrate, and polymer dissolution rates were all measured. Figure 8.13shows the dissolution of a poly(a-methyl styrene) film by MIBK diffus-ing from right to left. The images at the top plot E(x,y, 1600) forabsorbance and the images at the bottom plot E(x,y, 1730) for thesolvent. Detection limits of approximately 5% and quantification limitsof approximately 20% were achieved by using optimal coadditionstrategies. This result represented an order of magnitude improvementover untreated data.
224
A
I Fast FTIRAbsorbance Image
n co-added Data Sets
N Pseudo-Data Sets (N+I) Collected Data Sets
B
//(Higher Order)
Linear Sampling(Higher Order)
Fig. 8.11. (A) Collection and coaddition scheme to obtain absorbance images with ahigher SNR using fastest single-beam image collection. (B) Coaddition schemes to coaddpixels with the same true absorbance values. (Reproduced from Ref. [76] with
permission. Copyright (1999) Society for Applied Spectroscopy.)
Correlative x-ray photoelectron spectroscopy (XPS) and Fouriertransform infrared (FT-IR) studies of the complex heterogeneousstructure of 50:50 poly(vinyl chloride)lpoly(methyl methacrylate) (PVC/PMMA) polymer blends were also shown [77]. The comparable lateral
225
Y
B
Fig. 8.12. (A) An image of a polymer/air interface with ROI used for statistical analysis.(B) A comparison of spectra obtained from a pixel on the FPA using described parameterscompared to a spectrum of the film obtained by a rapid-scan FT-IR spectrometer.(Reproduced from Ref. [76] with permission. Copyright (1999) Society for Applied
Spectroscopy.)
226
A F
I 1j'2¢41
* S
,_ 1',,': Ari
rr =
V j, 5's
, 'M1: ·4
I 'i ti
.,,':, X
its
ut o lyme -20 Ij - U m11 t-o7 E , Z-I 1111
Polymer FJ(xy, 1600) 200 Ful Solvent E(x,y,1 730)Uo _nMWr A 0.25 2- teo L(
Fig. 8.13. The dissolution of a poly(a-methyl styrene) film by MIBK diffusing from right toleft. The images at the top plot E(x,y, 1600) for absorbance and the images at the bottomplot E(x,y, 1730) for the solvent. (Reproduced from Ref. [76] with permission. Copyright
(1999) Society for Applied Spectroscopy.)
resolution and parallel imaging capabilities of both techniques allowedfor a direct comparison of surface (XPS) and bulk (FT-IR) measure-ments of polymer blends. To eliminate substrate influence and film-to-film differences, the same areas on the polymer films were analyzed byboth methods. The effect of PMMA molecular weight on surfaceseparation and surface segregation was evaluated by using six blendswith a constant PVC molecular weight and a PMMA molecular weightvarying from 75 to 2132 kDalton. Imaging capabilities of both methodswere used for a qualitative comparison of the heterogeneous structureof the blends, while a quantitative comparison of the bulk and surfacecompositions of the same areas of the samples used small-areaspectroscopy from XPS and FT-IR. On the basis of the quantitativeanalysis, it was concluded that surface segregation of PMMA increaseswith increasing molecular weight. The determination of both surfaceand bulk properties of complex heterogeneous samples is important fora more complete understanding of the structure of complex films.
The application of infrared microscopic imaging to the study of bonedisease and fracture healing was also demonstrated. Samples ofnormal and osteoporotic human iliac crest biopsies were prepared andexamined. Figure 8.14 shows an optical micrograph of the majormineral-containing areas of bone. Two spectral parameters, one that
227
r,I
. tellI -
' --
91,"
: A'*
'. 1
',u ,'
I n r =am
- 1600 mm -
Trabecular Bone
Marrow
Nuclei
"Mineral Rings" -
Haversian canal"
- Osteon
- Cortical Bone
SingleOsteon
Fig. 8.14. Optical micrograph of the major mineral-containing areas of bone. The topfigure shows the spatial relationship between the cortical region, which is part of thecylindrical structure forming the outer shell of compact bone, and the inner regioncontaining trabecular bone and marrow. The bottom figure shows a single osteon inwhich mineral grows in 'tree-ring'-like fashion around the central blood vessel(Haversian canal). (Reproduced from Ref. [78] with permission. Copyright (2000) Society
for Applied Spectroscopy.)
monitors the extent of mineral (hydroxyapatite) formation in the tissueand another that monitors the size/perfection of the crystals, werecompared in the samples generated from normal and pathologicaltissues. Figure 8.15 shows a series of spectra acquired from a 300 mmwide region of normal human trabecular bone. The average minerallevels in the osteoporotic sample were reduced by 40% from the normal.In addition, the crystal size/perfection was substantially enhanced inthe disease state. The applicability of infrared imaging techniques tothe study of therapeutic intervention was also investigated in a study ofthe effects of estrogen therapy on fracture healing in rat femurs.Femurs were examined by IR microscopic imaging four weeks afterfracture. IR imaging showed that the mineral level was enhanced inestrogen-treated samples. In addition, the crystals were larger/moreperfect in the treated specimens. These data demonstrate the utility ofIR spectroscopic imaging for the study of pathological states of hard
228
4-*00400 p-m
UUI0WAr,
I40 2
>0
IToTo
tWavenumber (cm-') I
Fig. 8.15. Series of spectra acquired from a 300 mm wide region of normal humantrabecular bone. (Reproduced from Ref. [78] with permission. Copyright (2000) Society
for Applied Spectroscopy.)
tissue. Finally, Figure 8.16 shows the infrared images of the index ofmineral crystallinity/perfection and a histogram of this quantity for anestrogen treated site in a fractured rat femur and for an untreated site.
Fourier-transform IR microspectroscopy was used to study bonemineralization processes in an in vivo model and in enamel in osteo-genesis imperfecta [78]. The ability of this technique to map new boneformed in implanted macroporous calcium phosphate biomaterial fromsections was reported for the first time. This technique allowed thecorrelation of the microstructure of bone formation in the in vivo modelwith modifications in carbonate and phosphate environments of themineral phases during maturation. Analysis on enamel sectionsrevealed changes in the mineral environment of carbonate andphosphate ions and probably in the size of the enamel crystals. Thesemodifications contributed to the fragility of enamel in osteogenesisimperfecta. The infrared functional group imaging of a part of theimplanted biomaterial and the bone ingrowth provided the visualiza-tion of chemical modifications occurring in biomaterial implants at 20pm spatial resolution. The use of this technique, in conjunction withappropriate sampling methods and data analysis should provide furth-er insight into the molecular structure of mineral phases of calcified
229
I
CD
To
z;
r.
·--119-
m:-
.4: Z= I
00
, I 11 .2
400 pm 1(030)/1( 1020)
$s
-ii
10
.40E 0 10
40
12
1(030)/1( 1020)400 pm
Fig. 8.16. Infrared images of the index of mineral crystallinity/perfection and a histogram
of this quantity for an estrogen treated site in a fractured rat femur (bottom) and for an
untreated site (top). (Reproduced from Ref. [78] with permission. Copyright (2000)
Society for Applied Spectroscopy.)
tissues and help to elucidate mineralization processes, skeletal dis-
orders and properties of the biomaterials used as bone substitute.
The distribution of chemical species and the degree of orientation in
semicrystalline polymer systems have also been studied using fast
Fourier transform imaging [79]. A variety of poly(ethylene glycol)
systems, including pure polymer, high- and low-molecular weight
blends, and blends with amorphous polymers, were studied. It is shown
that fast FTIR imaging can be used to determine the distribution of
species with different molecular weights and can be used to determine
the degree of segregation of different components in blends with
amorphous polymers. Additionally, by employing an infrared polarizer,
230
11
'Y'"
111�
,~K
C)
I -I 12
the degree of orientation was determined in these systems by thegeneration of spatially-resolved dichroic ratio images.
Imaging spectrometry enables passive, stand-off detection andanalysis of the chemical compounds of gas plumes and surfaces overwide geographic areas [80]. The authors described the use of a long-wavelength infrared imaging spectroradiometer, comprised of a low-order tunable Fabry-Perot etalon coupled to a HgCdTe detector array,to perform multispectral detection of chemical vapour plumes. Thetunable Fabry-Perot etalon used in this research provides coverage ofthe 9.5 -1 4-pm spectral region with a resolution of 7-9 cm-l. The etalon-based imaging system provided the opportunity to image a scene atonly those wavelengths needed for chemical species identification andquantification and thereby minimized the data volume necessary forselective species detection. The authors present initial results using abrassboard imaging system for stand-off detection and quantificationof chemical vapour plumes against near-ambient temperature back-grounds. Model calculations were presented comparing the measuredsensitivity of the sensor to the anticipated signal levels for twochemical release scenarios.
In another study, a 64x64 Mercury-Cadmium-Telluride (MCT)focal-plane array detector attached to an FT-IR microscope was used tospectroscopically image 8-pm-thick cross-sections of wheat kernels inthe fingerprint region of the IR spectrum [81]. After fast-Fourier trans-formation of the raw image interferograms, the data can be displayedeither as a series of spectroscopic images collected at individual wave-lengths, or as a collection of infrared spectra obtained at each pixelposition in the image. Image contrast is achieved due to the intrinsicchemical nature of the sample at each pixel location in the image.Individual cell layers near the outer portion of the wheat kernel, as wellas the primary root within the germ, can be clearly differentiated in theIR images as a result of this enhanced chemical contrast.
Micro-imaging spectrometers incorporating focal plane array (FPA)detection require careful demarcation of cold shield aperture size forboth optimal performance and prevention of errors. One study exploredthe effects of changing the diameter of the cold shield aperture on theintensity and spatial homogeneity of the incident radiation [82]. Auniform polystyrene film was repeatedly imaged by using cold shieldsof varying aperture sizes. It was shown that a smaller than optimalaperture size led to image edge clipping, resulting in an inefficient useof the array, lower overall signal, spectral distortions, and higher noise
231
characteristics. Use of an aperture size larger than required caused adecrease in the effective dynamic range of measurements, resulting inhigher noise levels. The advantages and necessity of optimizingimaging spectrometer performance by employing a cold shield with anappropriately sized aperture were discussed.
The penetration of chemical reagents through human hair afterbleaching has been spatially characterized using IR microspectroscopywith a synchrotron source [83]. Chemical imaging of hair cross-sectionsbefore and after bleaching was achieved with high contrast, using thepeptide and lipid mid-infrared absorption bands which are charac-teristic of hair. The ability to make images using functional groups as acontrast mechanism can be applied to studies of other chemical groups,if present, in the structure of the hair. In this study it was shown howthe penetration of an organically active reagent in the hair structurecould be quantified with a spatial resolution of few microns. Theseresults demonstrated that synchrotron infrared microscopy is a power-ful tool for characterizing chemical interactions of hair samples withspecific cosmetic materials.
Infrared spectra of breast tumour cell lines and breast tumourtissues have been measured. Infrared measurements of tumour cellsrevealed that approximately fifteen cells are necessary to obtainspectra of good signal-to-noise ratio using an IR microspectrometerequipped with a conventional IR thermal source [84]. Comparativestudies of human breast tumour cell line suspensions demonstratedthat MCF-7 cells and drug-resistant NCI/ADR cells could be differenti-ated based on their infrared signatures. The most striking differencesbetween MCF-7 and NCI/ADR were found in features assigned to CH2and CH3 stretching vibrations of lipid acyl chains and PO,- stretchingvibrations of nucleic acids. To assess the potential of IR spectroscopyfor the diagnosis of breast tumour tissues, thin sections of tissue weremapped by FTIR microspectroscopy. The spectra of these maps wereanalyzed using functional group mapping techniques and clusteranalysis and the output values of the different approaches were thenreassembled into IR images of the tissues. A comparison of the infraredimages with the standard light microscopic images of the correspond-ing areas suggested that: (i) chemical mapping based on single bandintensities was an easy way to detect microscopic fat droplets withintissue; (ii) the comparison of IR images based on band intensities at1054 and 1339 cm-l provided information on tissue areas containingtumour cells; and (iii) cluster analysis of the spectra was superior to the
232
single band approach and more appropriate for differentiation betweentissue types.
In an different approach, using synchrotron radiation as an ultra-bright infrared source, the authors were able to map the distributionsof functional groups such as proteins, lipids, and nucleic acids inside asingle living cell with a spatial resolution of a few microns [85]. Inparticular, the changes in the lipid and protein distributions in both thefinal stages of cell division and also during necrosis were mapped.
FT-IR microspectroscopic maps of unstained thin sections fromhuman melanoma and colon carcinoma tissues were obtained on aconventional IR microscope equipped with an automatic x, y stage [86].Mapped infrared data were analyzed by different image re-assemblingtechniques, namely functional group mapping ('chemical mapping')and, for the first time by cluster analysis, principal component analysisand artificial neural networks. The output values of the differentclassifiers were recombined with the original spatial information toconstruct images whose colour or grey tones were based on the spatialdistribution of individual spectral patterns. While the functional groupmapping technique could not reliably differentiate between the differ-ent tissue regions, the approach based on pattern recognition yieldedimages with a high contrast that confirmed standard histopathologicaltechniques. The new technique turned out to be particularly helpful toimprove discrimination between different types of tissue structures ingeneral, and to increase image contrast between normal and cancerousregions of a given tissue sample.
Infrared absorption spectroscopy was used with other scatteringand imaging techniques to elucidate the interface reactions leading topermanent chemical bonding of joined hydrophilic wafers upon anneal-ing, and to uncover the thermal evolution of H-decorated defects in H-implanted Si wafers [87]. Detailed mechanisms were proposed wherebythe role of micro-voids as gathering sites for H2 is highlighted and thekinetic interplay between defect formation/evolution, H passivation ofinternal structures and molecular H2 formation was critical forexfoliation to occur.
The demand also of smaller device dimensions drives the need toimprove the lithographic and the metrological tools to produce them[88]. Characterization of the image formation during the lithographicprocess is key to any process control effort. Scanning probe microscopy(SPM) on exposed, unbaked and baked, undeveloped photoresist show-ed morphological details of the image formation process unachievable
233
with other techniques. The use of micro-FT-IR spectroscopy was in-vestigated for latent image chemical analysis. Both of these techniqueswere used in the study of the dependence of the latent image of anegative novolac-based chemically amplified resist, SAL 605 byShipley, with post-exposure bake (PEB) conditions. The objective of theexperiment was to understand how the thermal properties of the resistand the linking reaction taking place were related to each other duringPEB. Experimental results indicated that resist from unexposedregions diffused into the exposed resist during PEB. SPM results showthat this diffusion increased as the PEB temperature rose above theoxide glass transition temperature of the unexposed resist. Theseresults showed that the linker component of the resist, hexamethoxy-methylmelamine, was identified as one of the resist components thatdiffused into the exposed regions during PEB.
Traditional methods of cell wall analysis have provided valuableinformation on wall composition and architecture, but, by having torely on the use of bulk samples, have averaged out this intrinsicheterogeneity. FTIR microspectroscopy addresses this problem byproviding chemical information from an area as small as 10x 10 pm of asingle cell wall fragment or area of a tissue section that has beenimaged with a microscope accessory. The authors have used FTIRmicrospectroscopy as a powerful and extremely rapid assay for wallcomponents and putative cross-links. The spectra were sensitive topolymer conformation, and the use of polarizers in the microscopeaccessory allowed the orientation of particular functional groups to bedetermined, with respect to the long axis of elongating cells. Thespectra constituted species and tissue-specific 'finger-prints', and theuse of classical discriminant analysis may provide the opportunity forcorrelating spectral features with chemical, architectural or rheologi-cal wall properties. Spectral mapping of an area of a specimen allowedthe morphological features resulting from cell growth and differenti-ation to be characterized chemically at the single cell level. In addition,the fidelity of the spectral images was determined by the pixel numberof the focal-plane array [89].
In another study, an instrument was described that simultaneouslyrecorded images and spectra of materials in the infrared fingerprintregion using a long-wavelength infrared focal-plane array detector, astep-scan Michelson interferometer, and an IR microscope [90]. Withthe combination of step-scan Fourier transform Michelson interfero-metry and arsenic-doped silicon Si:As focal-plane array image
234
detection, an infrared spectroscopic imaging system was constructedthat maintained both an instrumental multiplex and multichanneladvantage and operates from approximately 4000 to 400 cm-l. Withthis method of mid-infrared spectroscopic imaging, the fidelity of thegenerated spectral images recorded through the microscope was solelydetermined by the number of pixels on the focal-plane array detector,and only a few seconds of data acquisition time were required forspectral image acquisition. This seamless combination of spectroscopyfor molecular analysis and the power of visualization represented thefuture of infrared microscopy.
8.5 APPLICATIONS TO INDUSTRIAL PROCESS
Recently, a new method for simultaneous determination of vulcanizedrubber additives by FT-IR using partial least-squares regression formultivariate calibration was developed [91]. The effect of various wave-number ranges and the use of the absorbance and first-derivativespectral modes on performance were studied by applying the method tothree different sample batches containing several additives in differentproportions, all of which were resolved with satisfactory results.
In another study, a simpler spectrometer design was employed forindustrial process. A Michelson type interferometer was used wherethe moving mirror was suspended by two fluxes and driven by a coilactuator [92]. Displacement of the mirror was monitored using a muchsmaller transducer with a better thermal stability than the convention-ally used HeNe laser. The beamsplitter is a CaF 2/Si and a thermo-electrically cooled PbSe is used as the detector. The spectral range wasfrom 5000 to 1800 cm-1 with resolution better than 8 cm-l .
Furthermore, the applications of FT-IR spectroscopy to industrialprocesses was greatly benefited by the use of mid-infrared optical fibres[93]. The ability to make measurements at a remote site or as a reactionoccurs offers a significant advance in these types of analyses. Mid-infrared fibres are used to transmit radiation outside of the spectro-meter, to the sample, and then to the detector. A section of the fibre,with the protective cladding removed, is used as the sampling device.In this decladded region the fibre, acting as an internal reflectanceelement, contacts the sample and provides the chemical information foranalysis. In one example, the use of a fibre to monitor the progress of acuring reaction in thermoset composite materials where the fibre wasimbedded in the matrix was studied.
235
Chalcogenide glass fibres based on sulphide, selenide, telluride andtheir rare earth doped compounds are being actively investigatedworldwide [94]. Great strides have been made in reducing optical lossesusing improved chemical purification techniques, but further improve-ments are needed in both purification and fiberization technology toattain the theoretical optical losses. Despite these problems, currentsingle-mode and multimode chalcogenide glass fibres are enablingnumerous applications. Some of these applications include laser powerdelivery, chemical sensing, imaging, scanning near field microscopy/spectroscopy, fibre infrared sources/lasers, amplifiers and opticalswitches.
8.6 APPLICATIONS TO ORGANIC THIN FILMS
In recent years, functional organic thin films have received keeninterest in the field of molecular electronics because of an increasingawareness that functional organic thin films exhibit a variety ofinteresting functions [95-97]. A number of molecular devices have beenproposed that are based on organic thin films such as Langmuir-Blodgett (LB) films with nonlinear optical properties, photovoltaiccells, piezoelectric and pyroelectric devices, resistance and conductingmaterials, and chemical and biological sensors. To sufficiently under-stand the functions of functional organic thin films, it is necessary toinvestigate the arrangement and orientation of molecules in a film, andfurther, structures (e.g., conformations, chemical bonds, intermolecu-lar interactions, electronic states) and the like. In addition, knowledgeabout the relationship between functions and structures is essential todesigning of a new organic thin film. While methods of exploring thestructure of an organic thin film include x-ray diffraction, atomic forcemicroscopy, ultraviolet and visible spectroscopy, fluorescence spectro-scopy, ESR, infrared spectroscopy, Raman spectroscopy, etc., theinfrared spectroscopy we describe in this section can be said to beprominent in terms of the diversity and quantity of information and thesimplicity of measurement [95-99].
8.6.1 Infrared spectra of Langmuir-Blodgett films
We will mainly describe here infrared studies on LB films which areattracting the greatest attention among a variety of organic thin films.In the following, LB films such as those shown in Fig. 8.17a and b will
236
(a) Y-type
(b) Y'-type
Fig. 8.17. Structure of (a) Y-film and (b) Y'-film.
237
C n H 2n+1
n=12; Dodecyl-TCNQn=15; Pentadecyl-TCNQn=18; Octadecyl-TCNQ
Fig. 8.18. Structure of 2-alkyl-7,7,8,8-tetracyanoquinodimethane.
be referred to as the Y-film and the Y'-film, respectively. When used forstructural investigations on LB films, infrared spectroscopy isadvantageous in the following points.1. It is possible to measure a spectrum non-destructively at room
temperature under a normal pressure.2. Operations for measurement of spectra are relatively easy.3. It is possible to measure a spectrum of even a one-layer LB film.4. Since an infrared spectrum can be measured for an LB film, a
solution, a solid and a crystal, one can compare a structure of asample in the LB film with structures of the sample in other states.
5. Various types of infrared measurement methods (transmissionmethod, the ATR method (Section 7.2.1), the RA method (Section7.2.4), a surface-enhanced method, etc.) may be applied.
As a vibrational spectrum sensitively reflects the arrangement ofatomic nuclei and nature of chemical bonds within a molecule, or aninteraction between the molecule and a surrounding environment it issuitable very much to study the molecular aggregation, orientation,and structure in an LB film. Knowledge obtained from infrared spectraof LB films are summarized as follows.1. Orientation of molecules; whether hydrocarbon chains and chromo-
phores are perpendicular to a substrate or tilted with respect to thesubstrate normal, etc. It is also possible to quantitatively estimate atilt angle [100-102].
2. Sub-cell packing of hydrocarbon chains [103,104].3. Conformations of hydrocarbon chains; whether hydrocarbon chains
have trans-zigzag structure or partially contain gauche forms, etc.[105,106].
238
4. Structures of chromophores; the conformation, chemical bonds, andelectronic states of chromophores and interactions betweenmolecules, etc.
5. Interactions between the substrate and the first layer.Infrared spectroscopy is useful not only for structural characterizationof an LB film, but also usable to assess whether the LB film has a highquality based on the knowledge (1) to (3).
8.6.2 What we can learn from infrared spectra of LB films
We will describe in more detail what we can learn from infrared spectraof LB films, citing an example of an LB film of 2-octadecyl-7,7,8,8-tetracyansquinodimethane (octadecyl-TCNQ) (see Fig. 8.18). Figure8.19 shows infrared spectra of octadecyl-TCNQ in a powder, in a bromo-form solution, and in a ten-layer LB film (the Y-film) [107]. In general,when we measure an infrared spectrum of dye molecule with a longhydrocarbon chain such as octadecyl-TCNQ, we typically observe infra-red bands due to the hydrocarbon chain and bands due to the chromo-phore. As the former, we can expect bands due to CH3 degeneratestretching, CH3 symmetric stretching, CH2 antisymmetric stretching,CH 2 symmetric stretching, CH 2 scissoring, and CH2 rocking vibrations.In the bottom spectrum of Fig. 8.19, bands at 2955, 2918, 2847, 1462 and1417 cm-l are assigned to CH3 degenerate stretching, CH2 antisym-metric stretching, CH2 symmetric stretching and CH 2 scissoringvibrations (CH 2 scissoring vibrations appear as a doublet). Although aband due to CH3 symmetric stretching vibrations should appear in thevicinity of 2875 cm-l, this band is weak and therefore cannot berecognized in the spectrum [107]. Furthermore, a band arising from theCH 2 rocking vibration is generally expected to appear in the vicinity of725 cml. Infrared bands due to the chromophore portion can be classi-fied into bands assigned to in-plane and out-of-plane vibrations. Bandsat 2223, 1546, and 1530 cm-' in the spectrum of the LB film are allbands due to in-plane vibrations of TCNQ portion, and assigned to C-Nstretching, C=C stretching and C=C stretching vibrations, respectively[107]. In general, for analysis of an infrared spectrum of an LB film, weusually identify bands due to a hydrocarbon chain first, and thereafterlook for bands arising from a chromophore. However, it is sometimes noteasy to distinguish a band due to CH2 scissoring vibrations from a banddue to the chromophore. In such a case, we may be able to distinguish
239
WILIz
coma:0C,)4
4000 3600 3200 2B00 2400 2000 1600 1200WAVENUMBER(cm')
Fig. 8.19. Infrared transmission spectra of octadecyl-TCNQ in a powdered micro-crystalline state (top), octadecyl-TCNQ in a bromoform solution (middle), and 10-layerLB film of octadecyl-TCNQ deposited on both sides of a CaF 2 substrate (bottom).(Reproduced from Ref. [1071 with permission. Copyright (1991) American Chemical
Society.)
them by measuring a spectrum of chromophore only which does nothave a hydrocarbon chain.
Now, what kind of information does a spectrum such as that shownin the bottom of Fig. 8.19 provide? First, we can obtain informationregarding the conformation of a hydrocarbon chain from thefrequencies of CH2 antisymmetric and symmetric stretching bands[105,106]. These bands are known to appear in the vicinity of 2918 cm -1
and 2848 cm - l, respectively, when the hydrocarbon chain assumestrans-zigzag structure but shift to the higher-wavenumber side if thehydrocarbon chain contains some gauche forms. Hence, the result
240
1 | h x
t1
shown in Fig. 8.19 tells us that the hydrocarbon chain of octadecylTCNQ has trans-zigzag conformations while in the LB film and solidpowder but contains a considerable number of gauche forms while in asolution [107].
We can learn about subcell packing of hydrocarbon chains frombands due to CH2 scissoring mode [103,104]. The CH 2 scissoringvibrations appear as a doublet at 1471 and 1462 cm-l when thehydrocarbon chains take orthorhombic subcell packing, but as a singleband at 1467 cm-l when the chains assume hexagonal subcell packing.
Since bands due to a CH2 scissoring vibration appear as a doublet inthe top and bottom spectra of Fig. 8.19, it is considered that thehydrocarbon chains of octadecyl-TCNQ assume orthorhombic subcellpacking both in the solid powder and the LB film (in the spectrum of thesolution in Fig. 8.19, the CH2 scissoring vibration appears as a singletband as it is naturally expected). However, special care must be takenfor the LB films of octadecyl TCNQ where the hydrocarbon chainsassume interdigitated and non-interdigitated parts. Morita et al. [108]assigned the two bands at 1471 and 1462 cm-l of the LB films ofoctadecyl-TCNQ to the CH2 scissoring modes of non-interdigitated andinterdigitated parts of the hydrocarbon chain.
If one wishes to study the molecular orientation in an LB film, onemust compare an infrared transmission spectrum with an infrared RAspectrum (Chapter 7.2.4). Let us introduce a simple example ofcomparison between a transmission spectrum and an RA spectrum.Figure 8.20 shows a transmission spectrum and an RA spectrum ofseven-layer LB films of cadmium stearate [102]. We can readily noticethe remarkable differences in the intensities of infrared bands betweenthe two spectra. It is these differences in the intensities that allow us todiscuss the molecular orientation in an LB film.
Now, let us consider which bands will appear strongly in thetransmission spectrum on an assumption that the molecular axis ofcadmium stearate is nearly perpendicular to a substrate (see Fig. 8.21).In the case of a transmission method, since an electric vector of aninfrared ray is parallel to the substrate, strong bands are those due tovibrations whose transition moments are perpendicular to the molecu-lar axis, such as CH2 antisymmetric and symmetric stretching vibra-tions (2919 and 2851 cm-l in Fig. 8.20, bottom), COO- antisymmetricstretching vibration (1543 cm l) and CH2 scissoring vibrations (1473and 1463 cm-l), whereas bands whose transition moments are parallelto the molecular axis, such as COO symmetric stretching vibration
241
v, COO-
0.02 vs CH2 vCH2 E
P V I c2 ll I r C00-l IcoCH2
fi 3 R00 1 8 0 0 1800 1 200Co
0coCo<g
3000 2800 1800 1600 1400 1200
WAVENUMBER(cm- )
Fig. 8.20 Infrared RA and transmission spectra of seven-layer LB films of cadmiumstearate on silver and ZnSe plates, respectively. (Reproduced from Ref. [102] with
permission. Copyright (1990) American Chemical Society.)
(1433 cm -1 ) and CH2 wagging vibrations (which appear as a series ofbands in the 1350-1200 cm-1 region), should be rarely observed. Thetransmission spectrum in Fig. 8.20 strongly supports the hypothesisdescribed above. According to the surface selection rule in infrared RAspectroscopy [100,101], molecular vibrations whose transitionmoments are perpendicular to a substrate surface appear strongly inan RA spectrum. As we have assumed above, if the molecular axis of thehydrocarbon chain is perpendicular to the substrate, COO- symmetricstretching and CH2 wagging vibrations (when a hydrocarbon chain hastrans-zigzag conformation, as all CH 2 groups vibrate in the same planeand couple with each other, a series of bands (band progression)appears which expresses phase differences of the vibrations) shouldappear as strong bands in the RA spectrum. Figure 8.20 exactly showsthis in reality, and accordingly proves that the hypothesis above iscorrect.
One may be able to quantitatively discuss the molecular orientationbased on comparison of the intensity of each band between the trans-mission spectrum and the RA spectrum. From the comparison of thetwo spectra shown in Fig. 8.20, Umemura et al. [102] calculated themolecular orientation in the LB film of cadmium stearate as shown inFig. 8.21.
242
TransmissionvaCH2
CH COO
77A77727 A\CH2
i I I , . i k F q q r
I - - - - - _ _ __ _ _I
I
IIIIIIIIIIIII
-18°
- 7o- 83'
TT11TTT777TTTTTT7, ..1111 1 ............
Substrate
Fig. 8.21 Calculated tilt angles in an LB films of cadmium stearate. (Reproduced fromRef. [102] with permission. Copyright (1990) American Chemical Society.)
Figures 8.22a and b compare infrared transmission and RA spectraof three-layer LB films of octadecyl-TCNQ [107]. Of particular note inFig. 8.22 is that the intensities of the bands due to in-plane TCNQmodes are much stronger in the RA spectrum than in the transmissionspectrum (it should be noted that three-layers of octadecyl-TCNQ aredeposited on both sides of a CaF2 substrate). Therefore, it seems thatthe TCNQ plane is nearly perpendicular to the substrate surface.
Transition moments of the two C=C stretching bands at 1547 and1531 cm-l are parallel with the molecular axis of the TCNQ chromo-phore and perpendicular to it, respectively. The relative intensity of thetwo bands is reversed between the transmission and RA spectra, but itshould be noted that both have comparable intensities in the twospectra. Therefore, it may be concluded that the molecular axis of theTCNQ chromophore is neither parallel nor perpendicular to thesurface, being in an intermediate direction [107]. The intensities of CH2antisymmetric and symmetric stretching bands are comparablebetween the transmission and RA spectra, suggesting that the alkylchain is tilted considerably with respect to the surface normal.
8.6.3 Three examples of infrared studies of LB films
In the following part of this section three examples of infrared studiesof LB films are discussed. For LB films of dodecyl-, pentadecyl-, and
243
LUz
M0C,)M
4000 3600 3200 2800 2400 2000 1600 1200 800WAVENUMBER(cm")
Fig. 8.22. A comparison of (a) infrared transmission and (b) RA spectra of three-layer LBfilms of octadecyl TCNQ. (Reproduced from Ref. [107] with permission. Copyright (1991)
American Chemical Society.)
octadecyl-TCNQ, not only molecular orientation and structure, but alsomolecular aggregation, morphology, and thermal behaviour have beenexplored by infrared and ultraviolet visible (UV-Vis) spectroscopy andatomic force microscopy [109-113]. The following conclusions could bereached about the morphology and thermal behaviour of the LB films ofalkyl-TCNQ: (i) The LB films of octadecyl-TCNQ consist of numerousplatelet micro-crystal domains, which have the layered assemblyformed by bi-molecular layers with a thickness of 3.7 nm. A periodicarrangement of octadecyl-TCNQ molecules with a period of 0.85 nmcan be observed inside the domains. The domains in the first layer (4.3nm) are thicker than those above the first layer (3.7 nm). In the case ofthe first layer, the direct interaction between the substrate andoctadecyl-TCNQ molecules plays an important role in determining thethickness. (ii) A one-layer LB film of octadecyl-TCNQ shows gradualthermally-induced structural changes while its multi-layer films showabrupt changes. The order-disorder transition in a multi-layer LB filmof octadecyl-TCNQ with the longer even-numbered hydrocarbon chain
244
o
0rC,0
(A
0
.0
en.0
Wavenumber/cm-1 Wavenumber/cm-1
eo
ID0
enC
(d) 1471
CD I 1 1462a
a II
.0 I· E!~ ~ I
1580 1560 1540 1520 1500 1500 1480 1460 1440
Wavenumber/cm-1 Wavenumber/cm-1
Fig. 8.23. Enlargement of time-dependent changes in the infrared RA spectrum of a one-layer LB film of pentadecyl-TCNQ on a gold-evaporated glass slide. (a) 3000-2800 cm - 1
region; (b) 2250-2190 cm-l region; (c) 1580-1500 cm-1; (d) 1500-1440 cm-1 region. Thespectra were obtained from 6 to 131 min after the film deposition. (Reproduced from Ref.
[108] with permission. Copyright (2000) American Chemical Society.)
occurs at a higher temperature than that in the corresponding LB filmof dodecyl-TCNQ with the shorter even-numbered hydrocarbon chain.A multi-layer LB film of pentadecyl-TCNQ with the odd-numberedhydrocarbon chain shows a transition temperature similar to thecorresponding film of dodecyl-TCNQ.
Infrared spectroscopy has also been employed to investigate agingeffects on molecular orientation and structure in LB films of dodecyl-,pentadadecyl-, and octadecyl-TCNQ [108]. Figures 8.23a-d show time-dependent changes in the 3000-2800, 2250-2190, 1580-1500, and1500-1440 cm- l regions of the infrared RA spectrum of a one-layer LBfilm of pentadecyl-TCNQ, respectively [108]. The spectra were meas-ured between 6 and 131 min after the film deposition. It is noted in the
245
3000-2800 cm- region that the bands due to the CH2 antisymmetricand symmetric stretching modes increase with time. This suggests thatthe alkyl chain is nearly perpendicular to the substrate surface in theLB film just after the film deposition, but that it becomes tiltedgradually with time.
The relative intensity of the two bands at 1471 and 1462 cm-assigned to CH2 scissoring modes of non-interdigitated and inter-digitated parts of the alkyl chain, respectively, changes as a function oftime (Fig. 8.23d). This result indicates that the proportion of theinterdigitated parts increases with time probably because of theevaporation of water molecules. Figures 8.23b and c reveal that theintensities of the C=C and C=C stretching bands increase during thetime course and that the relative intensity of the two bands at 1547 and1531 cm 1 varies. These observations lead to the conclusion that theTCNQ plane becomes more perpendicular with respect to the substratesurface and the molecular axis of the TCNQ chromophore becomesmore tilted with respect to the surface normal with time. Based uponthe observations in Fig. 8.23, Morita at al. [108] have proposed apossible model for time-dependent orientational changes in a one-layerLB film of pentadecyl-TCNQ. Figure 8.24 depicts the model [108].
One-layer LB films of dodecyl-TCNQ also show similar time-dependent changes, but the changes are much smaller than those forthe films of pentadecyl-TCNQ. One-layer LB films of octadecyl-TCNQdo not show appreciable time-dependent infrared spectral changes.
Fig. 8.24. Possible model for time-dependent (a) orientational and (b) morphologicalchanges in a one-layer LB film of pentadecyl-TCNQ. (Reproduced from Ref. [108] with
permission. Copyright (2000) American Chemical Society.)
246
The differences in the aging effects among the one-layer LB films of thethree kinds of alkyl-TCNQ may be caused by the differences in thestrength of the hydrophobic interaction between the interdigitatedalkyl-chains and in the degree of three dimensional microcystal growthin the one-layer LB films.
Ikegami et al. [114] studied structural changes in Langmuir (L) andLB films of 2-methyl-5-octadecyl-N, N'-dicyanoquinonediimine(C,,MeDCNQI) induced by charge-transfer (CT) reaction at the air-water interface by use of infrared and UV-Vis spectroscopy. Compari-son of UV-Vis spectra of pure C,,MeDCNQI L films with those ofC, 8MeDCNQI-CuI mixed L films suggests that CT reactions take placeat the air-water interface in the latter case. These L films weredeposited onto solid substrates as LB films by the horizontal liftingmethod. Polarized infrared and UV-Vis spectra and X-ray diffractionpatterns of the LB films indicate that an interdigitated bi-layer struct-ure of the pure films changes into a mono-layer structure for the CTfilms.
Figure 8.25 shows infrared spectra in the 3200-2700 cm-l region ofLB films of pure C,,MeDCNQI and the 1:5 mixture of C,,MeDCNQIand CuI [114]. The antisymmetric and symmetric stretching bandsappear at 2918 and 2848 cm-l, with the line widths of 14 and 11 cm-l,respectively, in the spectrum of pure C,,MeDCNQI film. The linewidths of these bands reflect the mobility of alkyl chain. Therefore, it is
0
a'o
n
ro
0C,
co.0
na
3.2 3.1 3.0 2.9 2.8 2.7wavenumber (103 cm-1 )
Fig. 8.25. Structure of Cis8MDCNQI and polarized infrared spectra in the 3200-2700cm -1 region of 56-layer LB films of (a) pure CMe,DCNQI and (b) a 1:5 mixture of
CNeDCNQI and Cul. Incident angle is 60 °.
247
wavenumber (103 cm- 1)
Fig. 8.26. Polarized infrared spectra in the 2300-1300 cm - 1 region observed for 56-layerLB films of (a) a pure C18MeDCNQI and (b) a 1:5 mixture of C1 8MeDCNQI and Cul. Theangle of incidence is 60° . (Reproduced from Ref. [114] with permission. Copyright (2000)
American Chemical Society.)
concluded that alkyl chains of C,,MeDCNQI molecules are closelypacked with highly ordered trans conformation in the LB film ofC,8 MeDCNQI. The corresponding bands are observed at 2921 and 2851cm-' with the line widths of 22 and 14 cm-', respectively, for the CTfilm, indicating that the alkyl chains in the CT film are rather looselypacked with non-negligible content of the gauche conformation.
Figure 8.26 depicts the tilting-incident polarized infrared absorp-tion spectra of an LB film of C,,MeDCNQI and a CT film ofC,sMeDCNQI and CuI [114]. In Fig. 8.26a, bands due to C=N (a'v 5 anda'v6), C=C (a'vs), C=N (a'vg), and C-C (a'vl2) stretching modes areobserved ; the vibrational modes are numbered as a'vm, according toLunardi and Pecile [115]. The CT degree in the LB film of C18MeDCNQIand CuI was estimated to be -1 by the downward shifts of the C=C andC=N stretching bands [114]. It is noted in Fig. 8.26 that all the infraredbands observed for the CT film are stronger with s-polarized light andthat the a'v8 and a'v,,2 bands for the LB film are more intense with p-polarized light. It is also of note that the C-N stretching bands and theelectronic excitations show stronger intensity with the s-polarizationfor both films. Therefore, it seems likely that the long axis of theDCNQI plane preferentially lies in the film plane in both films and itsshort axis is nearly perpendicular to the film plane in the pure film andlies in the film plane in the CT film.
248
Ikegami et al. [114] estimated the orientation of the alkyl chain andchromophore in the LB films of C18MeDCNQI and C, 8MeDCNQI-CuIbased upon the method proposed by Chollet and Messier [101]. Cholletand Messier showed that it is possible to take into account the multiplereflection due to the thin films and to calculate the out-of-planeorientation order parameter of a vibrational mode, S = <3cos20-1>,where 0 is an angle between the transition dipole moment and thenormal axis of the film plane, as
S=2-3(1+ n2B nln32C)
B= os n + Cos A() -cos cos 3Ap(O) (8.9)nl +- I
C = sin 1 sin/3 {A(0) + A (0)
where nl, n2, and n3 denote the refractive indexes of air, a LB film, and asubstrate, respectively; Ap (y) and As () are the absorbance due tothe transition moment with the angle of incidence being yl. w2 and W3denote an angle of reflection in the LB film and that in the substrate,respectively.
Ikegami et al. [114] calculated the S parameter for the alkyl chainby the following equation:
S (chain) = -S(va(CH2)) - S(vs(CH2)) (8.10)
where S (chain) is the S parameter for the alkyl chain and S(Va(CH 2)) -S(vs(CH 2)) are those of CH 2 antisymmetric and symmetric stretchingmodes, respectively. The averaged tilt angle of the alkyl chain wascalculated to be 40 and 50 °, respectively, for the pure LB and CT films.Similarly the averaged tilt angles of the long and short axes of theDCNQI group were estimated to be about 75 and 30 °, respectively, inthe pure LB film, and those in the CT film were calculated to be bothabout 70 ° .
Taking account of all information obtained from infrared spectro-scopy and x-ray diffraction patterns, Ikegami et al. [114] proposedpossible averaged structures of the LB and CT films as shown in Fig.8.27. As in the case of the LB films of alkyl-TCNQ, an interdigitated bi-layer structure was considered for the LB films of C, 8MeDCNQI.
Hasegawa et al. [116] investigated a hydrogen bonding networkformed between accumulated LB films of barbituric acid and
249
(b)
-- iW3-'Al-----~ ~ ~ ~ ~ 6
II84A-
'.4 A -
(c)Cu 1120 /
- ; 3 . t te
_- - - - - -
Fig. 8.27. Schematic illustration of(a) C1,MDCNQI molecular shape (rotational freedomis assumed for the connecting point between the C18MeDCNQI group and alkyl chain); (b)possible structure of pure LB films of Cs1MeDCNQI; (c) possible structure for CT LB filmsof the CMeDCNQI-Cul mixture. (Reproduced from Ref. [1141 with permission.
Copyright (2000) American Chemical Society.)
triaminotriazine derivatives (C,,BA and 2 C 8sTAZ) by use of infraredspectroscopy. They deposited the LB films at various surface pressureson a gold-evaporated glass slide covered with a deuterium cadmiumstearate (CdSt-d35) mono-layer. The layer configuration of IR//C,,BA/2C,,TAZ/CdSt-d35 /Au gave the most interesting results. The C,,BAlayer was deposited at various surface pressures on the 2 C,,TAZ mono-layer. Figure 8.28 shows the structures of C,,BA/2 C,,TAZ and RAspectra of accumulated C,,BA/2 C,,TAZ LB films deposited on CdSt-d 35monolayer on a gold-evaporated glass slide. At a low surface pressure(5 and 10 mN m-') of C,,BA monolayer, an Amide I (C=O stretching)band at 1740 cm-l arising from C1sBA almost disappears, and instead, astrong band appears at around 1700 ml. This observation suggeststhat the C=O group interacts with TAZ moiety through stronghydrogen bonding. A marked change takes place at 15 mN m-l; a newband appears at 1755 cm- '. This band becomes a dominant band whenthe surface pressure is increased to 20 mN m-l. The band at 1754 cm-lis characteristic of carbonyl group of BA, and it appears at 1754 cm-l
250
,
0 0
H'OA N--N
C ,-RA or. T7
m-1
-lI'- "'18^'4 Wavenumber I cm'' Wavenumber I cm'
Fig. 8.28. Structure of C18BA and 2G8TAZ and RA spectra of accumulated C1 8BA and2G8TAZ LB films deposited on Cd stearate-d 35 monolayer on a gold-evaporated glassslide. The C18BA monolayers were prepared at various surface pressures on 2G8 TAZmonolayer that was prepared at the fixed surface pressure, 20m Nm 1. (Reproduced from
Ref. [116] with permission. Copyright (2000) American Chemical Society.)
when BA molecules are dispersed in an argon matrix. This band showsa downward shift by about 60 cm-l, when BA is in the solid state at 20Kdue to hydrogen bonding formation. Therefore, it is very likely that theaccumulated layer has free C=O groups at 15 and 20 mN m -l .
With the increase in the surface pressure great changes are alsoobserved in the C-H stretching vibration region. At low surfacepressure both CH2 asymmetric and symmetric stretching bands arevery weak. When the surface pressure is increased to 15 mN m-l, theintensities of the bands increase largely. It is likely that the alkylchains tilt from the surface normal above 15 mN m-l. The CH 2 asym-metric and symmetric stretching bands appear at 2919 and 2850 cm- 'irrespective of surface pressure. This indicates that the alkyl chainsare highly organized and the molecular configuration is trans-zigzag.
The N-H stretching band shifts from 3144 and 3112 cm l upongoing from 5 to 20 mN m -l . This result suggests that the hydrogenbonding through the N-H group becomes stronger with the surfacepressure.
The tilt angles of the alkyl chain in the accumulated layer and theunder layer as a function of the surface pressure were calculated by a
251
30
· 25
I 20
C
5
ao
O
0 5 10 15 20 25Surface pressure of C BA monolayer I mN m"-'
Fig. 8.29. Tilt angle changes of alkyl chains in the accumulated layer and the underlayershown by solid and dashed lines, respectively. (Reproduced from Ref. [116] with
permission. Copyright (2000) American Chemical Society.)
procedure proposed by Hasegawa et al. [116]. The procedure can takeanisotropic optical constants into account. This allows one to take anymolecular orientation into account to yield expected absorbance. Fordetailed description, readers are referred to the literature. Figure 8.29illustrates changes in tilt angles of alkyl chains in the accumulatedlayer and the under layer shown by solid and dashed lines, respectively[115]. Figure 8.30 shows schematic models of the accumulated layer ata low and a high surface pressure of C,,BA, respectively [116]. At lowsurface pressures, the alkyl chains stand almost perpendicularly to thefilm surface. The chains stand perpendicularly also in the side view. Inthe same view BA and TAZ planes are a little tilted because of theconfiguration of the nitrogen atom. It is particularly noted that C,,BAand 2C1 8TAZ molecules are complementarily hydrogen bonded andthere is no free NH2 or C=O group.
The alkyl chain tilts 10° or 12° from the surface normal (Fig. 8.30b)at high surface pressure [116]. The coupling mechanism of the C,,BAand 2C,,TAZ molecules is largely different from that at low surfacepressure. The hydrogen bonding coupling is imperfect at high surfacepressure; one of the C=O groups in a BA ring remains as a free C=O
252
·.®under-layer
accumulated layers
. ' I I -
JjI
(a)
C18BA
2C18TAZ
Front view ofBA I TAZ: (BA at 5 and 10 mNm-1) Side view
5';
(b)
C18BA
free
2C18TAZ
/.-rFront view ofBA I TAZ: (BA at 15 and 20 mNm-1) Side view
Fig. 8.30. Schematic views of the accumulated layers. The images at (a) low surfacepressure and (b) high surface pressure are drawn. (Reproduced from Ref. [116] with
permission. Copyright (2000) American Chemical Society.)
253
group. It is very likely that the band at 1755 cm-l arises from this freeC=O group.
The highly condensed monolayer is formed when the surfacepressure of the C,,BA monolayer is high. It is difficult for the highlycondensed monolayer to incorporate into the condensed 2C,,TAZ mono-layer deeply. In other words, the interaction between the two layersbecomes weak. Therefore, the molecular aggregation by lateral hydro-phobic interaction plays a dominant role to lead the film to have a close-packed structure; the tilted stance is known to be most stable. Thus,the conclusion that the molecular tilting stance about 10° with all transconformation seems to be reasonable [116].
8.7 DEVELOPMENTS IN INFRARED SPECTROSCOPY OF BIOLOGICALMOLECULES AND MATERIALS
Infrared studies of biological molecules and materials have a longhistory [117-133]. As early as 1911, W.W. Coblentz [117] pointed outthat infrared spectroscopy had considerable promise in the studies ofbiological samples. One can find a number of papers published in the1950s reporting even medical applications of infrared spectroscopy[118,119]. In the 1960s infrared spectroscopy was extensively em-ployed to investigate the secondary structure of proteins [119]. Therelationship between the secondary structure elements of proteins andthe frequencies of amide I and amide II bands was found in the early1960s. Infrared spectroscopy was also applied to explore the hydrogenbonds of nucleic acid bases. Before NMR became a powerful tool forinvestigating the structures and functions of biological molecules andmaterials, infrared spectroscopy had been a major technique forstructural studies of biological molecules [119].
In 1971 one very famous book on biological applications of infraredspectroscopy was published [119] in which can be found many inter-esting applications even to microbiology and medicine. However, in the1970s infrared spectroscopy did not receive keen interest frombiological scientists because NMR and Raman spectroscopy, which arevery suitable for aqueous solutions or physiological conditions, weredeveloping rapidly. The revival of infrared studies on biological mater-ials happened in the 1980s because of the rapid development of FTtechniques which opened up a variety of possibilities for infraredmeasurements; for example, infrared measurements under physio-
254
logical conditions, time-resolved measurements, and measurements ofmicro samples became popular [121-131].
Infrared spectroscopy has several advantages for the studies ofbiological molecules and materials over other techniques such as NMR,CD, fluorescence, Raman, and X-ray crystallography [121-131]. First,it is possible to measure high-quality spectra of biological molecules ina variety of states such as aqueous solutions, films, crystals, andorganic solutions. Second, very small amounts of samples are enough toobtain good spectra and no or very little pretreatments are requestedfor the infrared measurements. Infrared spectroscopy is free from thelight-scattering (CD) or fluorescence (Raman) problem, and does notdepend on the molecular weight of biological molecules (NMR).Another important feature of infrared spectroscopy is the potential ofslow and first kinetic studies of biological molecules [127].
Today, biological applications of infrared spectroscopy may bedivided into three categories [122]. One is structural studies of bio-logical molecules such as proteins, lipids, nucleic acids, and biologicalpigments [123,124,126,127,130,131]. Another is investigations ofdynamics and excited states of biological molecules [125-127]. Repre-sentative examples of this category are studies of protein dynamics,mechanism of photosynthesis, and light-induced mechanism of bact-eriorhodopsin; time-resolved infrared spectroscopy and low-temp-erature infrared spectroscopy are usually employed for theseinvestigations. Yet another category is biomedical applications ofinfrared spectroscopy [128,129,132]. This category involves wide-spread researches and applications from non-destructive identifi-cations of bacteria, in situ determination of blood sugar to diagnosis ofcancer cells. In this section, representative examples selected fromeach category are introduced.
8.7.1 Infrared spectra of proteins
Most infrared studies of proteins are concerned with the conformationof peptide backbones, but there are some other interesting and import-ant infrared studies such as those on structures and functions ofchromophoric groups like hemes and retinals, the microenvironmentsof amino acid residues like cysteine residues (Cys) and the hydrogenbonding of water molecules in proteins [121-127,130,131,133-135]. Wediscuss here infrared studies of the secondary structure of proteins;
255
infrared studies of photoreceptor proteins will be described in Section8.7.6.
Infrared spectroscopy is powerful in investigating the conformationof the peptide backbones of proteins because the frequencies of amide Iand amide II bands are very sensitive to the conformation. Thus, byanalyzing the amide I and/or amide II band regions, one can estimatethe percentage of each structure element like a-helix, p-structure andrandom coil structure [123,124,130-135]. However, detailed quanti-tative analysis of amide I and amide II bands is not always an easy taskbecause a number of bands due to various secondary structures overlapheavily. Table 5.2 summarizes the relationship between the frequencyof amide I band and the secondary structure. For the analysis of theoverlapping amide bands, various spectral analysis methods have beenproposed [124,126,130-133]. Most are frequency-based methods whichrely on peak assignments in either second derivative or deconvolutedspectra. Recently, chemometrics [132] and two-dimensional (2D)correlation spectroscopy [133] have also been introduced to explore theamide I band region. The second derivative, deconvolution and 2Dcorrelation spectroscopy, enhance band resolution, enabling one toidentify the different structures in a protein and also to monitorstructural variations induced by protein denaturation. Calculation ofdifference spectra is also very useful to probe conformational changescaused by perturbation (for example, temperature, pH, and detergent)because the resultant difference spectrum only yields bands that arerelated to the groups involved in the conformational changes. Forquantitative analysis curve-fitting is often employed [124]. This anal-ysis usually provides a very good estimate of the secondary structurewhich is in good agreement with that obtained by x-ray crystallographyand CD spectroscopy. However, it must be kept in mind that the curve-fitting method needs some assumption. For example, it assumes thatthe amide bands arising from different secondary structures have theidentical molar absorptivities. Moreover, the curve-fitting analysisrequests precise assignments of all the component bands and the initialchoice of input parameters (the number of component bands and theirfrequencies and widths).
The potential of 2D correlation spectroscopy in the analysis of amideI and II regions is described in Section 9.7. The chemometrics methodneeds to use a calibration matrix of the infrared spectra of proteins ofknown x-ray structure [132]. Among various multivariate methods,partial least squares (PLS) and factor analysis (FA) are employed for
256
1750 1700 1650 1600 1550 1500
Wavenumber (cm-')
(b)
20°C
1750 1700 1650 1600
Wavenumber (cm-')1550 1500
Fig. 8.31. Temperature-dependent spectral changes of deconvoluted infrared spectra ofhuman transferrin receptor in D2 0. (a) pH 7.4, (b) pH 5.6. (Reproduced from Ref. [134]
with permission. Copyright (1994) Elsevier.)
the quantitative analysis of infrared spectra of proteins. This methodencounters difficulties when the spectral properties of the unknownprotein are not involved in the properties of the spectra within thecalibration set.
The amide I band region is particularly useful for monitoringstructural changes caused by protein denaturation. Figures 8.31 and8.32 show an example of infrared studies of protein denaturation [134].Figure 8.31 compares effects of temperature on deconvoluted spectra ofhuman transferrin receptor in D2 0 between extracellular pH (pH 7.4)and endosomal pH (pH 5.6). The quantitative analysis of the amide Iregion shown in Fig. 8.31 by Hadden et al. [134] indicated that theprotein consists of 56% a-helix, 19% P-sheet, and 14% turns at extra-cellular pH.
257
PH 7.4 1617cm l 1640cm-1 -14cmpH 7.4 1617 cm-1
1640cm- 1655cm 1 6 8 3 cm1 1549cm-
(I(U
n0.0
I
,AAAAAAAAAAA.&A A AA . . M ask
..
----As -- -----._-- ·. !. ------------------
III 60 so i M iiii · A 9.
I I iI I I Ittttt11 I
0 40 60 80 60 an n
Temperature (C)
H 5.6 61 140cmpH 5.6 1617 cm
- 11640cm
-11655cm
-11683cm
- 11549cm
- 1
a,C(U-ePco0'
/AA :.-... .
·1,(b) ................UI
-----__ _-IU
20 40 60 80 60 40 20Temperature (C)
Fig. 8.32. Temperature-dependent intensity variations of selected bands in deconvolvedspectra of human transferrin receptor in D2 0. (a) pH 7.4, (b) pH 5.6. (Reproduced from
Ref. [134] with permission. Copyright (1994) Elsevier.)
Figure 8.32 compares temperature-dependent intensity variationsof selected bands in the deconvoluted spectra of transferrin receptor atpH 7.4 and pH 5.6 in D2 0 [134]. It can be seen from Fig. 8.32 thattransferrin receptor at pH 7.4 undergoes thermal denaturation at thesharp midpoint temperature around 71 C while the thermal stability isreduced by approximately 15°C at endosomal pH (pH 5.6).
258
8.7.2 Infrared spectra of chlorophylls
Infrared spectra of chlorophylls (Chl) have been actively studied sincethe 1950s [136]. One recent progress in the infrared studies of Chl isthat infrared spectra of Chl in highly dilute solutions (-10- 6 M) can bemeasured [137]. Figure 8.33 shows infrared spectra of Chl-a in water-saturated carbon tetrachloride solutions of 8x10 -2 M, 3x10 -3 M, 5x10 -4
M, 6x10-5 M, and 9x10- 6 M. [137]. Note that the highly dilute solutionsof Chl-a provide the infrared spectra with fairly high signal-to-noise
2000 1800 1600 1400
WAVENUMBER (cmr )
Fig. 8.33. Infrared spectra of Chl-a in water-saturated carbon tetrachloride solutions of:(a) 8x 10- 2 M; (b) 3x10- 3 M; (c) 5x 104 M; (d) 6x 10- 5 M; (e) 9x 10-6 M. (Reproduced from Ref.
[137] with permission. Copyright (1993) American Society for Photobiology.)
259
ratio. The advantage of infrared spectroscopy in Chl-a research is thatit gives intense bands due to C=O stretching modes of the ester groupsand the 9-keto group, which play key roles in forming dimers andoligomers of Chl-a [138-141]. Bands near 1736, 1693, 1654, and 1608cm-l1 are assigned to a C=O stretching mode of the ester groups, a C=Ostretching mode of the free 9-keto group, a C=O stretching mode of the9-keto group which coordinates with the Mg atom of another Chl-amolecule, and a methine-bridge stretching mode (IR I-band),respectively [139].
In concentrated (above 10 - 3 M) carbon tetrachloride solutions Chl-aforms a five-coordinated dimer in which the 9-keto group of one Chl-acoordinates to the Mg atom of another Chl-a. It seems, therefore, thatthe bands at 1693 and 1654 cm-l in Fig. 8.33 are due to the free andcoordinated 9-keto groups of the dimer, respectively. With the decreasein the concentration of Chl-a, the intensity of the band at 1654 cm - ldecreases while that at 1693 cm-l increases concomitantly; the formeris almost missing in Fig. 8.33e. These observations led Okada et al.[137] to conclude that the monomer is predominant in the dilute water-saturated carbon tetrachloride solutions.
The coordination number of the Mg atom can be determined by thefrequency of IR I band [139]; the IR I band appears near 1608 cm- whenthe Mg atom of Chl-a assumes a five-coordination with one axial ligandwhereas it is observed near 1597 cm-l when it takes a six-coordinationwith two axial ligands. The IR I band is identified near 1609 cm-l in thespectra of the concentrated solutions (Fig. 8.33a,b), suggesting that theMg atom is five-coordinated. The frequencies of the IR I band are notreliable in the spectra of the dilute solutions because a strong bandnear 1550 cm-l due to carbon tetrachloride makes accurate subtractionof the solvent spectrum from the Chl-a spectra difficult in the1600-1500 cm-l region.
8.7.3 Infrared spectra of a model compound forphospholipids
Infrared spectroscopy is an excellent tool for investigating the struct-ure and phase transitions of fatty acids, phospholipids, and biomem-branes because the frequencies of CH2 antisymmetric and symmetricstretching bands are very sensitive to the conformation of hydrocarbonchains and those of C=O stretching bands reflect the strength of thehydrogen bonds of the C=O groups [126,130].
260
0II
H C\ / I H 2' 4' 6
O-\ 7 0H 0 CH~ CH, CH2
C-C- 5C-CH2 C 1 CH2 CH2 CH2/ H 1 6 11 ' ' 7'
K-C 0 8' lo' 12'
\ CH2 CH2 CH2H /\ / \ / \, \ / \
CH 29' 1
CH211'
22uj1.
1587
1585
1583
1581
1579 -
1577
1575 . ..l . . . l
14'CH2
CH213' 1
(b)I -
20 25 30 35 40 45
Wavenumber/cm 'l
Fig. 8.34. (a) Temperature-dependent spectral changes in the 1800-1500 cm 1 region ofpotassium salt of ascorbic palmitate (APK) in a deuterated aqueous solution (0.1 M). (b)The frequency of the C=C stretching band versus temperature. (Reproduced from Ref.
[106] with permission. Copyright (1981) National Research Council of Canada.)
Figure 8.34 shows temperature-dependent spectral variations inthe 1800-1500 cm-' region of potassium salt of ascorbic palmitate(APK) in a deuterated aqueous solution (0.1 M) [106]. Bands near 1740and 1580 cm-1 are due to the C=O and C=C stretching modes, respect-ively. It is noted that the C=O stretching band shows a downward shiftwith broadening as temperature is increased. This observationsuggests that the hydrogen bond of the C=O group becomes strongerwith temperature [140]. The C=C stretching band shows an upwardshift and Fig. 8.34b plots its frequency versus temperature. The plotreveals that the phase transition of APK from gel or core gel to micelletakes place near 47-48°C.
Figure 8.35a depicts the 3000-2800 cm-1 region of the same spectraas those in Fig. 8.34a. The CH2 antisymmetric and symmetric stretch-
261
16'CH2
/CH25'
0.
¢Q:0
50 55 60
Temperature/°C
_
I I
I I I I I i I2853. 5 - 8.0
2852 ..
E - .* ..2851.5 . 6.0 '
2850.5 5 0
3000 2960 2920 2880 2840 2800 20 25 30 35 40 45 50 55 60
Wavenumber/cm t Temperature/° C
Fig. 8.35. (a) The 3000-2800 cm- 1 region of the same spectra as those in Fig. 8.34 (a). (b)The frequency (circles) and bandwidth (triangles) of the CH2 symmetric stretching bandversus temperature. (Reproduced from Ref. [106] with permission. Copyright (1981)
National Research Council of Canada.)
ing bands are observed near 2920 and 2850 cm l, respectively. It is wellknown that when the alkyl chain is highly ordered (trans-zigzag confor-mation), the CH 2 antisymmetric and symmetric stretching bandsappear at 2918 and 2848 cm-l, respectively, while if conformationaldisorder (gauche forms) is included in the chain, they shift upward upto 2926 and 2856 cm-l depending upon the content of gauche con-formers [105,106].
In Fig. 8.35a, both bands due to the CH2 antisymmetric and sym-metric stretching modes shift upward with broadening with temper-ature [106]. Figure 8.35b plots the frequency of the CH2 symmetricstretching band and its bandwidth versus temperature [106]. It is ofnote that the frequency changes markedly near 47-48°C and that thebandwidth varies at slightly lower temperature. The frequency shift ofthe CH2 symmetric stretching band indicates that the conformation ofthe alkyl chain of APK changes from a trans-zigzag structure to astructure with some gauche conformers upon the phase transition. Theband broadening occurs even below 40°C, suggesting that the fluidity ofthe alkyl chain increases at much lower temperature than the phasetransition temperature. The frequency shifts of the two CH, stretchingbands and those of the C=O and C=C stretching bands happen in thesame temperature range, and thus the change in the strength of thehydrogen bond of the C=O group is linked with the conformationalchange in the alkyl chain [106].
262
(a)U.
aU0
-E0
r I (b)
In order to monitor the structural change of a particular part in thealkyl chain the deuteration of that part is very useful because the CD2stretching bands (2300-2000 cm- l region) are observed separately fromthe CH2 stretching bands [142]. Infrared spectroscopy has also beenapplied to studies of phase transition of biomembrane in living bacteria[143].
8.7.4 Infrared spectra of intact bacterial cells
Infrared spectra of proteins, Chls, and phospholipids are examples ofinfrared spectra of basic biological molecules. Let us examine infraredspectra of rather complicated biological materials. As an example ofsuch biological materials, infrared spectra of bacteria are describedhere.
The infrared measurements of bacteria are not difficult. In fact,even in the 1950s and 1960s infrared spectra of a number of bacteriawere measured and it was pointed out that infrared spectroscopy haspotential in the identification of bacteria [118,119]. However, it was themiddle of the 1980s that systematic infrared investigations ofcharacterizing intact bacteria started [129,144]. Figure 8.36a and b
2,a,E2
,:
at
Wavenumber [cm-1]
Fig. 8.36. Infrared spectra and their second derivative spectra of gram-positive andgram-negative bacteria. (A) Staphylococcus aureus, PS96; (B) Pseudomonaschlororaphis, American Type Culture Collection (ATCC) 17809. (Reproduced from Ref.
[144] with permission. Copyright (1991) VCH.)
263
shows infrared spectra of gram-positive and gram-negative bacteria,respectively. Their second derivative spectra are also shown in Fig.8.36. Table 8.2 summarizes proposed band assignments for infraredspectra of bacteria (from Ref. [144]). These band assignments are based
TABLE 8.2
Proposed assignment of some bands frequently observed in infrared spectra of bacteria(from Ref. [144])
Band Frequency Relative Assignment*numbering (cm) intensity*
-3500 m vOH stretching-3200 m-s vNH stretching (Amide A) of proteins
2959 w va(CH 3) stretching of methyl2934 vw va(CH 2) stretching of methylene2921 m va(CH 2) stretching of methylene in fatty acids
2898 vw vCH stretching of methine2872 w vs(CH3) stretching of methyl2852 m v,(CH2) stretching of methylene in fatty acids
1 1741 w vC=O stretching of esters1715 vw vC=O stretching of esters, carbonic acids1695 w different amide I band components resulting1685 w from antiparallel pleated sheets and -turns1675 w of proteins
2 -1655 s amide I of a-helical structures
3 -1637 s amide I of P-pleated sheet structures4 1548 s amide II band5 1515 m "tyrosine" ring vibration band
1498 w "pheylalanine" ring vibration band
6 1468 w-m 6(CH2) bending of methylene7 -1400 m m,(COO-) stretching of carboxylates
1310-1240 w amide III band components of proteins8 1250-1220 w-m va(PO2-) stretching of phosphodiesters
1084-1088 w-m v,(PO2) stretching of phosphodiesters9 1200-900 m C-O-C
720 vw p(CH 2) rocking of methylene900-600 w "fingerprint region"
264
*m = medium; s = strong; v = very weak; w = weak; s = symmetric; a = asymmetric orantisymmetric, v = stretching; 6 = deformation; p = rocking.
upon infrared spectral analysis of isolated substances and purecompounds such as proteins, lipids, and nucleic acids.
Infrared spectra of bacteria can be divided into several spectralregions [129,144]. The 1800-1700 cm -l region involves bands due to C=O stretching modes of phospholipids. The 1700-1500 cm-l region isdominated by the strong amide I and amide II bands. A few weakfeatures arising from amino acid residues are also observed in thisregion (see Table 8.2). The region between 1250 and 1200 cm-l showsmedium bands due to a PO,- antisymmetric stretching mode ofphosphodiesters. This region provides information about DNA, RNA,and phospholipids. The 1200-900 cm-l region involves a number ofweak to medium features arising from C-O-C and C-O stretchingmodes of polysaccharides and those from a PO,- symmetric stretchingmode of phosphodiesters. One can identify a number of bands in thesecond derivative spectra in this region. This region is most sensitiveand selective for the differentiations of bacteria down to the strain andeven serotype level [144]. The region between 900 and 600 cm-l isreferred to as the 'bacterial fingerprint region' because it exhibits manyweak, but extremely characteristic features [144]. Different speciesand strains of bacteria have different chemical composition and chemi-cal structures and each species or strain show a unique infraredspectrum. The recent development of FT-IR instruments together withthe availability of powerful personal computers has led to a variety ofinfrared studies of bacteria [144]. Current infrared spectroscopyenables differentiation at different levels, classification, and identifica-tion to genus, species or strain levels of bacteria. Infrared spectroscopyis also used for the detection and identification of particular cell compo-nents and for the investigation of growth-dependent phenomena andcharacterization of cell-drug interactions [144].
8.7.5 Application of infrared microspectroscopy and imagingto biological sciences
By combining an infrared spectrophotometer with a microscope,molecular information can be obtained with a spectral resolution of -10pm [71,145,146]. Infrared microspectroscopy has recently been appliedextensively to biological sciences and medicine because of thecapability of in situ chemical analyses of microscopic samples. One ofthe most exciting developments in infrared microspectroscopy is infra-red imaging technology (Section 8.4).
265
Figure 8.37A shows an example of an infrared imaging study of abiological tissue [71]; it is a cross-section of an unstained rat retina(image width, 500 pm) viewed with an infrared microscope/spectro-meter with all-reflecting differential interference contrast optics.Figures 8.37B and C depict infrared spectra obtained from the outersegment which is rich in lipid materials and from the outer nuclear celllayer, respectively. In both spectra, bands due to amide I and II areobserved very strongly. A band near 1700 cm-l is much stronger inspectrum B than in spectrum C. A band at 1235 cm - is assigned to a P=O stretching mode arising from the nuclei. Lipid chain length, branch-ing, and glycolipids are investigated by comparing the intensities ofbands due to C=O stretching, CH3 stretching, CH 2 stretching, andH-C-OH group vibrations. The degree of the unsaturation may beestimated from the CH stretching band at 3015 cm-l on the carbon thatis attached to the C=C band. In this way the molecular chemistry of theindividual retina layer has become possible by combining infraredspectroscopy and microscopy [71]. Various kinds of pathological tissueshave been subjected to infrared microspectroscopy studies [145]. Forexample, cancerous tissues, Alzheimer's disease plaques, and diseasedarteries have been investigated by infrared microspectroscopy.Infrared microspectroscopy combined with artificial neural networkshas been applied to the diagnosis of cervical cancer. This topic will beoutlined in Section 8.7.7.
IPL
INLOPLONLiSOS
Fig. 8.37. (A) A cross-section of an unstained rat retina (image width, 500 pm) viewedwith an infrared microscope/spectrometer with all-reflecting differential interference
contrast optics. (B and C: see opposite page,)
266
3500 3000 2500 2000 1500 1000
Wavenumber (cm-l)
Abs C
3500 3000 Z500 2000 1500 1000
Wavenumber (cm-1)
Fig. 8.37 (continued). Infrared spectra obtained from (B) the outer segment, and (C) theouter nuclear cell layer. (Reproduced from Ref. [71] with permission. Copyright (1999)
American Association for the Advancement of Science.)
267
8.7.6 Structure and function of bacteriorhodopsin studied bylow-temperature infrared difference spectroscopy
The photoreceptor proteins have been very attractive targets for infra-red spectroscopy [125,147,148]. The proteins can be divided into twogroups: those that use light as energy source and those that employlight as information source. The proteins in photosynthesis systems,bacteriorhodopsin, and rhodopsin belong to the former while visualpigments, phytochrome, and yellow proteins belong to the latter. Time-resolved infrared spectroscopy and low-temperature infrared spectro-scopy are very suitable to explore the light-induced mechanism of thesephotoreceptor proteins.
As a representative example of infrared studies on photoreceptorproteins, this section describes low-temperature infrared spectroscopystudies on the light-induced mechanism for proton pumping ofbacteriorhodopsin [148]. Bacteriorhodopsin, a protein present in thepurple membrane of Halobacterium salinarium, performs uni-directional transport of protons across the membrane by use of lightenergy absorbed in the retinylidene chromophore bound to lysine 216(Lys 216) through the protonated Schiff base. Figure 8.38a depictsseven helices of bacteriorhodopsin with important residues for thefunction and the structure of its photointermediates are shown in Fig.8.38b. The intermediates shown in Fig. 8.38b are emerged by the light-induced isomerization of the all-trans retinal. The photocycle is
f,*; WLtim
Fig. 8.38. (a) Seven helices of bacteriorhodopsin with a retinal bound to the -aminogroup of Lys216 via a protonated Schiff base. Opposite page: (b) Photocycle of bacterio-rhodopsin. (Reproduced from Ref. [148] with permission. Copyright (1997) Japanese
Biochemical Society.)
268
completed in less than 10 ms. One proton moves from the Schiff base toasparagine 85 (Asp 85) in the L-to-M process and another from Asp 96to the Schiff base in the M-to-N process.
BRLight
Nas
K0
N 3
Fig. 8.38. (b) Caption opposite.
269
-,
I
I"
g. z
0.02
0.00
-0.02
-0.04
I I I I I I I
C=O of COOHO-H of H20 C=O of petide
f-3486 1 A L148-1
3643
0 A04 I 0-II
I I I I I l I I I I3800 3600 3400 3200 3000 1800 1600 1400 1200 1000 800
wavenumber(cm 1 )
Fig. 8.39. A low-temperature infrared difference spectrum between L and BR of bacterio-rhodopsin (Reproduced from Ref. [148] with permission. Copyright (1997) Japanese
Biochemical Society.)
Of particular interest in studying bacteriorhodopsin is that itsdiscrete intermediate states can be investigated over a picosecond tomillisecond range. One can apply low-temperature infrared spectro-scopy as well as time-resolved infrared spectroscopy to explore thechemical process occurring in the photocycle [148]. Difference spectramay be measured at 80K for K, 170K for L, 230K for M, and 274K for N(the spectrum of O can only be obtained by time-resolved method).
Figure 8.39 shows a L minus BR spectrum of bacteriorhodopsin[148]. As is evident from Fig. 8.39, infrared studies provide informationabout the protonation states of carboxylic acid residues, hydrogen-bonding changes in water, peptide carbonyls, and others. Let us focusour attention on the 3750-3450 cm- l region where OH stretching bandsof water molecules and an NH stretching band of tryptophan 182 (Trp182) are expected to appear. Figure 8.40 shows infrared differencespectra in the 3750-3450 cm -' region between the unphotolyzed state(BR) and the intermediate (K, L, or M). Of particular note in Fig. 8.40is that the absorbance of each water band corresponds to one or a fewwater molecules [149]. In other words, one can investigate the struc-ture and environment of a water molecule from a frequency of the OHstretching band [148,149]. Water molecules play very important rolesin the intramembrane signalling mediated by its hydrogen-bonding.
270
K-BR
L-BR
] 3607 3577
M-BR
3643
3700 3600 3500wavenumber(cm 1 )
Fig. 8.40. Low-temperature infrared difference spectra in the 3750-3450 cm- 1 region ofbacteriorhodopsin between photointermediates (K, L, M) and unphotolyzed state (BR).
(This figure was prepared by H. Kandori.)
For example, in L the Schiff base forms strong hydrogen-bonding witha water molecule coordinated with Asp85. This structure leads totransfer of the Schiff base proton to Asp85 in the L-to-M process,triggering proton release from glutamic acid (Glu 204) to the extra-cellular surface. In addition, a string of hydrogen-bonding mediated byinternal water molecules and peptide carbonyls in helices B and C, andTrp182 in helix F induces structural changes around Asp96, which maybring about the structural variations occurring later during the M-to-Nprocess.
In the K minus BR spectrum of Figure 8.40 bands due to water arevery weak but large spectral changes take place in the OH stretchingband region of the L minus BR spectrum. Three bands at 3643, 3607,and 3577 cm-l are assigned to a water molecule present close to theunprotonated Asp85, that close to Asp96, and that close to the peptidecarbonyl of valine 49 (Val 49), respectively, based upon comparison ofthe spectrum with those of D85N, D96N, and V49M mutants [150].
271
Pro'
Asp85
Fig. 8.41. Hydrogen-bonding network from Asp85 to Asp96. (Reproduced from Ref. [1481with permission. Copyright (1997) Japanese Biochemical Society.)
Figure 8.41 illustrates a hydrogen-bonding network from Asp85 toAsp96 medicated by the above molecules, a long-range interactionbetween Asp85 and Asp96 148]. The low-frequency shifts of the threewater bands in the L minus BR spectrum reveal that all of the watermolecules form stronger hydrogen-bonding upon the L formation. Themost important part includes the water molecule that is linked toAsp85, Asp212, and the Schiff base, inducing distortion in the retinal.This structure provides the strong hydrogen-bonding of the protonatedSchiff base. The intervening water molecule may also play an import-ant role in the separation of the positive change of the protonated Schiffbase and the negative charge on Asp85 [151]. The proton transfer maybecome feasible by such a distorted structure by decreasing the pKavalue of the Schiff base.
An intense band at 3486 cm-l is due to an NH stretching mode ofTrp182, showing that its indole ring located in the hydrophobic envi-ronment has a specific interaction with the 9-CH 3 group of the retinalchromophore in L [151]. The structural change in Trpl82 favours theproton transfer from the Schiff base to Asp85 in the L-to-M process.
272
Upon conversion to M the proton transfer from the Schiff base toAsp85 occurs, collapsing the strong hydrogen-bonding of the Schiff baseN-H with the protein and directing the lone pair of the nitrogen of theunprotonated Schiff base to the side opposite from Asp85. In this way,the distortion in the retinal is abolished. This can be one of the switchreactions in the unidirectional proton pumping. The high-frequencyshifts of the OH stretching bands in the M minus BR spectrum aregood evidences for the weaker hydrogen-bonding in M.
Similar studies were carried out also for rhodopsin [148]. For thissort of studies polarized infrared spectroscopy is also powerful becausebacteriorhodopsin is oriented in purple membrane [153]. It was foundthat an O-H group in bacteriorhodopsin has an angle of 60° withrespect to the surface normal.
Another interesting study by Kandori et al. [154] is to use an S-Hstretching mode of cysteine as a hydrogen-bonding probe in bacterio-rhodopsin. An S-H stretching band is located in the 2580-2525 cm-lregion where other vibrations are absent. They substituted threonine89 (Thr89), which is present in the 'proton channel' of bacterio-rhodopsin for Cys (T89C) and observed the S-H stretching bands in thedifference spectra. From the S-H stretching frequency, they concludedthat the distance between the sulphur of Cys89 and the oxygen ofAsp85 becomes much closer in K, probably resulting from the chromo-phore motion in the restricted protein environment [154].
8.7.7 Diagnosis of cervical cancer by infraredmicrospectroscopy and artificial neural networks
Papanicolaou (Pap) smears are the current means for the initial screen-ing of cervical cancer. However, this method is not always highlyaccurate, with a reported 20% false-negative rate. The screening pro-cess involves a microscopic search by naked eyes, which is time-consuming, fatiguing, and reliant on human judgment. Thus, a morereliable and automated means of cancer screening has been desired[155].
It has been shown by several research groups that infrared spectro-scopy has great potential in the diagnosis of cancer, and in particularcervical cancer [155,156]. Infrared spectroscopy does not depend uponmorphological observations but directly monitors molecular structureand changes in cellular chemistry. Thus, it may lead to earlier detec-tion of abnormalities.
273
2
1.5
0.5
To
1700 1500 1300 1100 900
Wavenumber (cm-' )
Fig. 8.42. Infrared spectra of cervical cells showing various stages of disease state(Reproduced from Ref. [155] with permission. Copyright (1998) C.M.B. Association.)
In order to group the infrared spectra of cervical smears into ab-normal and normal classifications, multivariate statistical analysis orartificial neural networks (ANN) must be applied to the infraredspectra. Romeo et al. [155] have demonstrated that ANN has someadvantages over ordinary multivariate statistical analysis in the datatreatment for biomedical materials. The multivariate statisticalanalysis depends greatly upon data consistency for accurate perform-ance while biomedical objects, in particular those exhibiting a diseasestate, lack consistency because of variations in symptoms and degreesof severity of the given disease state. ANN shows better performancethan multivariate statistical analysis probably because non-linearstatistical analysis of the data tolerates considerable amounts ofimprecise or incomplete data [155].
Figure 8.42 compares representative infrared spectra obtained forsamples diagnosed as normal and dysplasia by biopsy [155]. Thespectrum of cultured HeLa cells is also shown in Fig. 8.42. The spectraconsist of contributions from proteins, nucleic acids, lipids and carbo-hydrates. The 1700-1500 cm-l region is dominated by amide I and IIbands due to the proteins while the 1300-900 cm l region containsbands due to C-O stretching modes of the proteins and carbohydratesand those assigned to the antisymmetric and symmetric phosphate(PO2) vibrations arising from the phosphodiester linkages in nucleicacids. Bands at 1047 and 1025 cm-' due to C-O stretching modes ofglycogen and those at 1244 and 1082 cm-l assigned to P02 - anti-
274
PC2 Scores0.4
0.3
0.2
0.1
0O
-0.1-
-0.2-
.0 -
n
r.t.1 cores
-1.0 -0.5 6 0.5 1.0
Fig. 8.43. Two principal component scores plot of data bank used to train the neuralnetwork. (Reproduced from Ref. [155] with permission. Copyright (1998) C.M.B.
Association.)
symmetric and symmetric stretching modes, respectively, showmarked changes between the spectra of representative normal andrepresentative dysplastic.
Infrared spectra of 88 normal and 32 abnormal (mild to severedysplasia) cervical smear samples were subjected to principal compo-nent analysis. Figure 8.43 depicts the resultant two principalcomponent (PC) scores plot obtained when the infrared data wasreduced to only 7 wavenumber values (1450, 1400, 1244, 1150, 1080,1050, and 1026 cm- ) [155]. It can be seen from the scores plot thatalthough most of the samples are separable, there are two obviousatypical spectral samples of the abnormal set that appear in the normalgroup. These were retained in the data base for the ANN analysis.
For the ANN analysis the infrared spectra were randomized toconstruct eleven data sets of training, validation, and testing sets eachcontaining 80, 20, and 20 samples, respectively. Training was carriedout systematically, starting with a simple architecture and graduallyexpanding the number of hidden nodes and layers. Table 8.3 sum-marizes thirteen kinds of ANN architectures that could differentiatebetween the normal and abnormal cervical smears [155]. Havinggenerated these architectures, it was of importance to ascertain which
275
-v .,
TABLE 8.3
All architecture types used (from Ref. [1551)
Architecture no. Architectural configuration* No. of weights
1 7:1:1 10
2 7:2:1 19
3 7:3:1 28
4 7:4:1 37
5 7:1:1:1 11
6 7:1:2:1 13
7 7:1:3:1 15
8 7:2:1:1 20
9 7:2:2:1 23
10 7:2:3:1 29
11 7:3:1:1 28
12 7:3:2:1 35
13 7:3:3:1 40
*Architectural configuration: number of nodes in input layer:hidden layer/:output layer.
data sets and architectures yield the best learning. For this purposetwenty samples with known biopsy results and previously unseen bythe networks, were selected and assigned an output according tonormality. This external data set of samples consisted of 10 normal and10 abnormal samples. Comparison between the expected and actualoutputs for each of the 20 samples in the external testing set was madeto determine the network performance.
A two PC scores plot of the external testing set obtained by archi-tecture of 7:4:1 is shown in Fig. 8.44 [155]. The plot demonstrates aseparation between the abnormal and normal samples, with samples19 and 20 (mild dysplasia) closer to the normal/abnormal divide. Inorder to increase the ability of the network to make generalizations andpredictions, it is necessary to train the network on hundreds of samplesfrom each category, ranging from normal, through the three dysplasticcategories to cancerous. This study indicated that infrared spectro-scopy coupled with ANN may provide an objective and automatedscreening technique for the diagnosis of cervical cancer.
276
I I Pr are
0.4
0.2
U
-0.2
-0.4
o0 a)
0
o0 #19
O #20
11
-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6
Fig. 8.44. Two principal component scores plot of external testing set. (Reproduced fromRef. [155] with permission. Copyright (1998) C.M.B. Association.)
REFERENCES
1. C.D. Craver and T. Provder (Eds.), Polymer Characterization -PhysicalProperty, Spectroscopic, and Chromatographic Methods. Advances inChemical Series No. 227, American Chemical Society, 1990.
2. R.S. Stein, J. Appl. Phys., 32 (1961) 1280.3. W.M. Grim III, J.A. Graham, R.M. Hammaker and W.G. Fateley, Am.
Lab., 16(3) (1984) 22.4. J.L. Koenig, Spectroscopy of Polymers. American Chemical Society, 1991.5. N.I. Afanasyeva and R.F. Bruch, Surf. Interface Anal., 27(4) (1999)
204-212.6. A.N. Theodore and R.O. Carter III, J. Appl. Polym. Sci., 49(6) (1993)
1071-1080.7. G.L. Grobe III; J.A. Gardella Jr., W.L. Hopson, W.P. McKenna and E.M.
Eyring, J. Biomed. Mater. Res., 21(2) (1987) 211-229.8. G. Conti and A. Sommazzi, J. Mol. Struct., 294 (1993) 275-278.9. T. Rische, S. Zschoche and H. Komber, Macromol. Chem. Phys., 199(8)
(1998) 1539-1545.10. M. Johnck, L. Muller, A. Neyer and J.W. Hofstraat, Eur. Polym. J., 36(6)
(2000) 1251-1264.11. D. Ostrovskii, A.-L. Kjoniksen, B. Nystroem and L.M. Torell, Macro-
molecules, 32(5) (1999) 1534-1540.12. D. Das, S. Chattopadhyay, A.K. Barua and R. Banerjee, J. Appl. Phys.,
78(5) (1995), 3193.
277
I, I1 11
11
· · · · ·
13. A.Z. El-Sonbati and M.A. Diab, Polym. Degrad. Stab., 22(4) (1988)295-302.
14. V. Vettegren, V. Teubner-Texte Phys. 9 (Prog. Polym. Spectrosc.), (1986),158-66.
15. M.W. Urban and C.D. Craver (Eds.), Structure-Property Relations inPolymers: Spectroscopy and Performance. Advances in Chemical SeriesNo. 236, American Chemical Society, 1993.
16. C. Qin, A.T.N. Pires and L.A. Belfiore, Polym. Commun., 31(5) (1990)177-182.
17. L.O. Faria and R.L. Moreira, J. Polym. Sci. B, 38 (2000) 34-40.18. H.W. Siesler and K. Holland-Moritz, Infrared and Raman Spectroscopy of
High Polymers. Marcel Dekker Inc., New York, NY, 1980, pp. 243-29219. R. Zbiden, Infrared Spectroscopy of High Polymers. Academic Press, New
York, NY, 1964.20. S. Krim, J. Phys. Chem., 32 (1960) 1780.21. S. Krim, Adv. Polym. Sci., 2 (1960) 51.22. L. Monnerie, Faraday Symp. Chem. Soc., 18 (1983) 57.23. T. Thormann, M. Rogojerov, B. Jordanov and E.W. Thulstrup, J. Mol.
Struct., 509(1-3) (1999) 93-104.24. F.R. Steenstrup, K. Christensen, C. Svane and E.W. Thulstrup, J. Mol.
Struct., 408 (1997) 139-148.25. V.G. Gregoriou and R.A. Palmer, Macromol. Symp., 94 (1995) 75-95.26. C.J. Manning, J.L. Chao and R.A. Palmer, Rev. Sci. Instrum., 62 (1991)
1219.27. I. Noda, A.E. Dowrey and C. Marcott, J. Polym. Sci. Polym. Lett. Ed., 21
(1983) 99.28. I. Noda, A.E. Dowrey and C. Marcott, Polym. Prep. (Am. Chem. Soc., Div.
Polym. Chem.), 24(1) (1983) 122.29. I. Noda, A.E. Dowrey and C. Marcott, Polym. Prep. (Am. Chem. Soc., Div.
Polym. Chem.), 25(2) (1984) 167.30. I. Noda, A.E. Dowrey and C. Marcott, Appl. Spectrosc. 42, 203 (1988).31. A.W. Mantz, Appl. Spectrosc., 30 (1976) 459; A.A. Garrison, R.A.
Crocombe, G. Mamantov and J.A. de Haseth, Appl. Spectrosc., 34 (1980)399.
32. P.R. Griffiths and J.A. de Haseth, Fourier Transform InfraredSpectroscopy. Wiley, New York, NY, 1986, pp. 407-425.
33. V.G. Gregoriou, C. Marcott, I. Noda, A. Dowery and R.A. Palmer, J. Polym.Sci.-B Polym. Phys., 31 (1993) 1769.
34. F. Ozanam and Chazalviel, Rev. sci. Instrum., 59(2) (1988) 242.35. R.A. Palmer, J.L. Chao, R.M. Dittmar, V.G. Gregoriou and S.E. Plunkett,
Appl. Spectrosc., 47(9) (1993) 1297-310.36. M. Hashimoto, T. Yuzawa and H. Hamaguchi, Jasco Rep., 37(3) (1995)
27-33.
278
37. G. Ellis, C. Marco, J. del Pino, J. Lorente, M.A. Gomez and J.G. Fatou, Vib.Spectrosc., 9(1) (1995) 49-56.
38. A. Hatta, Mol. Crys. Liq. Cryst., 74 (1981) 195.39. M.L. Forman, W.H. Steel and G.A. Vanasse, J. Opt. Soc. Am., 56 (1966) 59.40. V.G. Gregoriou, J.L. Chao, H. Toriumi and R.A. Palmer, Chem. Phys. Lett.,
179 (1991) 491.41. H.J. Coles and J. Tipping, Nature 316 (1986) 136; Mol. Cryst. Liq. Cryst.
Lett., 2 (1985) 23.42. A. Kaito, Y.K. Wang and S.L. Hsu, Anal. Chim. Acta, 189 (1986) 27.43. H. Toriumi, H. Sugisana and H. Watanabe, Jpn. J. Appl. Phys., 27 (1988)
L935.44. V.G. Gregoriou, J.L. Chao, H. Toriumi and R.A. Palmer, Chem. Phys. Lett.,
179 (1991) 491.45. H.W. Siesler, Adv. Polym. Sci., 65 (1984), 1-7746. M.W. Urban and T. Provder (Eds.) Multidimensional Spectroscopy of Poly-
mers. ACS Symposium Series No. 598, American Chemical Society, 1995.47. I. Noda, Chemtracts, Macromol. Chem., 1 (1990) 89.48. I. Noda, A.E. Dowrey and C. Marcott, J. Polym. Sci. Polym. Lett. Ed., 21
(1983) 99.49. R.A. Palmer, R.M. Dittmar, V.G. Gregoriou and J.L. Chao, Polym. Prepr.,
32 (1991) 673.50. I. Noda, A.E. Dowrey and C. Marcott, J. Mol. Struct., 224 (1990) 265.51. D. Lefebvre, B. Jasse and L. Monnerie, Polymer, 22 (1981) 1616.52. B.R. Nair, V.G. Gregoriou and P.T. Hammond, Polymer, 41 (2000) 2961.53. B.R. Nair, V.G. Gregoriou and P.T. Hammond, J. Phys. Chem. B., 104
(2000) 7874.54. F. Papadimitrakopoulos, K. Konstadinidis, T.M. Miller, R. Opila, E.A.
Chandross and M.E. Galvin, Chem. Mater., 6(9) (1994) 1563-1568.55. D. Muller, M. Gross, K. Meerholz, T. Braig, M.S. Bayerl, F. Bielefeldt and
O. Nuyken, Synth. Met., 111/112 (2000) 31-34.56. A. Bacher, C.H. Erdelen, W. Paulus, H. Ringsdorf, H.-W. Schmidt and P.
Schuhmacher, Macromolecules, 32(14) (1999) 4551-4557.57. J.C. Scott, S.A. Carter, S. Karg and M. Angelopoulos, Proc. SPIE-Int. Soc.
Opt. Eng., 3002 (1997) 86-91.58. J. Davenas, V. Massardier and V.H. Tran, Nucl. Instrum. Meth. Phys.
Res., Sect. B, 112 (1996) 120-124.59. Y. Furukawa, M. Tasumi and G. Zerbi (Eds.), Mod. Polym. Spectrosc.
(1999), 207-237.60. H. Ericson, C. Svanberg, A. Brodin, A.M. Grillone, S. Panero, B. Scrosati
and P. Jacobsson, Electrochim. Acta, 45(8/9) (2000) 1409-1414.61. Y. Furukawa, J. Phys. Chem., 100(39) (1996) 15644-15653.62. K. Saravanamuttu, X.M. Du, S.I. Najafi and M.P. Andrews, Can. J.
Chem., 76(11) (1998) 1717-1729.
279
63. D.L. Thomsen III, J. Mwaura and F. Papadimitrakopoulos, Polym. Prepr.(Am. Chem. Soc., Div. Polym. Chem.), 39(2) (1998) 1120-1121.
64. F. Papadimitrakopoulos, P. Wisniecki and D.E. Bhagwagar, Chem.Mater., 9(12) (1997) 2928-2933.
65. T. Ubukata, T. Seki, S. Morino and K. Ichimura, J. Phys. Chem. B, 104(17)(2000) 4148-4154.
66. J. Wang, B. Zou, X. Hong and D.M. Collard, Synth. Met., 113(3) (2000)223-226
67. M. Blazewicz, M.C. Gajewska and C. Paluszkiewicz, J. Mol. Struct.,482-483 (1999) 519-524.
68. J.M. Pope, T. Sotomura and N. Oyama, Batteries for Portable Applicationsand Electric Vehicles. Proc. Electrochem. Soc., 97-118 (1997) 116-123.
69. P.W. Faguy, W. Ma, A.J. Lowe, W.P. Pan and T. Brown, J. Mater. Chem.,4(5) (1994) 771-772.
70. J. Mijovic, S. Andjelic, B. Fitz, W. Zurawsky, I. Mondragon, F. Bellucci andL. Nicolais, J. Polym. Sci., Part B: Polym. Phys., 34(2) (1996) 379-388.
71. D.L. Wetzel and S.M. LeVine, Science, 285(5431) (1999) 1224-1225.72. M.C. McCann, L. Chen, K. Roberts, E.K. Kemsley, C. Sene, N.C. Carpita,
N.J. Stacey and R.H. Wilson, Physiol. Plant. 100(3) (1997) 729-738.73. L.H. Kidder, I.W. Levin and E.N. Lewis, Fourier Transform Spectroscopy.
AIP Conf. Proc., 430 (1998) 148-158.74. Max-Planck-Institut fur Biochemie. Nature (London), 399(6732) (1999)
134-137.75. E.N. Lewis and I.W. Levin, Appl. Spectrosc., 49(5) (1995) 672-8.76. R. Bhargava, T. Ribar and J.L. Koenig, Appl. Spectrosc., 53(11) (1999)
1313-1322.77. K. Artyushkova, B. Wall, J. Koenig and J.E. Fulghum, Appl Spectrosc.,
54(11) (2000) 1549-1558.78. S. Bohic, D. Heymann, J.A. Pouezat, O. Gauthier and G. Daculsi, C. R.
Acad. Sci., Ser. III, 321(10) (1998) 865-876; R. Mendelsohn, E.P.Paschato, P.J. Sherman, A.L. Boskey, Appl. Spectrosc., 54 (2000)1183-1191.
79. C.M. Snively and J.L. Koenig, J. Polym. Sci., Part B: Polym. Phys., 37(17)(1999) 2353-2359.
80. W.J. Marinelli, C.M. Gittins, A.H. Gelb, B.D. Green, Appl. Opt., 38(12)(1999) 2594-2604.
81. C. Marcott, R.C. Reeder, J.A. Sweat, D.D. Panzer and D.L. Wetzel, Vib.Spectrosc., 19(1) (1999) 123-129.
82. R. Bhargava, D.C. Fernandez, M.D. Schaeberle and I.W. Levin, Appl.Spectrosc., 53(12) (2001) in press.
83. J.-L. Bantignies, G. Fuchs, G.L. Carr, G.P. Williams, D. Lutz and S.Marull, Int. J. Cosmet. Sci., 20(6) (1998) 381-394.
84. H. Fabian, R. Wessel, M. Jackson, A. Schwartz, P. Lasch, I. Fichtner, H.H.
280
Mantsch, D. Naumann, Infrared Spectroscopy: New Tool in Medicine.Proc. SPIE-Int. Soc. Opt. Eng., 3257 (1998) 13-23.
85. N. Jamin, P. Dumas, J. Moncuit, W.-H. Fridman, J.-L. Teillaud, G.L. Carrand G.P. Williams, Proc. Natl. Acad. Sci. USA, 95(9) (1998) 4837-4840.
86. P. Lasch and D. Naumann, Cell. Mol. Biol. (Paris), 44 (1998) 189.87. M.K. Weldon, V.E. Marsico, Y.J. Chabal, A. Agarwal, D.J. Eaglesham, J.
Sapjeta, W.L. Brown, D.C. Jacobson, Y. Caudano, S.B. Christman andE.E. Chaban, Semiconductor Wafer Bonding: Science, Technology, andApplications. Proc. Electrochem. Soc., 97-36 (1998) 229-248.
88. L.E. Ocola, F. Cerrina and T. May, J. Vac. Sci. Technol., B, 15(6), (1997)2545-2549.
89. L.H. Kidder, I.W. Levin, E.N. Lewis, V.D. Kleiman and E.J. Heilweil, Opt.Lett., 22(10) (1997) 742-744.
90. E.N. Lewis, L.H. Kidder, J.F. Arens, M.C. Peck and I.W. Levin, Appl.Spectrosc., 51(4) (1997) 563-567.
91. M. Blanco, J. Coello, H. Iturriaga, S. Maspoch and E. Bertran, Appl.Spectrosc., 49(6) (1995) 747-753.
92. E. Herrala, P. Niemela and T. Hannula, In-Process Opt. Meas. Ind.Methods. Proc. SPIE-Int. Soc. Opt. Eng., 1266 (1990) 86-90.
93. N.A. Wright, R. Curbelo, D.A.C. Compton and S.L. Hill, Infrared FiberOpt. Proc. SPIE-Int. Soc. Opt. Eng., 1048 (1989) 153-160.
94. J.S. Sanghera and I.D. Aggarwal, J. Non-Cryst. Solids, 256/257 (1999)6-16.
95. A. Ulman, An Introduction to Ultrathin Organic Films. Academic Press,New York, 1991.
96. G.G. Roberts, Langmuir-Blodgett Films. Plenum Press, New York, 1990.97. T. Nakamura, Handbook of Organic Conductive Molecules and Polymers,
Vol. 1. (H.S. Nalwa, Ed.). Wiley, Chichester, 1997, p. 727.98. T. Takenaka and J. Uemura, in: J.R. During (Ed.), Vibrational Spectra
and Structure, Vol. 19. Elsevier, Amsterdam, 1991, p. 215.99. J.D. Swalen, Annu. Rev. Mater. Sci., 21 (1991) 373.
100. T.G. Greenler, J. Chem. Phys., 44 (1969) 310.101. P.-A. Chollet and J. Messier, Thin Solid Films, 99 (1983) 197.102. J. Umemura, T. Kamata, T. Kawai and T. Takenaka, J. Phys. Chem., 94
(1990) 62.103. R.G. Snyder, J. Mol. Spectrosc., 7 (1961) 116.104. M. Tasumi and T. Shimanouchi, J. Chem. Phys., 43 (1965) 1245.105. J. Umemura, D.G. Cameron and H.H. Mantsch, Biochim. Biophys. Acta,
602 (1980) 32.106. H. Sapper, D.G. Cameron and H.H. Mantsch, Can. J. Chem., 59 (1981)
2543.107. M. Kubota, Y. Ozaki, T. Araki, S. Ohki and K. Iriyama, Langmuir, 7 (1991)
774.
281
108. S. Morita, K. Iriyama and Y. Ozaki, J. Phys. Chem., B, 104 (2000) 1183.109. J. Umemura, T. Kamata, T. Kawai and T. Takenaka, J. Phys. Chem., 94
(1990) 62.110. S. Terashita, Y. Ozaki and K. Iriyama, J. Phys. Chem., 97 (1993) 10445.111. Y. Wang, K. Nichogi, K. Iriyama and Y. Ozaki, J. Phys. Chem., 100 (1996)
368.112. Y. Wang, K. Nichogi, K. Iriyama and Y. Ozaki, J. Phys. Chem., 100 (1996)
374.113. S. Morita, K. Iriyama and Y. Ozaki, J. Phys. Chem. submitted.114. K. Ikegami, M. Lan and T. Nakamura, J. Chem. Phys., 112 (2000) 881.115. G. Lunardi and C. Pecile, J. Chem. Phys., 95 (1991) 6911.116. T. Hasegawa, Y. Hatada, J. Nishijo, J. Umemura, Q. Hao and R.M.
Leblanc, J. Phys. Chem., B, 103 (1999) 7505.117. W.W. Coblenz, Bull. Natl. Bur. Stand. (US), 7 (1911) 619.118. K.P. Norris and J.E.S. Greenstreet, J. Gen. Microbiol., 19 (1958) 566.119. F.S. Parker, Application of Infrared Spectroscopy in Biochemistry,
Biology, and Medicine. Plenum Press, New York, NY, 1971.120. F.S. Parker, Application of Infrared, Raman, and Resonance Raman
Spectroscopy in Biochemistry. Plenum Press, New York, NY, 1983.121. R.E. Hester and R.B. Girling (Eds.), Spectroscopy of Biological Molecules.
Royal Society of Chemistry, London, 1991.122. H.H. Mantsch and D. Chapman (Eds.), Infrared Spectroscopy of Bio-
molecules. Wiley, New York, 1996.123. S. Krimm and J. Bandekar, Adv. Protein Chem., 38 (1986) 181.124. H. Susi and D.M. Byler, Arch. Biochem. Biophys., 258 (1987) 465.125. W. Mantele, Trends Biochem. Sci., 18 (1993) 197.126. R.J.H. Clark and R.E. Hester (Eds.), Biomolecular Spectroscopy, Part A
and Part B. Wiley, Chichester, 1993.127. F. Siebert, in: H.H. Mantsch and D. Chapman (Eds.), Infrared Spectro-
scopy of Biomolecules. Wiley, New York, 1996, p. 83.128. M. Jackson and H.H. Mantsch, in: H.H. Mantsch and D. Chapman (Eds.),
Infrared Spectroscopy of Biomolecules. Wiley, New York, 1996, p. 311.129. D. Naumann, D. Helm and C. Schulz, in: F.G. Priest, A. Ramos-
Cormenzana and B.J. Tindall (Eds), Bacterial Diversity and Systematics.Plenum, New York, 1994, p. 67.
130. P.I. Haris and D. Chapman, in: H.H. Mantsch and D. Chapman (Eds.),Infrared Spectroscopy of Biomolecules. Wiley, New York, 1996, p. 239.
131. M. Jackson and H.H. Mantsch, CRC Crit. Rev. Biochem. Mol. Biol., 30(1995) 95.
132. Y. Ozaki and K. Murayama, in: Infrared and Raman Spectroscopy ofBiological Materials. Marcel Dekker, New York, 2000, p. 515.
133. Y. Ozaki and I. Noda, in: R.A. Meyers (Ed.), Encyclopedia of AnalyticalChemistry: Instrumentation andApplications. Wiley, Chichester, 2000, p. 322.
282
134. J.M. Hadden, M. Bloemendal, P.I. Haris, I.H.M. Stokkum, D. Chapmanand S.K.S. Srai, FEBS Lett., 350 (1994) 235.
135. H. Torii and M. Tasumi, in: H.H. Mantsch and D. Chapman (Eds.),Infrared Spectroscopy of Biomolecules. Wiley, New York, 1996, p. 1.
136. K. Ballschmiter and J.J. Katz, J. Am. Chem. Soc., 91 (1969) 2661.137. K. Okada, K. Uehara and Y. Ozaki, Photochem. Photobiol., 57 (1993) 958.138. H. Scheer (Ed.), Chlorophylls. CRC Press, Boca Raton, FL, 1991, p. 1097.139. M. Tasumi and M. Fujiwara, in: R.J.H. Clark and R.E. Hester (Eds.),
Advances in Spectroscopy, Vol. 14. Wiley, Chichester, 1987, p. 407.140. M. Lutz and W. Mantele, in Ref. [138], p. 855.141. K. Uehara, T. Tachibana, M. Tsunooka and Y. Ozaki, Photochem.
Phytobiol., 62 (1995) 496.142. D.G. Cameron. H.L. Casel, H.H. Mantsch, Y. Boulanger and I.C.P. Smith,
Biophys. J., 35 (1981) 1.143. D.G. Cameron, A. Martin, D.J. Moffatt and H.H. Mantsch, Biochemistry,
24 (1985) 4355.144. D. Naumann, C.P. Schultz and D. Helm, in: H.H. Mantch and D. Chapman
(Eds.), Infrared Spectroscopy of Biomolecules. Wiley, New York, 1996, p.279.
145. Cellular Mol. Biol. Special issue for infrared microbiology (1998).146. M.D. Schaeberle, I.W. Levin and E.N. Lewis, in: H.-U. Gremlich and B.
Yan (Eds.), Infrared and Raman Spectroscopy of Biological Materials.Marcel Dekker, New York, 2000, p. 231.
147. E. Nabedryk, in: H.H. Mantsch and D. Chapman (Eds.), Infrared Spectro-scopy of Biomolecules. Wiley, New York, 1996, p. 39.
148. A. Maeda, H. Kandori, Y. Yamazaki, S. Nishimura, M. Hatanaka, Y.-S.Chon, J. Sasaki, R. Needleman and J.K. Lanyi, J. Biochem., 121 (1997)399.
149. A. Maeda, J. Sasaki, Y. Shichida and T. Yoshizawa, Biochemistry 31(1993) 462.
150. Y. Yamazaki, S. Tuzi, H. Saito, H. Kandori, R. Needleman, J.K. Lanyi andA. Maeda, Biochemistry, 35 (1996) 4063.
151. S. Scheiner and X. Duan, Biophys. J., 60 (1991) 874.152. Y. Yamazaki, J. Sasaki, M. Hatanaka, H. Kandori, A. Maeda, R.
Needleman, T. Shinada, K. Yoshihara, L.S. Brown and J.K. Lanyi, Bio-chemistry 34 (1995) 577.
153. H. Kandori, N. Kinoshita, Y. Shichida and A. Maeda, J. Phys. Chem. B,102 (1998) 7899.
154. H. Kandori, N. Kinoshita, Y. Shichida, A. Maeda, R. Needleman and J.K.Lanyi, J. Am. Chem. Soc., 120 (1998) 5828.
155. M. Romeo, F. Burden, M. Quinn, B. Wood and D. McNaughton, CellularMol. Biol., 44 (1999)179.
156. P.T.T. Wong, R.K. Wong and K. Fung, Appl. Spectrosc., 47 (1993) 1058.
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Chapter 9
Modern data analytical methods forinfrared spectroscopy
Infrared spectrometry is the most universally useful of all analyticaltechniques [1] available for material characterisation. Quantitativeanalysis using infrared spectrometry involves the measurement of theinfrared spectrum first. There are several different samplingtechniques available for this purpose depending on the availability andphysical state of the sample. Development in infrared instrumentationand analytical methods such as diffuse reflectance, total internalreflectance, specular reflectance, photo acoustic, GC-IR, LC-IR, infraredmicrospectrometry, etc. have made this possible.
The mid-infrared profiles arise from the intensities of absorption ofthe fundamental frequencies and describe chemical structure, whichare indirectly related to the physical and chemical properties of thesystems analysed.
When a sample is measured, the absorbance of a sample or afunctionality measured at a particular wavelength is proportional tothe concentration of the sample or the functionality measured (Beerslaw). The traditional quantitative analysis in infrared spectrometry is,in general, based on this relationship.
9.1 UNIVARIATE APPROACH IN INFRARED SPECTROSCOPY
As mentioned above, the success of quantitative analysis using theunivariate approach in infrared spectrometry is based on the relation-ship between absorbance and concentration of the sample. A precisequantitative determination using univariate technique is possible incases where one can isolate an absorption arising from a functionalgroup and relate it entirely to the concentration of the sample. The
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accuracy of the analysis increases with the increase in the proportion-ality constant (molar absorptivity) of the functionality at that wave-number.
Most textbooks on infrared spectrometry deal with quantitativeanalysis using univariate technique and the approach to the techniquecan be found elsewhere.
9.2 MULTIVARIATE APPROACH IN INFRARED SPECTROSCOPY
9.2.1 The need for multivariate approach and types ofmultivariate systems
If the infrared spectra obtained in chemical systems, whether static ordynamic, contain an isolated non-overlapping absorption of a partic-ular functional group that it is necessary to quantify then one variableapproach will be successful. However, in mixtures where the absorp-tions arise from contributions from different functional groups, thequantification of a particular functional group using the one-variableapproach becomes difficult and sometimes impossible. Quantitativeanalysis using infrared spectra produced by these types of systemsrequires some intelligent procedures.
In many industrial applications measurements are made on systemscontaining several different chemical components, for example, on calib-ration standard mixtures of components for quantitative prediction ofcomponents in unknown samples. The infrared spectra measured on thecalibration mixtures will contain contributions from the components inthe mixtures. The spectral profiles vary with the quantities of differentcomponents present. A procedure that can model the spectral variationswith the change in the quantities of components and predict the compo-nents quantitatively in unknown samples could reduce the analysisburden on industrial laboratories. The separation of chemical compo-nents using other analytical techniques and quantification of thesecomponents individually increases the cost of quality control.
A chemical system can be dynamic or static. For example a reactionthat is studied by using infrared spectroscopy can produce severalhundred spectra over a period of time showing the changes taking placein the system. These spectra represent the total spectra of thereactants and products in the mixture. Likewise, a chemical systemmay be static and contain several components. These components can
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change in concentration in the system. For example, a packaginglaminate contains several layers of polymer material. The concen-trations of the components change across the depth of the laminate dueto the inter-diffusion of the components. An infrared analysis acrossthe depth of the layer will produce spectra that reflect the concentra-tion of the components present at a particular depth.
In certain applications one might need to characterise samples byusing similarity of their spectral profiles in order to classify them intodifferent classes. In these cases one needs tools that can compare thewhole infrared profiles of the samples measured.
If one is interested in studying these systems using infrared spect-rometry then the use of procedures suitable for resolving the spectrainto their contributing components and their concentrations areneeded. The procedures and techniques required to solve problemsinvolving most of the above types of systems involve the handling ofmatrices with several thousands of entries. These put very high dem-and on the capacity of the computers. The past decade has witnessedrapid growth in both computer hardware capacity and the developmentof new methodologies for the resolution of analytical profiles andquantification of mixtures.
Statistical procedures that can be used in applications of the typesmentioned above are widely available from several vendors. We will notdiscuss any particular multivariate package in general because allthese packages are based on the same mathematical and statisticalprocedures.
In order to understand the approach used in handling the tasksmentioned above, a theoretical treatment of the relevant chemometrictechniques is given in Sections 9.2.3 to 9.2.4.
9.2.2 Presentation of data
In most chemometric techniques data are presented in the form ofmatrices so that the software can handle them and process the model-ling needed in particular applications. In mid-infrared spectroscopy,the spectral profiles are presented as absorbances (or percentagetransmittances) against wavenumbers. It is obvious that one shoulduse wavenumbers as the variables. For example, if a spectrum ismeasured over m wavenumbers then the spectrum can be representedby a lxm matrix. Here, the matrix elements are absorbances atdifferent wavenumbers (Fig. 9.1).
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The absorbances can be represented as a vector and it is customaryto give all the vectors as column vectors in multivariate data analysis.A column vector x' can represent the data from the above object. Theprime indicates the transpose of the vector x.
If this spectral profile is going to be correlated to a property y(dependent variable or response variable) then the measure of theproperty is represented by a single value y. The variables x1 i are calledindependent variables (or predictor variables). This can be extended toseveral measurements n (objects). As shown above, each measurementcan be represented as follows as a row in a matrix of dimension nxm.
Y1
Y2Y3
Y4
Yn -
Xll X12 X1 3 X1 4 Xlm
X2 1 X2 2 X2 3 X2 4 X2m
X31 X3m
Xnl Xn2 Xn3 Xn4 Xnm
The matrix representing the dependent variables contain n entries (nrows). Likewise the spectral profiles matrix contains n rows eachrepresenting absorbances over m variables. The whole set of dependentvariables can be represented by a column vector y. The independentvariables from the n objects can be represented by a matrix Xcontaining n rows and m columns. In our general notation, the datamatrix X is a matrix with object vectors (Xk'; k = 1, 2...m).
If a relationship between the x variables and y variables is desired,one sets up a mathematical equation of the type shown below.
y=f(x) +E (9.1)
y=Xb +E (9.2)
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f0 a , bsorbance
4000 3000 i 2000 loo1000 400
Wavenumbers cm
I[XI X12 X13 X14 . . Xlm
Fig. 9.1. An example of an infrared absorption spectrum and the presentation ofabsorbances in a row matrix.
Here, b is an mx 1 matrix containing m coefficients and E is the residualmatrix of nxl.
Y1 X11 X1 2 X13 X1 4 . . . . . X b el
Y2 X21 X2 2 X23 X24 ..... X2m b2 e2
Y X31 .. . X3m b3 e3
Y4
Yn Xnl Xn2 xn3 Xn4 n.....x en
The solution for b can be found mathematically as follows.
b =X-y (9.3)
X-1 is the inverse of the data matrix X.
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-
F -
There are three possible cases from the above representations:
1. When the number of samples and variables are equal (n = m) thenthere is a unique solution for b provided that X has a full rank.
2. If the number of samples is less than the number of variables (n < m)then there are infinite number of solutions for b.
3. If the number of samples is more than the number of variables (n >m) then a solution for b can be obtained by multiple linearregression (minimising the length of the residual vector E (/el )).
The solution (Eq. (9.6)) is obtained by forming the generalisedinverse of X.
XTy =XrXb (9.4)
(X)-'X T y = (XTx)-XTX b (9.5)
b = (XX)-X T y (9.6)
We have to remember at this stage that only non-singular (thedeterminant is non-zero) square matrices have inverses. The techniqueshown above in multiple linear regression is to make the data matrix Xinto a square matrix (nxn matrix) by multiplying by its transpose X .
However, the inverse of this product matrix can exist only when theresulting matrix is non-singular (or has full rank; see appendix).
When the measurements are made in infrared spectroscopy, it canbe seen that there is a lot of redundant information in the data. Itmeans that there is 'collinearity' in the data profiles and the underlyingvariables (latent variables) responsible for the variation in the data arefewer than m. Modern multivariate techniques such as principalcomponent analysis (PCA) and partial least squares calibration (PLS)are developed to handle data with such problems.
In multivariate data techniques, the aim is to decompose the datamatrix into the product of two matrices that can give us information onvariables and objects. The criterion for the decomposition variesdepending on the type of model one is trying to build with the datameasured.
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... k01J
Fig. 9.2. Decomposition of the data matrix X into score matrix T and loading vectormatrix P. The figure illustrates the data matrix containing five measurements reduced tothe product of three score vectors and three loading vectors. Dimensionality of the
matrices X, TPT and E are the same.
9.2.3 The data matrix X and its decomposition
The data matrix X can be written as the sum of A matrices of rank 1(Eq. (9.7)) and a residual matrix E.
X=X 1 + X 2 + X3+ ... +XA + E (9.7)
The decomposed matrices can be written as the products of score vectorta and a loading vector pa (Eq. (9.8)).
X = tlpl'+ t2P2' + t3' ... + tAPA' + E (9.8)
Equation (9.8) is illustrated in Fig. 9.2.
X = TPT + E (9.9)
9.2.4 Graphic representation of spectral profiles
The data matrix containing the spectral profiles of n objects and mvariables can be viewed in two different ways (1) objects in variablespace and (2) variables in object space. In the first case the objects (n)are represented as data points in M dimensional (m orthogonaldimensions) variable space. In the second case the variables (m) arerepresented as data points in n dimensional (n orthogonal dimensions)object space. Graphic representations of more than three dimensionsare impossible on paper. A plot obtained for the objects in the variablespace displays quantitatively the relationships between the objects,and the variables plotted in the object space displays the relationships
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between the variables. All the information contained in the data matrixcan be explained by these two plots.
·I Column vector (variable vector)
Row vector (object vector) -> X1 1 X1 2 X13 X1 4 . . . Xm
X2 1 X2 2 X23 X24 .. X2m
X3 1 . . . .. X3m
Xnl X2 X,3 Xn4 .... . Xnm
9.3 PRINCIPAL COMPONENT ANALYSIS (PCA)
Principal component analysis is one of the several multivariatetechniques to decompose the total data matrix into data matricescontaining information regarding the system (objects and variables) weare dealing with. The criterion used for the decomposition of the datamatrix X is to extract latent variables in the direction of maximumvariance in the data; that is, the first latent variable-the first princi-pal component (PC 1)-is a linear combination of the original variablesthat explain the largest variance in the data X. The informationexplained by this latent variable is then removed from the data matrix.The second latent variable-the second principal component (PC2)-isthen extracted in the direction that explains maximum variance in therest of the data. These two principal components are orthogonal to eachother. The decomposition of the data matrix X into principal compo-nents represents an ordinary least-squares solution which minimisesthe residuals E. One can extract several principal components toexplain as much as possible variance in the data. The sum of theresiduals goes down with the number of principal componentsextracted and reaches a minimum and then increases with the
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I
extraction of more principal components (overfitting) [2]. The numberof principal components needed to explain the information in the dataset could be calculated by a process called cross-validation [2].
If the data matrix is column centred (i.e., each variable is adjustedin relation to the average of the variables), the origin of the variablespace moves to the point represented by the averages of the variables inthe data matrix. The principal components then pass through thispoint.
We understand that the principal components are linear combi-nations of the M original variables. The projections of objects on theprincipal components (latent variables) are called scores. The scores ofthe objects on the principal components can be calculated by the scalarproduct between the unit vector (Wa) along the respective principalcomponent and the object vector.
ta =Xwa (9.10)
All these scores are extracted in the score matrix T. The scores describethe similarities between the objects. These scores can be presented inthe form of a projection plot on the plane containing PC1 and PC2, orPC2 and PC3, or PC1 and PC3. These plots are called score plots (Fig.9.3). The samples that are similar group together in the score plots. Thesamples that are atypical to the other samples in the set will be isolated
X2
xlCos P
PC1
Fig. 9.3. Scores are obtained by projecting object vectors onto the principal components.
293
in the score plots and can be easily identified. These samples are called'outliers'.
The interpretation of a single latent variable and of the features of alatent variable model is possible through the connection to the originalvariables. This information is best displayed in loading plots. The co-ordinates of a variable in a loading plot are its loadings on the principalcomponents. A loading plot displays the contribution of a variable to amodel directly (proportional to the square of the distance from theorigin). Variables that are lying near the origin contribute little andvariables that are lying far away from the origin contribute more in thediscrimination of the samples. Variables located in the same directionof a principal component carry similar information.
Scores and loadings can be displayed simultaneously in plots calledbiplots [3]. These plots give information on the similarity between thesamples and the variables that are responsible for the discrimination ofthe samples.
9.4 MULTIVARIATE CALIBRATION
9.4.1 Partial least-squares (PLS) calibration
In many applications, one wants to relate some measured property y toa spectral profile x of intensities. The task is performed by measuringseveral pairs of(y, x) and subsequently constructing a model such that
y=fAx) (9.11)
The model is commonly calculated using least-squares proceduresunder the constraint of linear models. When there is only one propertyto be correlated with the spectral profile the PLS model buildingprocess is called PLS1, and PLS2 when there are more than two. InPLS1, the data is modelled in two stages, namely compression andcalibration. In the data compression stage the spectral data aremodelled in terms of a set of common latent regression factors {tl, t 2, t3... tA) (scores). These are n dimensional orthogonal column vectors for adata set with n samples and m spectral variables. These factorsdescribe the major variations in the spectral data and at the same timeare relevant for predicting the dependent variable. The compressionand calibration steps can be written as follows for column centredspectral and response variables (see Fig. 9.4):
294
x · I UI r I
Fig. 9.4. A figure showing the decomposition of a data matrix X in principal componentanalysis and partial least-squares calibration. The details regarding the decomposition
in these techniques are given in the text.
X= t 1 + t 2 + t3p 3 '... + tAPA' +E (9.12)
y = tlql+ tq 2+t 3q3 ... + tAqA + F (9.13)
In the PLS1 algorithm, the vectors t, p and q are calculated startingwith an equation relating the spectral data and dependent variable.
X=yw' + E' (9.14)
wl is a column vector (weightings) and is estimated as follows:
w 1'=y'X/ y'X (9.15)
w, is then normalised to unity. The estimated w, is then used tocalculate t, Pl and q1 [4]. These estimates are again used to calculatethe residuals of spectral and dependent variables. The process isrepeated untilA factors which minimise the prediction error are found.
The prediction of an unknown sample from the spectral profile xiproceeds as follows. First score t is found using the estimate for w1 andequation
Xi = tl w' + el (9.16)
Then the next score t2 is calculated from the solution of the aboveequation and the estimate for w2. The process is repeated until the Athfactor. The dependent variable is predicted by
y = tq, + t2q2 + t3 q3... + tAqA (9.17)
295
Alternatively the same prediction can be written as
y =Xb (9.18)
In PLS calibration a generalized inverse X+ is constructed as
b =X'y (9.19)
and the calibration coefficients vector b is determined by Eq. (9.20) [5]
b = W'(PW')-1 q (9.20)
The parameters b are estimated so as to predict the property y as wellas possible, for instance by means of cross validation [2]. By use of theparameters b the propertyy can be predicted from the infrared profiles.The predicted values of the property y for the training set samples isobtained by inserting Eq. (9.19) into Eq. (9.18):
y =XXy (9.21)
If there is a strong relationship between the property y and the intens-ities at some wavelengths, the predicted and the measured property ywill be similar and the correlation coefficient between measured andpredicted y will approach 1.
9.4.2 An application of multivariate calibration (PLS):determination of coal maturity (rank)
Maturity or coal rank is used extensively by geochemists to charac-terise coal and kerogen samples [6]. Several methods have been used todetermine maturity, including vitrinite reflectance, spore colour esti-mation, isotope ratios and chemical analysis such as biomarkers [7].
Coal consists mainly of three types of macerals: vitrinite, exinite,and inertinite. There is a correspondence between these three maceralgroups and the chemical composition. Coal petrologists and chemistshave linked the coal rank with maceral reflectance measurements [8].Vitrinite reflectance is the most widely used method for maturitydeterminations. However, the analysis is time consuming and sub-jective [9]. Additionally, vitrinite is only one of the organic componentsin the sample and is not the major oil precursor. Assessing maturity by
296
measuring the major oil precursors or determining the chemicalcomposition of geological specimens should provide more meaningfuland accurate characterisation for petroleum geological purposes.
Fourier-transform infrared spectroscopy was early taken into usefor determination of maturity of kerogen [10-11] and coal [12]. Theblack or dark brown colour of the samples made it very difficult toanalyse the samples by traditional transmission techniques. The dif-fuse reflectance technique then became popular for studying coal rank[13-14]. In these studies, specific functional group regions assigned toaromatic, aliphatic and C-H bending and stretching modes werecorrelated with chemical C/H ratios and rank. Fredericks et al. [15]used factor analysis to correlate specific parts of the FTIR spectra withvarious chemical and physical factors.
In this example, randomly selected, vitrinite-rich coal samples fromdifferent parts of the world varying in vitrinite reflectance and ingeological age were subjected to petrological, spectrometric and multi-variate analysis.
Twenty-five vitrinite reflectance measurements were made on eachof the collected samples in the usual manner and then averaged [8].The standard deviations for a selection of low-ranked coals (vitrinitereflectance 0.38-1.08) ranged from 0.03 to 0.13 vitrinite reflectanceunits, with an average of 0.06.
Diffuse reflectance spectra of the samples were recorded in therange 4000-600 cm-l using 64 scans and a resolution of 4 cm-l. Threedifferent spectra for each coal sample were averaged to give onespectrum for each sample. Each spectrum, consisting of 3401 datapoints, was transformed into Kubelka-Munk format [16].
Typical FT-IR spectra are given in Fig. 9.5 for five coal sampleshaving different rank and vitrinite reflectance. It can be seen that thealiphatic/aromatic ratio, as determined by the ratio of the peaks at2950 and 3050 cm l, decreases with increasing rank. It is difficult todraw qualitative conclusions about the other peaks, probably becauseof the interference from minerals.
The wavenumber variables were reduced by approximately a factorof 10 through a maximum-entropy data reduction process [17-18]. Thereduction process provides smaller matrices for computers to handlewith concomitant decrease in the computing memory and time requiredand an increase in speed.
After rejecting the abnormal and outlier calibration samples across-validated calibration model was established between the spectral
297
4000 3000 2000 1600 1200 600
Wavenumber cm'
Fig. 9.5. Typical FT-IR spectra of coal samples in Kubelka-Munk format.
profiles and the vitrinite reflectance values. The total prediction errorwas then computed at the end and the number of PLS componentsgiving the minimum prediction error was determined.
Forty-six coal samples with vitrinite reflectances ranging from 0.38to 1.08 were analysed. A total of five of these 46 samples were rejected,leaving 41 coal samples for the calibration.
Multivariate calibration on the 41 samples gave an absoluteprediction error of ±0.09 for determining the vitrinite reflectance of this
298
i
C
t
0 1 2 3 4 5 6 7 8 9
Number of PLS components
Fig 9.6. The progress of prediction error with the number of principal componentsextracted.
population. This prediction error is of the same order of magnitude asthe average standard deviation of the corresponding vitrinite reflect-ance measurements (s = 0.06). This low prediction error is probably thebest that can be obtained unless the measurement uncertainty in thevitrinite reflectance can be lowered.
The model developed by cross-validation gave an optimumprediction using seven PLS components as evident by the minimum inFig. 9.6, a plot of the Standard Error of Prediction (SEP) [2], vs. thenumber of PLS components. A plot of predicted vitrinite reflectance vs.measured vitrinite reflectance (Fig. 9.7) confirms the good performanceof the model.
The above results, obtained with coal samples from different partsof the world, produce one model that is generally applicable to vitrinite-rich coal samples with maturity within the range defined as the oilwindow (0.5-1.2). Thus, with the developed model and the combinationof diffuse reflectance FTIR spectroscopy and PLS, we can predict thecoal rank over the important oil production window on coal samplesfrom different locations. The values of rank obtained are equivalent tothose determined by vitrinite reflectance measurements, and areobtained with more objectivity, greater efficiency and less samplepreparation.
299
CdQQe)
U
C 0.8Q
Cd,) o . a
:0s
- 0. 6
._'6
0.4
0. 4
O
0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1
Measured vitrinite reflectance
Fig. 9.7. A plot showing the correlation between the measured and predicted vitrinite
reflectance of the coal samples used in the analysis.
9.5 TARGET PROJECTIONS
In certain applications, it will be of interest to find out which wave-numbers in the infrared profiles are most closely correlated to theproperty y. This can be done directly by calculating the covariancebetween measured y and the intensities at each wavenumber, i.e. bycalculating the covariances ry,x as
ry,, =ytX (9.22)
For spectral profiles the covariances can be plotted as a covariancegraph [19]. However, a better approach is to calculate the covariancebetween the predicted values of the property y and the intensities ateach wavenumber:
ry, = y tX (9.23)
The result of the so-called target projection can be plotted as a graph toshow the connection between a spectral profile andy. The point of usingpredicted instead of measured values of the property y in thecorrelation, is that wavenumbers of the infrared profiles with both high
300
0
00
00 o0 00
0 Q2) 000
0 000
0 0
O
lI
I / · / I I (
1.0
n
predictive ability and high correlation with y are given increasedimportance compared to those that has only a good correlation. Thiscan be shown by inserting Eq. (9.18) in Eq. (9.23):
ry, = bTXTX (9.24)
The product XTX is the variance-covariance matrix for the infraredprofiles. Equation (9.24) can be expanded to provide
m n m
ry,i bjExkikj =bjrxixj; i -,2,...,mj=1 k=l j=l
From Eq. (9.25), it is clear that the covariation ryxi between the pre-dicted values of y and the intensities at a wavelength y is calculated asa weighted sum of covariances ri,xj between intensities at two wave-lengths i andj. The regression coefficients bj are used as weights. Thisshows that the target projection procedure weights the importance ofprediction (bj) and correlation (rxi,xj) so that wavelengths that areimportant for predicting the property y have large variance (sensi-tivity) and are well correlated with other predictive wavelengths will behighlighted in the target projection plots. This is exactly the wave-lengths that are important for the interpretation of the structuraldescriptor in relation to the property y [19].
Equation (9.25) further shows that for wavelengths where thecovariance ry,i = 0, the variance in the intensities are probably zerossince it is quite improbable that a linear dependence should exist tomake this correlation exactly zero. Thus, target projection can be usedto find wavenumbers that gave the same intensity independent of theproperty we are examining.
The target projection plots are easy to interpret and can be used toname factors influencing a system. Furthermore, for systems wherevariation in the multivariate data with a given dependent variable issmall, target projection can amplify the changes in the targetprojection plots.
In infrared spectroscopic data, the profiles are generally broad andoverlapping. In many complex chemical systems the infrared spectraare featureless and contain very few broad bands. The changes in thespectra with external dependent factors are small and sometimesundetectable by visual inspection. Target projection analysis is verybeneficial in such systems for interpretational purposes.
301
9.5.1 Understanding the dehydration process and bandassignment of the overtone vibration of the water ofcrystallization of calcium oxalate monohydrate
Calcium oxalate was among the first compounds to be studied bythermogravimetric analysis and it has been used as a standard forthermal analysis [20,21]. The diffuse reflectance infrared spectra ofcalcium oxalate monohydrate is shown in Fig. 9.8. The bands repre-senting the H-O-H stretchings of the crystal water in calcium oxalateis broad over the range 3700-2600 cm- '. It exhibits five bands in thecharacteristic O-H stretching region. Band assignments of these peaksmade by Petrov and Soptrajanov [22] are given in Table 9.1.
Calcium oxalate crystal structure contains two non-equivalentoxalate ions and provides two different environments for the watermolecules in the crystal structure. Furthermore, each water moleculehas one of their OH groups involved in much stronger hydrogen bond-ing than the other. This should give rise to four O-H stretching bands.
L -
o -
(D
Zz
-o_Li
Mo
O
I
4~~~~~~~~~~~~~w R ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
302
oo00 3820 3240 2860 2480 2iOO ;720 i340 960 580NVENUMBE
Fig. 9.8. A diffuse reflectance spectrum of calcium oxalate monohydrate in KBr (2% w/w).(Reproduced from Ref. [69] with permission.)
I
I
I
1 �,-) �r
I
I 1 i i _n I
TABLE 9.1
Infrared band assignments of the OH stretching vibrations of the water molecules inthe calcium oxalate monohydrate crystals
CaC2O4.H2 0 Absorption (cmn1) Assignment
3486 v(OH) (2)
3428 v(OH) (1)
3336 v(OH) (1)
3250 26(OH) (?)
3058 v(OH) (2)
The fifth band, the lowest in intensity appears around 3258 cm- l . Thisis due to the overtone of the HOH bending mode reinforced by Fermiresonance [22]. The first and the last in the group (3486 and 3058 cm-l )
are due to one type of water molecule (type 2, as denoted by Petrov andSoptrajanov) and the remaining (3428 and 3336 cm-1) are due to theother type of water molecules (type 1). The oxalate stretching vibrationbands appear around 1627, 1320 cm-l and bending vibrations bandappear around 782 cm-l .
Several authors have investigated the dehydration mechanism ofcalcium oxalate monohydrate [20-21,23-24]. However, none of themwere able to demonstrate that there are two water molecular environ-ments present in the crystal and their order of elimination duringheating. In this application we will show that all these are possible incombination with target projection analysis.
A Nicolet 800 FT-IR spectrophotometer and a diffuse reflectanceaccessory manufactured by Spectra-Tech, USA, were used for thespectral measurements. A high temperature-high pressure chamber(also from Spectra-Tech) was placed in the diffuse reflectance accessoryin place of the ordinary sample cup. Calcium oxalate sample preparedas a 2% w/w in finely ground KBr was placed in the sample cup andheated to 80°C and held isothermally for 30 min to eliminate physicallyabsorbed water from calcium oxalate and KBr. Then it was heated at arate 5°C/min. and spectra were scanned at regular intervals. Eachsample spectrum measured during heating was ratioed with thecorresponding background (KBr measured under identical conditions)spectrum and the resulting relative reflectance spectrum [25] wastransformed into Kubelka-Munk format. The area under the OH
303
*10-s
Wavenumber cm-'l
Fig. 9.9. The infrared spectral profiles of the OH stretching vibrations of 2% (w/w)calcium oxalate monohydrate in KBr measured at different temperatures. (Reproduced
from Ref. [691 with permission.)
stretching bands was integrated. The area under OH stretchings wastested for linearity in advance and it can be used as a measure of thewater molecules in the crystal.
The diffuse reflectance infrared spectra acquired in the tempera-ture range 80-155°C, the dehydration profiles obtained using the inte-grated area under the OH stretching peaks and the first derivatives ofthe dehydration profiles of calcium oxalate monohydrate sample (2% w/w) at 5°C/min heating rate (rate of dehydration profiles after datasmoothing) are shown in Figs. 9.9, 9.10 and 9.11, respectively.
The derivative curves clearly show that there are at least tworeactions taking place during the dehydration. At a minimum, there isa first water release step occurring between 90 and about 125°C and asecond release step occurring between about 125 and 150°C. Thisobservation is the first one of this kind. The shape of the reaction rateprofiles suggests two different environments for the water molecules inthe calcium oxalate monohydrate crystal structure, and may corresp-ond to these different types of water molecules.
304
a
.aaD
.W
1.0
0.8
e 0.6
= 0.4
0.2
N n
iWd
I
I
I ~/.
80 102.5 125 147.5 170
Temperature oC
Fig. 9.10. The dehydration profiles of the 2% calcium oxalate monohydrate sample inKBr. (Reproduced from Ref. [69] with permission.)
0.04
" 0.02
0.0
'1'a .
A -I ~ , XA1 / tI // a!is_. .c _ _
80 102.5 125 147.5 170
Temperature oC
Fig. 9.11. The rate of dehydration of 2% calcium oxalate monohydrate in KBr. (Repro-duced from Ref. [69] with permission.)
In order to differentiate between the two different types of watermolecules, we divided the dehydration rate profiles (derivative data) of2% calcium oxalate sample (at 5C/min) into two subsets A and B (seeFig. 9.11).
These two subsets indicate the temperature ranges of the dehydra-tion where one can expect different types of reactions to take place.These temperature intervals in these two subsets were identified as80-120 and 120-133°C. The raw spectral profiles of the water stretch-ing vibrations in the temperature intervals 80-120 and 120-133°C
305
·- -- .- ---- ·-- · · '
0.000
-0.080
-0.160
-0.240
2 -0.320
is -0.400
0.00
: -0.07
-0.14
-0.21
-0.28
-0.35
3857 3517 3177 2837 2497
Wavenumber (cm-l)
Fig. 9.12. Target projection plots obtained with dehydration spectral profiles in the
temperature range: (a) 80-120°C; and (b) 120-133C. (Reproduced from Ref. [69] with
permission.)
were calibrated against their respective temperatures and maximumcorrelating factors were obtained for each of the subsets by targetprojection [26-27]. These plots are shown in Fig. 9.12a and b,respectively.
Target projection plots show the relative variation of each variablewith temperature and each of the plots is an expression of thebehaviour of the spectral data with increase in temperature. Zero linein the target plots separate the spectral profiles that is correlatingpositively and negatively with increase in temperature. The spectralprofiles shown in Fig. 9.12 are below the zero line. This indicates thatthe peaks decrease in intensity (due to loss of water stretching vibra-tions) with increasing temperature, which is also obvious from Fig. 9.9.However, if the water molecules disappear at the same time and at thesame rate then the target projection plots will be exact mirror images ofthe original spectral profiles. The figures show that this is not the case.Figure 9.12a shows without any doubt that the peaks at 3428 and 3336cm -1 , which are due to type 1 water molecules, disappear at a faster ratethan the type 2 water molecules (compare the depletion profiles of the
306
*10--
qI
peaks at 3486 and 3428 cm-'). The plot in Fig. 9.12b shows the dis-appearance of the type 2 water molecules at a slightly faster rate thanthe type 1 (observe that the peak at 3486 cm-l has a maximumdepletion profile). However, a higher rate of depletion of the peak at3058 cm ' together with the peaks at 3428 and 3336 cm-l was notexpected. This may be an indication that there is a peak relating to type1 water molecules under the peak at 3058 cm-1 . They may be havingoverlapping maximums and seen as one peak in the infrared spectrum.Furthermore, these plots clearly show that the dehydration of bothtypes of water molecules takes place at the same time but withdifferent rates. Obviously, the type 1 water molecules are attached tothe crystal structure with weaker hydrogen bonds than the type 2water molecules. This is in agreement with the crystal structuredetermination of calcium oxalate monohydrate by Cocco et al. [28-29].
Petrov and Soptrajanov [22] in their analysis of the infraredspectrum of calcium oxalate monohydrate assigned the weak band(peak at 3258 cm-l) for an overtone of the bending vibrations of one ofthe types of water molecules. They were unable to assign the band toany specific type of water molecules because of the strong oxalatestretchings appearing in the same region as the bending modes ofwater molecules. Our target projection plots indicate that this bandalso decreases in intensity with temperature. This is reasonablebecause this overtone arises from one type of water molecules. A closeanalysis of Fig. 9.12 reveals that this overtone has a slow rate ofdisappearance during the first part of the dehydration (Fig. 9.12a) anda higher rate during the second part of the dehydration. This leads us toconfirm that the overtone arises from the type 2 water molecules.
The approximate maximas obtained with the dehydration rateprofiles indicate that these occur around 0.3 and 0.75 conversion. Theseshow that the two different types of water molecules are equimolar.
9.6 DATA ANALYSIS AND RESOLUTION BY ALTERNATING LEASTSQUARES
If N spectra were obtained with mixtures containing A chemicalcomponents at M wavenumbers, they would define a two-way datamatrix X of size N by M. If the components do not interfere with eachother, one can express each spectrum as linear combinations of thespectra of the contributing components (Eq. (9.26)).
307
A
X =CS T +E =Zcsi +E (9.26)i=1
where A is the number of chemical components. ST is the spectralmatrix of the pure components (of dimension AxM) and C is theconcentration matrix of dimension NxA. The experimental noise isexpressed by the matrix E. The superscript, T, implies transposition ofa column vector into a row vector. By applying Eq. (9.26), we assumethat each measured spectrum adds up contributions from A purespecies with concentrations defined by the concentration profiles ci, i =1, 2, ..., A} and spectra by the spectral profiles {si, i = 1, 2, ..., A}. Asmentioned above, the equation is valid for chemical components that donot react or interfere with each other. However, if there are inter-actions between different species, then one has to include a set offactors that model the non-linearity caused by the interactions. Thenwe can write Eq. (9.26) with additional factors that model the inter-actions.
A A'
X =C *S +E =CisiT + E'Ci s'T +E (9.27)i=1 i=1
The number of factors (A') needed to model the interactions, isdependent upon spectral similarity, similarity of spectral changes dueto the interactions, as well as the noise level in the data set. Bothadditive and multiplicative errors like baseline shift and intensityvariation due to, e.g., different path length for each spectrum, willcontribute to the noise.
The resolution of the component spectra and concentrations wereaccomplished by using the ALS [5,30] procedure. With the constraint ofnon-negative concentration and spectral profiles, the iterative processof calculating the least square estimate of the spectral profiles in S* isgiven by
S *T = (C*TC*)- 1C*TX (9.28)
and the estimate of the concentration profiles in C* by
C* =XS*(S*TS*) 1 (9.29)
308
For every cycle, negative intensities are set to zero. Prior to enteringinto a new cycle, the concentration profiles are normalised to sum toone as shown in Eq. (9.30). If one has any selective informationregarding spectra or concentration profiles, the calculated values aresubstituted for by the selective information.
The relative concentrations for each component can be calculated,taking into account that they should sum to one, by:
A
Cb = cib i =1 (9.30)i=1
and the constants necessary to scale the concentration profiles arefound by least squares as
b = (CTC)-iCT1 (9.31)
9.6.1 Resolution of infrared spectra and concentrationprofiles of the components of a multilayer laminate
Polymers and plastics play a very important part in the life of 21stcentury man. A wide variety of things are made using plastics andpolymers. Thin sheets containing multilayers of polymer componentsare used as packaging material in industry. The following example is toillustrate the analysis of such a polymer laminate using infraredmicrospectroscopy and alternating least squares. Application of chemo-metric techniques to the infrared microspectrometric data acquiredfrom the laminate can reveal the spectra of individual layers and theirconcentration profiles. Furthermore, the chemical changes takingplace at the interfacial regions can also be detected and their chemicalinformation can be extracted in the form of the layer's infrared spec-trum. The chemical changes taking place over a period of time can bemonitored by comparing the infrared spectra of the layers at regularintervals. This will help the industry in determining the life span of thelaminate.
The problem at hand is a static multicomponent system becausethere are no dynamic changes in the concentrations of the componentsin the system when the measurements are made. The chemical compo-sition varies across the cross-section of the laminate and this variationdoes not change during the analysis.
309
12x100o pm apenure
/
I laminate layers
Fig. 9.13. A sketch showing the redundant aperturing technique used in the analysis ofpolymer laminate.
3500 3000 2500 2000 1500 1000
Wavenumber cm-'
Fig. 9.14. A stack plot showing the infrared microspectroscopic spectra acquired by usingthe redundant aperturing technique. (Reproduced from Brune et al., Surface Character-
ization, 1997, with permission.)
310
.1 ... .. 1.11-1..... .. ......
r��... ----.. , ........ --.- ....-... I...............--- ........1 .... I._-- .......1 ............ I. ......11. -.... --
1:x-.: .
I.9
The multilayer laminate sample was prepared by cutting a 5-pmthick cross-section using a microtome (Reichert-Jung, model 2050-Leica).
The sample was then mounted between NaCI windows in a com-pression cell (Spectra-Tech, Inc.). A small crystal of KBr was alsoplaced in the same cell and this was used for collecting the backgroundspectrum. The spectra of the laminate sample were collected at inter-vals of 2 lam, with a 12x100 pm2 sample area defined by redundantaperturing technique (Fig. 9.13). A total of 256 scans were co-added at aresolution of 8 cm-'. A total of 52 spectra of the laminate was collectedin this way.
The infrared microspectrometric data profiles of the 52 spectra (Fig.9.14) were subjected to multiple component analysis using alternatingleast squares regression (ALS).
The stack plot in Fig. 9.14 shows the presence of at least threecomponents. The components arising from interactions and otherunderlying components are difficult to visualise in the data set. Theanalysis by alternating least squares resulted in five real components.The infrared spectra of the components are shown in Fig. 9.16 and theirconcentrations are given in Fig. 9.15.
The components 1, 2, 4 and 5 are carbonated poly(vinyl chloride),poly(vinyl acetate), polyethylene and poly(vinyl dichloride) respect-ively. The component number 5 is an interaction product betweenpoly(vinyl acetate) and polyethylene. The depth span of the compo-nents is 40, 20, 34 and 24 pm for the components 1, 2, 4 and 5,respectively. The interaction product (component 3) has a doubledistribution and spans about 60 pm.
Step-number
Fig. 9.15. The concentration profiles of the components resolved. The total concentrationprofiles across the laminate are normalised to unity.
311
Wavenumber, cm-'
Fig. 9.16. The resolved infrared spectra of the components in the laminate sample.
312
9.6.2 Determination of the equilibrium constant andresolution of the HOD spectrum by alternating least squaresand infrared analysis
When water and deuterated water are mixed, a disproportionationreaction takes place and an equilibrium established with the productHOD as shown below
H2 0(1) + D20(1) = 2 HOD(1) (9.32)
The equilibrium constant for the equilibrium is given by the equation
K = [HOD] 2/{ [H2 0] [D2 0] } (9.33)
This equilibrium between water and deuterated water was first studiedby Topley and Eyring [31] in 1934. The equilibrium in gaseous phasehas been studied by several investigators [32-43]. The theoreticalvalue of K for the equilibrium in gas phase has been determined fromstatistical mechanical calculations using measured and theoreticalvibrational frequencies and anharmonicity constants obtained frominfrared spectroscopy [34]. The best theoretical value (K = 3.85) for theequilibrium in the gaseous phase was determined by Wolfberg et al.[41] This led to a theoretical value of 3.88 for the liquid phase equilibria[44].
The interest in the theoretical determination of K was due to thedifficulty in determining the equilibrium constant by experiment. Thisis because the species HOD can only exist in the presence of H2 0 andDO, and the analysis of HOD in the presence of H20O and DO back-ground is difficult.
The use of infrared spectroscopy in the study of H2 0 and D20O hasbeen almost absent because of the strong absorptions of the OH/ODfundamental stretching vibrations. These vibrations generally givevery broad absorptions due to extensive intermolecular bonding in thebulk of the liquid and created difficulty in obtaining the pure infraredspectrum of HOD by subtraction routines.
When the modern sampling techniques such as total internalreflectance became available [45], spectra with reasonable intensitiesof absorptions that are suitable for quantitative analysis could beobtained. However, the resolution of the infrared spectrum of HODrequired the use of the statistical equilibrium constant of 4 [46]. This
313
was needed to calculate the concentrations of the components in themixture so that subtraction of H2 0O and D2 0O spectra could be made.
In this application, the alternating least squares technique wasused to resolve the infrared spectra of H2 0O, D2 0O and HOD present inthe equilibrium mixture, their concentrations and to determine theequilibrium constant K for the reaction. Furthermore, the resolvedHOD spectra was used in assigning the bands.
The change in the concentrations in the equilibrium mixture wasachieved by changing the proportions of water and deuterated water.
A macro circle cell manufactured by Spectra-Tech was modified inour laboratory to suit our experimental set up [47]. Samples were takenapproximately to suit previously calculated amounts that could allowthe analysis of the mixture in the range that is gradually changing frommole ratio 1 - 0 (for water) and 0 - 1 (for D20 sample). The experi-ment started with a particular amount of water in the cell. The equili-brium concentrations were changed by adding deuterated watergradually in the cell. The D2 0 sample was measured in the cell alone toachieve mole fraction 1 for D2O.
A Nicolet 800 FT-IR spectrophotometer equipped with a mediumband MCT detector was used to acquire the infrared spectra. A total of100 scans were made each time in the range 4000-650 cm-l at aresolution of 1 cm- '. The spectra were then transformed into log(l/R).
The infrared spectra of pure water, deuterated water and a mixtureof water and deuterated water are shown in Fig. 9.17. The infraredspectra of the pure components and mixtures in log(l/R) format weretransferred to a PC for processing and data handling. The spectralprofiles were subjected to alternating least squares technique.
With the assumption that the hydrogen bonded structures in waterdo not change upon isotopic dilution, it appeared that we needed onlythree components in order to describe the equilibrium between H2 O,HOD and D2O.
Collecting the measured mixture spectra in a matrix X, the matrixcan be expressed as a product of a concentration matrix C and aspectral matrix S, as shown in Eq. (9.26) (omitting the experimentalerror matrix, E). The dimensions of the matrices are as given in Eq.(9.26). The concentration profiles of the equilibrium mixtures can beobtained by Eq. (9.29).
During the iterative procedure, for every cycle, negative intensitiesin the spectra were set to zero. In addition to the non-negativityconstraints used by Maeder and Zuberbuehler [30] and Karjalainen
314
I
DO
WAVENUMBER, cm- 1
Fig. 9.17. The infrared spectra of pure water, deuterated water and a mixture of the twoin log(l/R) format. (Reproduced from Ref. [31] with permission from Society for Applied
Spectroscopy.)
[48] for the concentration profiles, we imposed the constraints of zeroconcentration of D2 0O and HOD when only H2 0O was present and zeroconcentration of H2O and HOD when only D2O was present. Prior toentering into a new cycle, the concentration profiles were normalised.
Red shifts of the peaks were observed during the addition of deuter-ated water to the water in the cell. This shift is due to the isotopiceffects on peak positions upon dilution. This created problems in usingonly three components in the ALS procedure. In order to compensatefor the shift an additional component was included in the iteration. Theconcentration profiles and the shift-factor were normalised to unitlength before entering into a new cycle. The iterative process wasterminated when the change in the difference between the measuredand reconstructed mixture spectra was less than 0.01%.
The first four score vectors obtained from a PCA-decomposition ofthe bending region (1800-1000 cm-l), were used as seeds for the con-centration profiles and the shift-factor.
The resolved concentration profiles, normalised to unit length, forH2O, D2 0O and HOD are plotted vs. mole fraction added H2 0O, in Fig.9.18a. Together with the concentration profiles the shift-factor's
315
z0
z0C)
MOLE FRACTION ADDED D20
Fig. 9.18. (a) The resolved concentration profiles together with the shift factor's variationwith isotopic composition. (b) The molar concentration profiles of H2 0, D2 0 and HOD.
(Reproduced from Ref. [31] with permission from Society for Applied Spectroscopy.)
316
6
5.5
5
4.5
4
3.5
3
2.5
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7
MOLE FRACTION ADDED D20
Fig. 9.19. The equilibrium constant K vs the molar fraction of added D2 0. (Reproducedfrom Ref. [31] with permission from Society for Applied Spectroscopy.)
variation with isotopic dilution is plotted. The molar concentrations ofHO, D2 0 and HOD are plotted in Fig. 9.18b. The molar concentrationswere obtained from a least-square fit between the normalised con-centration profiles and the known total concentration. The predictedmolar concentrations were used to calculate the equilibrium constantaccording to Eq. (9.33). The average equilibrium constant was calcu-lated to 3.86 + 0.07, based on the concentrations between 30 and 70%water. We avoided the values in the other regions in order to reduce theerror in the equilibrium constant. A plot of K vs. molar fraction of addedH2 0 is given in Fig. 9.19. There is an excellent agreement both withvalues determined by experiment [39,40] and theory (K = 3.88) [44].
With the additional shift-factor incorporated in the iterativeprocess, the resolved spectra of H2 0 and D2 0 fit almost perfectly withthe measured spectra of pure H2 0 and DO. The resolved spectra forH2 0 and D2 0 correlates 99.99% with the measured spectra of the twopure analytes.
317
, AI
IY
~~~~i . .
-
i
z
WAVENUMBER, cm-
Fig. 9.20. The resolved spectrum of HOD and the shift factor. (Reproduced from Ref. [31]with permission from Society for Applied Spectroscopy.)
The resolved HOD-spectrum is shown in Fig. 9.20 together with thespectral part of the shift-factor. There are three main bands appearingin the HOD-spectrum at approximately 3385 (VoH), 2490 (oD) and 1450cm-l (v2). In addition there are two weaker bands at 2930 (2v2) and 1850cm-l (analogue to the association band in normal water (v2 + VL)).
Isotopic dilution impose spectral shift in the bending regions of D2 0Oand H2 0O. The shift is too extensive to be exactly portrayed by only oneform factor and leads to the observed small derivative-like bands in theHOD spectrum in the vicinity of 1640 and 1210 cm 1. The resolved HODspectrum has the same spectral features as the HOD spectrumresolved by Mar6chal [46].
9.7 TWO-DIMENSIONAL CORRELATION SPECTROSCOPY
The direct observation of a correlation between an infrared band and aRaman band, the examination a correlation between a certain bandand other bands in the same spectrum, etc. are now possible by general-ized two-dimensional (2D) correlation spectroscopy, which we willdescribe in this section. In addition, this method allows one to highlight
318
various information which cannot be extracted easily from a ordinaryone-dimensional spectrum.
9.7.1 Principle of two-dimensional correlation spectroscopy
One may associate 2D NMR above anything else with 2D spectroscopy.It is true that 2D NMR is an essential tool today to analyze NMRspectra of complex compounds. However, 2D spectroscopy is not neces-sarily limited to NMR. In recent years, more and more people havestarted using 2D spectroscopy in various areas related to spectroscopy.Two-dimensional correlation optical spectroscopy, in particular, whichwas proposed by Noda [49-51] about ten years ago, is attractingincreased attention as a new method for analyzing an infraredspectrum. The truth is that 2D correlation optical spectroscopy has anextremely wide variety of applications, ranging from variousspectroscopic analysis including infrared spectroscopy to even x-raydiffraction.
As shown in Fig. 9.21 [52], 2D correlation optical spectroscopyrequires to expand a spectrum in both the X and Y axis directions (the
vvavenumDer, v1
Fig. 9.21. An example of a 2D correlation spectrum. 2D infrared-Raman heterospectralcorrelation map generated from temperature-dependent spectral variations of N-methylacetamide in pure liquid. (Reproduced from Ref. [52] with permission. Copyright
(1996) American Chemical Society.)
319
spectra to be drawn in the X and Y axis directions may be the same aseach other or different from each other) and examines correlationsbetween bands which appear in the expanded spectra. Studying thecorrelations, we can more clearly note spectral features (e.g., over-lapping bands) which cannot be easily extracted from an one-dimensional spectrum. Although the basic idea of 2D correlationoptical spectroscopy is similar to that of 2D NMR, the methods ofcalculating correlation spectra are different [49-51]. In 2D correlationoptical spectroscopy, a dynamic cross-correlation between intensityvariations in bands induced by an external perturbation is calculatedto thereby obtain a 2D correlation spectrum.
We will explain 2D correlation spectroscopy in easier words withreference to Fig. 9.22 [51]. To obtain a 2D correlation spectrum, first ofall, we must externally apply a certain perturbation (e.g., a timechange, a temperature change, a concentration change) to our systemof interest [51-55]. Subjected to the perturbation, componentscontained in the system generally respond differently from each other.To observe the responses, the system is irradiated with an electro-magnetic wave. In other words, a series of spectra are measured. Now,assume that we applied a time change. In this case, we can obtain time-dependent spectra. As we will explain using formulas, to obtain 2Dcorrelation spectra, it is necessary to calculate dynamic spectra (Fig.9.22). Based on the calculated dynamic spectra, we thereafter calculate2D correlation spectra.
While Fig. 9.22 shows a thermal change, a chemical change andvarious other changes as an external perturbation, 2D correlationspectroscopy, when initially proposed, could be applied only to aninfrared signal which changes sinusoidally with time [49,50]. Althoughvery effective for studying a system which is applied with a smallexternal mechanical or electric perturbation as in the case of stretchinga polymer film [56], the initial 2D correlation spectroscopy was sub-
£ Mechanical, electrical,Perturbation ' chemical, magnetic,
t.. optical, thermal, etc.
Electro-magneticprobe (eg, IR, UV) Dynamic
System spectra
Fig. 9.22. A general scheme for constructing generalized 2D correlation spectra. (Repro-duced from Ref. [51] with permission. Copyright (1993) Society for Applied Spectroscopy.)
320
jected to a restriction that a change of a dynamic spectral intensity withtime (waveform) must be a simple sinusoidal wave. Hence, applicationsof the initial 2D correlation spectroscopy were rather limited.
To remove the above restriction and further generalize 2D correla-tion spectroscopy, Noda [51] proposed generalized 2D correlationspectroscopy based on a new mathematical algorithm in 1993. The new2D correlation spectroscopy is applicable to any waveforms, and hence,usable to various types of perturbations [51-55]. Further, the newcalculation method is readily applicable to a variety of spectroscopicmethods. In addition, generalized 2D correlation spectroscopy can beeasily developed into hetero 2D correlation spectroscopy such asinfrared-Raman and infrared-near infrared.
9.7.2 Synchronous and asynchronous correlation spectra
We will describe the principles of generalized 2D correlation spectro-scopy in more detail. Assume that we apply some perturbation whichchanges with time to a system. In this case, we obtain a series of spectray(v, t) (where v denotes an infrared wavenumber, a Raman shift, etc.)which change during a time period from -T/2 to T/2. Meanwhile,dynamic spectra y(v, t)] are calculated by subtracting a referencespectrum y(v) from the series of spectra yt(v, t)}
y(vt)y(v,t) = v)...-T............... T / (9.34)..................... and the other
Although the selection of the reference spectrum is somewhatarbitrary, in general, an average spectrum as follows is used
Y(v)= 12 y(v,t)dt (9.35)
In the case we use the formula (9.35), the dynamic spectra are devi-ations from the average of the spectra. Let us explain dynamic spectraby showing an actual example. Figure 9.23(A) shows temperature-dependent changes in near-infrared spectra of Nylon-12 [57]. In theregion from 6000 to 5500 cm-l, we can find bands due to first overtonesof CH2 stretching vibrations of the alkyl chain of Nylon-12. Since theconformation of the alkyl chain changes with temperature, the
321
A
B
wavenumber, v
Nylon 12 (30*C - 150GC)
Fig. 9.23. (A) Temperature-dependent near-infrared spectra obtained from 30 to 150°C inthe 6000-5500 cm- 1 region of Nylon-12. (B) Dynamic near-infrared spectra calculatedfrom original near-infrared spectra shown in (A). (Reproduced from Ref. [57] with
permission. Copyright (1997) American Chemical Society.)
intensities of the first overtones may change accordingly. This, how-ever, is not very clear in Fig. 9.23A. As soon as we calculate thedynamic spectra (induced by the temperature changes in this example),we can find the spectra as shown in Fig. 9.23B and immediately tellwhich bands change [57].
322
Now, in order to obtain generalized 2D correlation spectra, it isnecessary to Fourier-transform the dynamic spectra measured in thetime-domain into the frequency domain. The following is Fouriertransform of dynamic spectral intensity changes y(v1 , t) observed atsome spectral variable v1.
Y(Co) = y(v,te itdt (9.36)
= ylRe(o) + iIm ())
In the formula, yRe () and Y Im (io) denote a real part and an imaginarypart, respectively, of the complex Fourier transform of y(v1, t). TheFourier frequency co represents the individual frequency component ofthe time-dependent variation of (vl, t). In a similar manner, Y2 * (co), theconjugate of the Fourier transform of dynamic spectral intensity, y(v2,t), at spectral variable v2 is expressed as:
Y2 (o) =| Y(v2,t e+it dt (9.37)
= YIRe(o) -iYLm(o)
Once we find the Fourier transform, Y,(co) and Y* (co) of the dynamicspectra in the time domain measured at v1 and v2, respectively, we cancalculate the complex 2D correlation intensity between them by thefollowing formula.
X(v i(),v Y 2* ()don (9.38)
Equation (9.38) is a formula for calculating a dynamic cross-correlationbetween spectral bands. The formula (9.38) consists of a real part 'D(vl,v2) and an imaginary part i(v 1 , v2) as shown in the formula (9.39):
X(V1, V2 ) =( (v 1, V2 ) + i(V 1, V2 ) (9.39)
The real part 4)(vl, v2) and the imaginary part i(v,, v2) are called thesynchronous and asynchronous correlation spectra of the dynamicspectral intensity variations, respectively. In other words, these repre-sent that time-dependent changes in the spectral intensities at the twofrequencies v1, v2 are in-phase to each other (synchronous correlation
323
intensity) or out-of-phase to each other (asynchronous correlationintensity) [51].
While we consider time-dependent changes as perturbation inrelation to the formulas (9.34) through (9.39), since classic time seriesanalysis allows us to replace time with any other continuous variables,it is possible to calculate 2D correlation functions corresponding tovarious types of external stimuli such as a temperature change, a pHchange and a pressure change instead of a time change.
We will now explain the synchronous and asynchronous correlationintensities with reference to schematic diagrams. Figures 9.24a and bshow 1D(v,, v2) and T(v,, v2) as two-dimensional contours which arecalled synchronous and asynchronous correlation spectra, respectively[51]. In the synchronous correlation spectrum, there appear on thediagonal line a few peaks called auto-correlation peaks which corres-pond to v = v2. The larger a band intensity change in response to anexternal perturbation (such as a temperature change), the stronger theintensity of an auto-correlation peak is. An auto-correlation peakalways has the positive sign. Needless to say, a band having a strongintensity does not necessarily shows a strong auto-correlation peak.Hence, bands which overlap each other in a one-dimensional spectrummay be observed as separate bands in 2D correlation spectra because ofdifferent levels of responses to a perturbation.
Peaks located at the off-diagonal positions of the synchronousspectrum are called cross peaks. The existence of a cross peak at (vl, v2 )in the synchronous spectrum means that two bands at v, and v2 changein a similar manner to each other in response to a certain perturbation.A cross peak has the positive or the negative sign. A cross peak has thepositive sign when the intensities of both bands increase or decreasewith a perturbation. When one band increases while the otherdecreases, a cross peak shows the negative sign.
An asynchronous correlation spectrum provides complementaryinformation to information from a synchronous correlation spectrum.Of course, an asynchronous correlation spectrum does not show anauto-correlation peak. A cross peak at (v1, v2 ) in an asynchronouscorrelation spectrum means that the intensities of two bands at v, andv2 exhibit out-of-phase responses to a certain perturbation. Forexample, a cross peak appears when the intensities of two bandschange at different temperatures. If an intensity change at v occurs ata higher temperature than an intensity change at v2, a cross peaklocated above the diagonal line has the negative sign. On the other
324
I.5c·0
U)
M
m
rn
Spectral variable, v,
r
o
Spectral variable, v
Fig. 9.24. (a) Synchronous and (b) asynchronous 2D correlation spectra constructed fromdynamic spectra. One-dimensional reference spectrum is also provided at the top and
side of the 2D map. (Original figures were prepared by Noda.)
hand, if the former occurs at a lower temperature than the latter, thesign of the cross peak is positive. This rule, however, is reversed if D(v,v2) < 0. One of the major features of generalized 2D correlation spectros-copy lies in asynchronous correlation spectra. This is because we canclarify in which order the intensities of various bands change if weanalyze asynchronous correlation spectra.
325
9.7.3 What we can learn from 2D correlation spectroscopy
The advantages of generalized 2D correlation spectroscopy are sum-marized as follows [51-68].
1. Enhancement of apparent spectral resolution of overlapped bands.2. Band assignments through observations of correlations between the
bands.3. Studies of inter and intra-molecular interactions through selective
correlation between bands.4. Probing the specific order in which the intensities of various bands
change.
Thus far, generalized 2D correlation spectroscopy has been applied, forexample, to time-, temperature-, pressure-, concentration-, pH-, andphase angle-dependent spectral variations in the fields of infrared,Raman, near-infrared, visible, mass and fluorescence spectroscopy[51-681. Generalized 2D correlation spectroscopy has been utilized notonly for basic research but also for applications such as those inbiomedical sciences and food sciences. As an example of 2D correlationspectroscopy studies, we will describe a 2D infrared correlationspectroscopy study on the secondary structure of proteins usinghydrogen-deuterium (H-D) exchange [58].
As described in Section 8.7.1, infrared spectroscopy has long beenused as a valuable tool for qualitative and quantitative estimation ofthe secondary structure of proteins. Although the assignment of thecomponents of the amide I band to secondary structure such as a-helixand 3-sheet has been the object of much effort, it is still a matter of con-troversy. Two-dimensional infrared correlation spectroscopy enhancesthe spectral resolution of the amide I and II regions and makes possibleto assign some of the amide I and II bands to given conformations.
Nabet and Pezolet [58] reported a 2D infrared correlationspectroscopy study of the secondary structure of myoglobin. They usedH-D exchange of the amide protons as an external perturbation togenerate the 2D synchronous and asynchronous spectra [58]. Becauseof the fact that the amide protons associated with each conformationare not exchanged simultaneously, the contributions from differentconformations to the amide bands may be separated. The analysis ofsynchronous and asynchronous maps of myoglobin show that thismethod is very useful to unravel the different component bands underthe poorly resolved amide I, II, and II' bands of proteins.
326
They prepared thin films of myoglobin of microgram quantity on anattenuated total reflection (ATR) crystal [58]. The H-D exchange wasinduced by hydrating the films with a flow of nitrogen containing D2 0Ovapour. In general, there are two kinds of amide groups as to thekinetics of deuteration; some amide groups that are readily accessibleto water are exchanged rapidly at the beginning of the deuterationprocess, whereas those involved in structures that are less accessible tothe solvent show a slower exchange kinetics. Thus, in order to separatemore efficiently the fast kinetics from the slower ones, differentsampling time domains were used.
Figure 9.25 shows A synchronous and B asynchronous 2D infraredcorrelation spectra of myoglobin calculated from the first 10 spectrarecorded during the H-D exchange process [58]. In the amide I region ofthe synchronous correlation map for the rapidly exchanging protons(Fig. 9.25A) three correlation peaks appear at 1675, 1640, and 1615cml. These amide I components are assigned to the -turns, randomcoil, and intermolecular P-sheets, often found in aggregated proteins,respectively. Therefore, it is very likely that the amide groups associ-ated with these three conformations are exchanged first during thedeuteration process. The strongest peak in the synchronous map isobserved in the amide II region at 1530 cm-l, while in the amide II'region two major peaks can be identified at 1440 and 1350 cm-1 . Theasynchronous map of myoglobin for the rapidly exchanging protonsdevelops two cross peaks at 1675-1640 cm-l and 1640-1615 cm-l in theamide I region, confirming that the three peaks at 1675, 1640, and 1615cm-1 appearing in the synchronous map are ascribed to three differentconformations.
Figure 9.26 depicts the corresponding synchronous spectrum calcul-ated from 10 spectra obtained approximately 1 h after the beginning ofthe H-D exchange process [58]. It shows one autopeak at 1655 cm - , afrequency that is generally assigned to the amide I mode of the a-helixconformation. Thus, it seems that the amide protons of the a-helixconformation are exchanged more slowly than those associated withintermolecular -sheets, random coil, and 3-turns [58]. The other intensepeaks observed at 1545 and 1345 cm-l may be assigned to the amide IIand amide II' modes of the a-helices of myoglobin, respectively.
The synchronous spectrum for the slow exchanging system (Fig.9.26) also shows a weak component at 1625 cm-l. This component couldbe due to the 3-sheet conformation. Since the random coil and the -turn structures do not develop the amide I components in the
327
50 1250
A Wovenumbers, vt B
1350 1450 1550 1650 1750
Woverurmbers,
Fig. 9.25. (A) Synchronous and (B) asynchronous 2D infrared correlation spectra ofmyoglobin calculated form the first 10 spectra recorded during the H-D exchangeprocess. (Reproduced from Ref. [58] with permission. Copyright (1997) Society for Applied
Spectroscopy.)
S
Ike
3
Ec3C}
-A Wovenurnbers,
Fig. 9.26. Synchronous 2D infrared correlation spectra of myoglobin calculated from 10spectra measured approximately 1 h after the beginning of the H-D exchange process.(Reproduced from Ref. [58] with permission. Copyright (1997) Society for Applied
Spectroscopy.)
328
13
synchronous map calculated for the long time domain, the H-Dexchange rate for the P-sheet structure seems to be slower than thosefor the random coil and -turn structures.
ACKNOWLEDGEMENTS
Some of the text and figures are reprinted from: D. Brune et al., SurfaceCharacterization, 1997, pp. 410-424 (with permission from Wiley-VCH). F.O. Libnau and A.A. Christy, Determination of equilibriumconstant and resolution of the HOD spectrum by alternating least-squares and infrared analysis,Appl. Spectros., 49 (10) 1995 1431-1438;A.A. Christy, E. Nodland, O.M. Kvalheim, A. Burnham and B. Dahl,Determination of kinetic parameters for the dehydration of calciumoxalate mono hydrate by diffuse reflectance FT-IR spectroscopy. Appl.Spectros., 48 (5) (1994) 561-568 (with permission from Society forApplied Spectroscopy).
REFERENCES
1. R.S. McDonald, Infrared spectrometry. Anal. Chem., 56 (1984)349R-372R.
2. H. Martens and T. Naes, Multivariate Calibration. Wiley, Chichester,1989.
3. K.R. Gabriel, Biometrica, 58 (1971) 953.4. H.A. Martens, Multivariate calibration: Quantitative interpretation of
non-selective chemical data, Dr. Techn. Thesis, Technical University ofNorway, Trondheim, 1985.
5. S. Wold, A. Ruhe, H. Wold and W.J. Dunn III, SIAM J. Sci. Stat.Computat., 5 (1984) 735-743.
6. F.L. Staplin, W.G. Dow, C.W.D. Milner, D.I. O'Connor, S.A.J. Pocock, P.van Gijzel, D.H. Welte and M.A. Ytikler, How to Assess Maturation andPaleotemperatures, Short Course Number 7, SEPM, Box 4756, Tulsa, OK74104, USA, pp. 1-289.
7. B.P. Tissot and D.H. Welte, Petroleum Formation and Occurrence -A Newapproach to Oil and Gas Exploration. Springer Verlag, Berlin, Heidelberg,New York, 1984.
8. E. Stach, M.Th. Mackowsky, M. Teichmiiller, G.H. Taylor, D. Chandraand R. Teichmuiller, Stach's Textbook of Coal Petrology, 3rd edn. GebrtiderBorntraeger, Berlin, 1982.
9. D.H. Dembicki, Jr., Geochim. Cosmochim. Acta, 48 (1984) 2641.
329
10. P.L. Robin and P.G. Rouxhet, Geochim. Cosmochim. Acta, 42 (1978) 1341.11. T.V. Verheyen and R.B. Johns, Geochim. Cosmochim. Acta, 45 (1981)
1899.12. T.V. Verheyen, R.B. Johns and R.J. Esdaile, Geochim. Cosmochim. Acta,
47 (1983) 1579.13. M.P. Fuller, I.M. Hamadeh, P.R. Griffiths and D.E. Lowenhaupt, Fuel, 61
(1982) 529.14. R.E. Anacreon, Application of diffuse reflectance for analysis of coal
samples, Perkin-Elmer IR Bulletin, IRB-92, Instrument Division,Norwalk, CT, pp. 1-29.
15. P.M. Fredericks, J.B. Lee, P.R. Osborn and D.A.J. Swinkels, Appl.Spectrosc., 39 (1985) 303.
16. P. Kubelka and F. Munk, Ein Beitrag zur Optik der Farbanstriche.Zeitschrift fur Technische Physik, 11a, (1931) 593-601.
17. W.E. Full, R. Ehrlich and S.K. Kennedy, J. Sed. Petrol., 54 (1984) 117.18. T.V. Karstang and R.J. Eastgate, Chemom. Intell. Lab. Syst., 2 (1989) 209.19. O.M. Kvalheim and T.V. Karstang, Chemom. Intell. Lab. Syst., 7 (1989) 39.20. R.L. White and J. Ai, Appl. Spectrosc., 46 (1992) 93.21. L.A. Sanchez and M.Y. Keating, Appl. Spectrosc., 42 (1988) 1253.22. I. Petrov and B. Soptrajanov, Spectrochim. Acta, Part A, 31 (1975) 57.23. C. Bremard, C. Depecker, H. Des Grousilliers and P. Legrand, Appl.
Spectrosc., 45 (1991) 1278.24. E.S. Freeman and B. Carrol, J. Phys. Chem., 62 (1958) 394.25. A.A. Christy, R.A. Velapoldi, T.V. Karstang, O.M. Kvalheim, E. Sletten
and N. Telnaes, Chemom. Intell. Lab. Syst., 2 (1987) 199.26. O.M. Kvalheim and T.V. Karstang, Chemom. Intell. Lab. Syst., 2 (1987) 235.27. A.A. Christy, O.M. Kvalheim, F.O. Libnau, G. Aksnes and J. Toft, Vib.
Spectrosc., 6 (1993) 1.28. G. Cocco, Atti Acad. Naz. Lincei, Rend. Classe Sci. Fis. Mat. Nat., 31 (1961)
292.29. G. Cocco and C. Sabelli, Atti Soc. Toscana Sci. Nat. Pisa Mem. PV Ser. A,
69 (1962) 247.30. M. Maeder and A.D. Zuberbuehler, Anal. Chim. Acta, 181 (1986) 287.31. B. Tropley and H. Eyring, J. Chem. Phys., 2 (1934) 217.32. H.C. Urey, J. Chem. Soc., (1947) 562.33. A.J. Narten, Chem. Phys., 41 (5) (1964) 1318.34. J.W. Pyper and F.A. Long, J. Chem. Phys., 41 (1964) 2213.35. A. Narten, J. Chem. Phys., 42 (1965) 814.36. R.A. Weston, Jr., J. Chem. Phys., 42 (1965) 2635.37. L. Friedman and V.J. Shiner, Jr., J. Chem. Phys., 44 (1966) 4639.38. J.W. Pyper, R.S. Newbury and G.W. Barton, Jr., J. Chem. Phys., 46 (6)
(1967) 2253.39. A.J. Kresge and Y. Chang, J. Chem. Phys., 49 (1968) 1439.
330
40. V. Gold, Trans. Faraday Soc., 64 (1968) 2270.41. M. Wolfsberg, A.A. Massa and J.W. Pyper, J. Chem. Phys., 53 (8) (1970)
3138.42. J.W. Pyper and L.D. Christensen, J. Chem. Phys., 62 (7) (1975) 2596.43. G. Jancso and W.A. Van Hook, Chem. Rev., 74 (1974) 689.44. D.V. Fenby and A. Chand, Aust. J. Chem., 31 (1978) 214.45. A. Lorber, Anal. Chem., 58 (1986) 1167.46. Y. Marechal, J. Chem. Phys., 95 (8) (1991) 5565.47. F.O. Libnau, A.A. Christy and O.M. Kvalheim, Appl. Spectrosc., 49 (10)
(1995) 1431.48. E.J. Karjalainen, Chemom. Intell. Lab. Syst., 7 (1989) 32.49. I. Noda, Bull. Am. Phys. Soc., 31 (1987) 520.50. I. Noda, Appl. Spectrosc., 44 (1990) 550.51. I. Noda, Appl. Spectrosc., 47 (1993) 1329.52. I. Noda, Y. Liu and Y. Ozaki, J. Phys. Chem., 100 (1996) 8674.53. I. Noda, A.E. Dowrey, C. Marcott, Y. Ozaki and G.M. Story, Appl.
Spectrosc., 54 (2000) 236A.54. Y. Ozaki and I. Noda, Two-dimensional Correlation Spectroscopy. Am-
erican Institute of Physics, New York, 2000.55. Y. Ozaki, in: J.M. Chalmers and P.R. Griffiths (Eds.), Handbook of Vibra-
tional Spectroscopy. Wiley, Chichester, 2001, in press.56. I. Noda, A.E. Dowrey and C. Marcott, in: G. Zerbi (Ed.), Modern Polymer
Spectroscopy. Wiley-VCH, Weinheim, 1999, pp. 1-32.57. Y. Ozaki, Y. Liu and I. Noda, Macromolecules, 30 (1997) 2391.58. A. Nabet and M. Pezolet, Appl. Spectrosc., 51 (1997) 166.59. I. Noda, Y. Liu, Y. Ozaki and M.A. Czarnecki, J. Phys. Chem., 99 (1995)
3068.60. S.J. Gadalleta, A. Gericke, A.L. Boskey and R. Mendelsohn, Biospectros-
copy, 2 (1996) 353.61. M. Muller, R. Buchet and U.P. Fringeli, J. Phys. Chem., 100 (1996) 10810.62. I. Noda, Y. Liu and Y. Ozaki, J. Phys. Chem., 100 (1996) 8665.63. K. Ataka and M. Osawa, Langmuir, 14, 951 (1998).64. Y. Nagasaki, T. Yashihara and Y. Ozaki, J. Phys Chem., B, 104 (2000)
2846.65. M.A. Czarnecki, P. Wu and H.W. Siesler, Chem. Phys. Lett., 283 (1998) 326.66. C.P. Schultz, H. Fabian and H.H. Mantsch, Biospetrosc., 4 (1998) 19.67. L. Smeller and K. Heremans, Vib. Spectrosc. 19 (1999) 375.68. B. Czarnik-Matusewicz, K. Murayama, R. Tsenkova and Y. Ozaki, Appl.
Spectrosc., 53 (1999) 1582.69. A.A. Christy, E. Nodland, O.M. Kvalheim, A. Burnham and B. Dahl,
Determination of kinetic parameters for the dehydration of calciumoxalate mono hydrate by diffuse reflectance FT-IR spectroscopy. Appl.Spectros., 48 (5) (1994) 561-568
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Appendix I
Physical constants, conversion factorsand atomic masses
A. Some physical constants
Quantity Symbol Value Units
Speed of light c 2.99792x103 ms - 1
Planck Constant h 6.62608xO134 Js
Avogadro constant NA 6.02214x10 2 3 mo1-1
Atomic mass unit u 1.66054x10- 2 7 kg
Electron mass me 9.10939xl10-3 kg
Proton-mass mp 1.67262x10 27 kg
Neutron mass ms 1.67493x10- 2 7 kg
Elementary charge e 1.60218x10-1 9 C
Gas constant R 8.31451 JK - 1 mol- 1
B. Conversion factors
Quantity Conversion factor
1 eV 1.60218x10-19J
1 cal 4.184 J
1 atm 101.325 kPa
1 A 10-1° m
1 Nm- l 103 gl
333
C. Some atomic masses
Element
Hydrogen (H)
Carbon (C)
Nitrogen (N)
Oxygen (0)
Phosphor (P)
Sulphur (S)
Chlorine (Cl)
Iodine (I)
Mass x10-2 7 kg
1.6738
19.9450
23.2587
26.5676
51.4332
53.2369
58.8867
210.7299
334
Appendix II
Some character tables and point groups
Cs E GxE
A' 1 1 x,yR z xy,z,xy
A" 1 -1 zR,R,Ry xzyz
Ci E iAg 1 1 R,RyRz x ,y z ,xy,xz,yz
A. 1 -1 Xy,z
C2 l E C2(z)
A i 1 ZR z x2,y 2z
2, xy
B 1 -1 xyRx,y xz,yz
C2v and C3v are found in the text of Chapter 4.
C4, E 2C4(z) C2 2(,y 2Gd
A1 1 1 1 1 1 z X2 + y2,z2
A2 1 1 1 -1 -1 Rz
B1 1 -1 1 1 -1 2 _y2
B2 1 -1 1 -1 1 xy
E 2 0 -2 0 0 (xy) (Rx,Ry) (yz,xz)
335
C5 E 2C5(z) 2C52 5y v 4 = 72°
41 1 1 1 1 z z2
,X2 +y2
A2 1 1 1 -1 Rz
E1 2 2cos4 2cos2 0 (xy) (R,Ry) (yz,xy)
E2 1 2cos2 2cos 0 x2
y2,xy
C,, E 2C, ... ooCV
+ (A1) 1 1 ... 1 z x2 +y2,z2
Z- (A2) 1 1 ... -1 Rz
n1 (El) 2 2cos4 ... 0 (x,y) (Rx,Ry) (yzxz)
A (E2) 2 2cos25 ... 0
· (Eg) 2 2cos35 ... 0 (x2 -y 2xy)
C2h E C2 i ah
Ag I 1 1 1 Rz 2,2,y2
Bg 1 -1 1 -1 Rx,Ry xy
Au 1 1 -1 -1 z yz,xz
B, 1 -1 -1 1
D2 E C2 (z) C2 (y) C2 (x)
A 1 1 1 1 Rz z2,X
2,y
2
B1 1 -1 1 -1 ZRz xy
B2 1 1 -1 -1 y,Ry xz
B3 1 -1 -1 1 x,Rx yz
D3 E 2C3 3C2 '
Al 1 1 1 z2x 2 + y2
A2 1 1 -1 ZR z
E 2 -1 0 (xy),(RxRx) (x2-y2 ,xy),(yz,xz)
336
D4 E 2C4 C2 2C 2 ' 2C2"
A1 1 1 1 1 1 z2,x2+y
A2 1 1 1 -1 -1 z,R
B1 1 -1 1 1 -1 x2_y 2
B2 1 -1 1 -1 1 xy
E 2 0 -2 0 0 (xy),(R R,) (yz,xz)
D2 d E 2S4 (z) C2 2C 2 ' (x) 2
3d
A1 1 1 1 1 1 z2,x2+y2
A2 1 1 1 -1 -1 R
,B1 1 -1 1 1 -1 x2y 2
B2 1 -1 1 -1 1 z xy
E 2 0 -2 0 0 (xy),(R,,Rv) (yz,xz)
D3d E 2C3 3C2 ' i 2S6 3cd
Alg 1 1 1 1 1 1 z2+y2
A2g 1 1 -1 1 1 -1 Rz
Eg 2 -1 0 2 -1 0 (Rz,Ry)
Alu 1 1 1 -1 -1 -1 2_y 2
A2 u 1 1 -1 -1 -1 1 z xy
iE, 2 -1 0 -2 1 0 (x,y) (yz,xz)
D2h E C2(z) C2(y) C2 (x) i oy cz y
Ag 1 1 1 1 1 1 1 1 z2,x2y 2
Big 1 1 -1 -1 1 1 -1 -1 Rz xy
B2g 1 -1 1 -1 1 -1 1 -1 Ry xz
Bg 1 -1 -1 1 1 -1 -1 1 R yz
AU 1 1 1 1 -1 -1 -1 -1
Bl1 1 1 -1 -1 -1 -1 1 1 z
B2. 1 -1 1 -1 -1 1 -1 1 y
B3 . 1 -1 -1 1 -1 1 1 -1 z
337
D31, E 2C3 3C2' Ch 2S 3 3c,
A1' 1 1 1 1 1 1 z2
A2 1 1 -1 1 1 -1 R,
E' 2 -1 0 2 -1 0 (x,y) (x2-y2 ,xy)
Al" 1 1 1 -1 -1 -1
A2" I 1 -1 -1 -1 1 z
E" 2 -1 0 -2 1 0 (Rx,RY) (yz,xz)
D6h E 2C6 2C 3 C2 3C 2' 3C2" i 2S 3 2S 6 , 3, d 3V =
lg 1 1 1 1 1 11 1 11 1 2,X2+y2
A2g 1 1 1 1 1 1 1 1 1 -1 -1 R
Big 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1
B2g 1 -1 1 -1 -1 1 1 -1 1 -1 -1 1 (yz,xz)
Ig 2 1 -1 -2 0 0 2 1 -1 2 0 0 (R~,Ry) (x2-y2,xy)
2 -1 -1 2 0 0 2 -1 -1 2 0 0
Alu 1 1 1 1 1 1 -1 -1 -1 -1 -1 -1
Blu 1 -1 1 -1 1 -1 -11 -1 1 -1 1
lu
lu 2 1 -1 -2 0 0 -2 -1 1 2 0 0 (x,y)
2 -1 -1 2 0 0 -2 1 1 -2 0 0
D.h E 2CO ... ooa, i 2S, ... moC
Z(Ag) 1 1 1 1 1 1 z2,x2+y2
g(A 2g) 1 1 -1 1 1 -1 R
[lg(Elg) 2 2cosl 0 2 -2cos 0 (RRy) (yz,xz)
Ag(E2g) 2 2cos2? 0 2 2cos2o 0 (x2-y2 ,xy)
,S(Alu) 1 1 -1 -1 -1 -1
XZ(A 2 u) 1 1 -1 -1 -1 1
F[I(E1u) 2 2coso 0 -2 2coso 0
A(E 2 u) 2 2cos2o 0 -2 -2cos2o 0 (XY)
338
Appendix III
Matrices
A. A matrix
A matrix is an array of elements of the following form. The horizontalsets of elements are called rows and the vertical sets of elements arecalled columns. A matrix is represented by a single symbol.
A = [aj] =
all a, 2 a13 all a,.
a2 l a2 2 a23 a2j a2m
ail ai 2 ai3 ai3 aim
ani an 2 an an anm
The element aij is the entry belonging to the ith row andjth column ofthe matrix. The above matrix has n rows and m columns. These arecalled dimensions of the matrix. The above matrix is said to be an nxmmatrix. When the dimensions are equal, the matrix will have an equalnumber of rows and columns (m = n) and the matrix is a square matrixwith m2 entries. Matrices follow certain rules and we shall learn moreabout their behaviour in the following sections.
B. Matrix addition
Matrices of same dimensions can be added. IfA and B are two matricesof the same dimensions then the sum of the matrices is a matrix of the
339
same dimension as A and B. The resulting matrix C will contain entriescij which are given as cij = a + b.
For example, the addition of matrices A and B are shown below
A= 0 1 -
1 2 0
0 -1 2
B= 1 2 0
-1 -1 0
1 -1 3
A+B= 1 3 -1
0 1 0
Matrix addition is commutative. It means that whether we add matrixB with A or A with B, the resulting matrix is the same.
A+B=B+A=C
C. Scalar product of a matrix
A matrix A can be multiplied by a real number k. The multiplicationcan be written as kA. The resulting matrix is of the same dimension asA and contains elements kaij as entries. For example 3A is
0 33A= 0 3 -3
3 6 0
D. Matrix subtraction
The subtraction of a matrix B from A can be considered as an addition aA+ (-1)B. Matrices of the same dimensions can be subtracted from each
340
other. The resulting matrix is a matrix of the same dimension. Thematrix would contain elements cij = aj - bvi if B is subtracted from A ordi = bj - aij ifA is subtracted from B. It is easy to see that the result ofthe subtraction is not the same. For example, the subtractions wouldresult into the following matrices.
1 1 -- -1 -1 I
A-B=fi -1 B B -A = 12 3 0 -2 -3 0
E. Matrix multiplication
Two matrices C and D can be multiplied if the number of columns inthe matrix C is the same as the number of rows in D. For example if C isan nxm matrix then D has to be an mxk matrix. The product of thematrices C and D is an nxk matrix.
If the resulting matrix is E then the element ej is given by
ei = Zcikdkjk=l
where m is the number of columns in the matrix C and number of rowsin the matrix D. There is no product between two matrices that doesnot satisfy the requirement above.
For example, if
C=[' 2] and D =[ -1 1]
then the product E = CD is
CD = 5 2
For example, the product between matrices A and B given above is
341
0 1 0 -1 2 1 0 2AB= 0 1 -1 1 2 0 = 2 3
12 0 -1 -1 0 2 3 2
The product between B and A is
0 -1 2 1 0 1 2 3 1BA= 1 2 = 1 -1 1 2 -1
-1 -1 0 1 2 0 -1 -1 0
As we can see from above, the product of two matrices is not generallycommutative.
F. Identity matrix
All square matrices have an identity matrix of the same dimension.The identity matrix has elements i, = 0 when i j and 6ij = 1 when i =j.The identity matrix is denoted by the symbol I.
The identity matrix for all 3x3 matrices is then
-1 0 O
I= 0 1 00 I
The product of a square matrix with its identity matrix is the squarematrix itself. That is IA = A.
0 1 0 1 1 0 1IA= 0 1 0 0 1 -1 0 1 -1=A
0 0 1 1 2 0 1 2 0
One can also show that the product of any square matrix multiplied byits identity matrix yields the same square matrix.
0 1 1 0 0 1 0 1AI= 0 1 1 0 = 0 1 -1=A
1 2 0 0 0 1 1 2 0
342
G. Transpose of a matrix
A matrix can be transposed so that the elements in the rows of thematrix become columns of a matrix. For example, the matrix D can betransformed into a matrix so that the elements dij become dji of the newmatrix. The new matrix is the transpose and is denoted by D'.
D = [i -1 ] D'= l-1 3]2 3 1
H. Determinant of a matrix
Certain products of the elements compute determinant of a matrix. Itcan only be evaluated for a square matrix (number of rows = number ofcolumns). For example the determinant of the matrix
X = xL
11 12 X is computed as x11 x22 - x21 xl 2 and is denoted by
det(X)= XI = Xll X12
x2 1 2 2
where x22 and x12 are called co-factors of x1 and x21. When the number ofelements increases, the evaluation of the determinant becomes tedious.
For a 3x3 matrix
Z11 Z1 2 Z13
Z = Z2 1 22 Z23
LZ31 Z32 Z33
the determinant can be evaluated by the sum of the products betweenthe elements of a particular row or column and their co-factors.
The determinant is then
343
det (Z) = z11 Z11 + 21 Z21 + z31 Z31 = Zll (- 1)+l Z2 2 Z23 +z32 Z33
2 (1)2+1 Z12 Z13 Z31 (_1)3+1 Z12 Z13Z3 2 Z33 Z22 Z23
- Z1 1 Z1 1 + 1 2 Z1 2 + z1 3 Z13
The determinant of matrix A = 0 1 1
is then det (A)+ 1(0-1)
is then det (A) =A=11(0 + 2) -0 + 1(0-1)} = 1
I. Cofactor
The co-factor of an element zij in a square matrix Z of dimension nxn isthe determinant of the matrix of dimension [(n-1)x(n-1)] obtained bydeleting the ith row andjth column from the matrix Z. The cofactor isthen ()i+j I [zi]1. The co-factor is denoted by Zij.
J. The co-factor matrix
The co-factor matrix of a square matrix Z of dimension nxn is thematrix obtained with all the determinants of the co-factors of theelements in the matrix Z. The cofactor matrix is denoted by [Z,,]. Theco-factor matrix of Z given above is then
Z2 2 Z23 Z2 1 Z2 3 Z2 1 Z2 2 -
Z3 2 Z33 31 Z33 Z3 1 Z3 2
Z1 2 Z13 Z1 1 Z1 3 Zll Z1 2
Z32 Z3 3 3Z31 33 Z3 1 Z3 2
Z Z13 _Z 1 1 Z13 Zll Z1 2
Z2 2 Z23 Z2 1 Z2 3 Z2 1 Z2 2
The co-factor matrix of the matrix given above is then
344
0 -1 0 1
1 1 21
1 11 1 2l1 Il 11 0
0 X 0 °1
I 1; o:2
2 -1 1= -2 -1 -2
-1 1 1
K. Inverse of a matrix
Inverse A-1 of a non-singular (non-zero determinant) square matrix Ais a non-singular square matrix that satisfies the following
A-1A = I
Inverse of a matrix A can be evaluated from its determinant and thetranspose of the co-factor matrix.
A-1 I (1/det (A)][Aij]'
2 2 -1
= 1 -1
-1 -2
L. Solution of simultaneous equations
The knowledge of matrices can be applied to solve simultaneousequations. For example consider the following set of equations.
X1 + x3 = 3
X2 -X 3 = -3
x1 + 2x2 = 5
The above equations can be written as follows
345
11 -1
200 1
-]2 001
11 -1
X1 + OX2 + x 3 = 3
OX1 + x2 - X3 = -3
x, + 2 x2 + OX3 = 5
In matrix form the equations can be written as
0 1 -1O x2= -3
The matrix at the right hand side is the same as matrix A given above.So the equations can be written as
Ax = y where x and y are x21 and -3, respectively.
X3 -1
The equations can be solved by multiplying the equation by the inverseof A. That is
A-l Ax = A-l y
Ix =A-l y
x =A-ly
That is, the solution for the above equations is
x = A-ly
x2 = -1 1 -3 =-1
X3 -1 -2 1 -1 2
that is, x1 = 1, x2 = -1 and x, = 2.
346
M. Eigen values
If P is a square matrix of order n, then the k matrix [P - IX] is called thecharacteristic matrix of P. The determinant IP - /I1 is called thecharacteristic determinant of P. The expansion of the above determi-nant expressed as a polynomial of degree n in X is called the character-istic function of P. The equation f(X) = 0 is called the characteristicequation of P and its roots are called the characteristic roots or eigenvalues.
For example, for the matrix
[-2 2]'
the determinant becomes
1-k 1
-2 2-X}
This leads to the equation (1 - X)(2 - X) + 2 = 0.The solution to the above equation gives values = 3 and X = 1.
These are the eigen values of the matrix P.
N. Eigen vectors
For any square matrix P of order n, the eigen value equation can bewritten as
Px = Xx
where x is a lxn matrix and the X one of the eigen values. There are nsolutions to this equation corresponding to n eigen values. This vector xis called an eigen vector of the matrix P. The eigen vectors can be foundby solving the above equation.
O. Trace (character) of a matrix
If A is a square matrix, the trace of A is defined as the sum of theelements on the principal diagonal. The trace is denoted by tr(A). Thetrace of matrix A given above is
347
tr 0 1 -1=2112 -_
P. Similarity transformation of a matrix
If Q is a non-singular square matrix then the product RQR - = F isknown as a similarity transformation of Q by R. The matrices Q and Rare similar. Their determinants, eigen values and traces are equal.
tr(RQR1 ) = tr(F)
For example, if Q is
0 -1 2
1 2 (the same as B above) and R is
-1 -1 0
O1 -1 (the same as A above), then
1 2 0
1 0 1 0 -1 2 2 2 -1 -2 -4 1RQR- = ABA- 1= 1 -1 1 2 0 -1 -1 1 = 1 11
1 2 0 -1 -1 -1 -2 1 -1 -33
det(ABA - l) = det(B) = 2
tr(ABA -1) = tr(B) = 2
eigen value equations ofABA - and B are the same as ;3 - 22 + 3R -2 =0.
348
Q. Diagonalisation of matrices
A non-singular square matrix Q can be diagonalised by another matrixR by similarity transformation (RQR - 1 = G) such that the resultingmatrix G has only non-zero diagonal elements. These diagonalelements are the same as the eigen values of the matrix. The columns ofthe matrix Q are the same as the eigen vectors corresponding to theeigen values taken in the same order.
Diagonalisation by similarity transformation is used in reducingthe matrices representing operations of a point group. To illustratethis, let us use the matrices A, B, C, and D used in Section 4.6. Thematrices A and C are in the diagonal form. The matrices B and D arethe same. They have eigen values X = -1, -1 and 1. When the matricesare diagonalised they have -1, -1 and 1 as diagonal elements. Thediagonalisation of the matrix B and D can be done by finding the eigenvectors of the matrices B and D. These matrices have one diagonalelement (-1) in the middle row each. Therefore it is enough to diagon-alise the first and the last rows
B=D= -1 0
-1 0 0
For k = -1
[0 -- 1 [ 01[X
The1 normalizing condition leads to 2 + =
The normalising condition leads to x2 + 1
2x2 = 1 x = +1I and z = 1/2.
For k = 1
349
0°1 -ol=-,Lo l0x-1 -iL o o z]
with normalising condition as above, we get x = +1/F2 and z = -1/42.The matrix Q that diagonalises the matrices B and D can be written
as
Q1/ Q / 0o -1/2]
-1 0
o 1/ jand Q =1 0
Q l= 2
o 1/2]--1 0
o 1/J2
-1/ 2 0 -1/ 2- 0O
QBQ - = 0 -1 O
L1/ 0 11 2 I-1
= -1 0
0 0 -1
o -1- 1/ 0 -1/--1 O O -1 0
0 O / 0 1/]
Therefore, the matrices A, B, C and D representing the symmetryoperations E, C2, %a, and %z are reduced to
1 0 O, 10 1 0,OOO 1O
0 0 1 0 0 i 0O 0-1 i 1 0 and -1 00 - 0 1 0 0 -1
, respectively.
350
Index
absorbance, 21, 133, 285absorption spectrum, 18absorptivity, 131accidental degeneracy, 95acrylonitrile- butadiene-styrene
(ABS), 165alkyl chains, 252allowed transition, 19alternating least squares, 309amide I, 142,255amide II, 142,256amplitude, 3anharmonic constant, 35anharmonic terms, 35anharmonicity, 33, 37,38anionic surfactant sodium dodecyl
sulphate, 198anisotropic distribution, 204anti-Stokes lines, 79anti-symmetric stretching vibrations,
29anti-tumour agen, 170apodization, 121arsenic-doped silicon, 234ascorbic palmitate, 261assembled cells, 134asymmetric stretching, 239asynchronous correlation spectra,
321,325attenuated total reflection (ATR)
method, 131, 136, 141, 196
auto-correlation peak, 324azobenzene, 220
bacterial cells, 263bacteriorhodopsin, 255, 268barbituric acid, 249beamsplitters, 107, 116bending vibrations, 29benzaldehyde, 38biological materials, 195biomarkers, 296biomembranes, 260biplots, 294bisacrylates, 215bolometric effect, 110bone disease, 227breast tumour, 232
cadmium stearate, 241, 242caffeine, 187calcium oxalate, 302carbon nanoparticles, 171cassegrain type, 188cellulose ether, 197centreburst point, 120cervical cancer, diagnosis of, 273chalcogenide glass, 235character table, 71characteristic absorption bands, 31charge-transfer reaction, 247chemometrics, 256
351
chlorophylls, infrared spectra of, 259chromophores, 238chromophoric groups, 255classical least-squares, 181coal rank, 296CO-ethylene- propylene alternating
copolymers, 197colon carcinoma, 233combination modes, 33, 37commutative, 59concentration, 285conducting polymers, 218conjugate operations, 65Connes advantage, 120continuous-scan FT-IR, 124continuum model, 151corpuscular, 6cross peaks, 324crystallinity, 212curve-fitting, 257cycle, 3cysteine residues, 255
degenerate stretching, 239degenerate vibrations, 29dehydration profiles, 304dependent variables, 288detectivity, 113detector, 109detector responsivity, 113deuterated triglycine sulphate
(DTGS), 106deuterated water, 313deuteration studies, 202di(carboxystyryl)benzene, 219diatomic molecule, 23dichroic ratio, 204diffuse reflectance (DR) method, 131,
147, 285diffuse-reflected light, 148diffusion depth, 156dioctyl phthalate, 185dipole moment, 82
direct deposition, 185dispersive instruments, 117dispersive spectrometers, 207distinct operations, 45dynamic FT-IR procedures, 207dynamic IR spectroscopy of polymers,
212dynamic spectral intensity, 321
elastomer sealing rings, 165electric dipole moment, 20electroluminescence, 219electromagnetic spectrum, 1emission spectroscopy, 131epitaxial layers, 146essential oil constituents, 183etendue advantage, 120exinite, 296external perturbation, 320
fast Fourier transform, 127fatty acids, 260Fellgett advantage, 120Fermi resonance, 38,95fingerprint region, 18fixed cells, 134fluoranthene, 185focal-plane arrays, 222forbidden transition, 19force constant, 25Forman algorithm, 123Fourier transform, 323Fourier transform dynamic infrared
spectroscopy, 208frequency, 25frequency domain, 125FT-IR instrumentation, history of,
105functional group, 22,285fundamental vibrations, 17,80fundamentals, 32
gauche conformation, 248
352
gauche forms, 240GC/FTIR, 180Globar source, 107Golay detector, 110ground vibrational state, 21group frequencies, 18, 31, 97
Halobacterium salinarium, 268harmonic oscillator approximation,
23harmonic oscillator model, 33harmonic vibrations, 23heavy water, 135hemes, 255Herman orientation function, 205Hermite polynomial, 28hexaalkoxytriphenylenes, 215homomorphous, 59, 64human melanoma, 233hydrocarbon chains, 238hydrogen bonds, 199Hz, 3
identical operation, 43improper rotation axis, 47impulse-response technique, 207incident light, 148independent variables, 288inertinite, 296infrared absorption, 19infrared active, 20infrared detectors, 109infrared inactive, 21infrared light, 19infrared linear dichroism, 203, 212infrared microspectroscopy, 131infrared spectra of a model
compound for phospholipids, 260infrared spectra of chlorophylls, 259infrared spectra of intact bacterial
cells, 263infrared spectra of proteins, 255infrared spectroscopy, 22
interferometer, 105inversion centre, 47irreducible representations, 71isotope shift, 99isotopic exchange, 202
Jacquinot advantage, 120Johnson noise, 112
KBr method, 136Krimm's rule, 202Kubelka-Munk equation, 147, 150
Lambert-Beer's law, 131Langmuir-Blodgett films, 146, 220,
236LC/FT-IR, 172light-emitting diodes, 216linear dichroism, 203linear momentum, 7liquid crystal polymers, 211liquid crystals, 206liquid samples, 134lithium cells, 221loading plots, 294low-temperature infrared
spectroscopy, 255
MCT detector, 114, 188, 231Mertz algorithm, 123methacrylic acid, 218methacryloxy-
propyltrimethoxysilane, 218Michelson interferometer, 118micro-crystal domains, 244mirror misalignment, 124mirrors, 107, 116molar absorption coefficient, 133molar absorptivity, 286mole, 12molecular electronics, 236molecular orientation, 245molecular vibration, 19, 23
353
monochromatic radiation, 12Morse's function, 34Mulliken symbols, 71multiple linear regression, 290multiplex advantage, 120mutual exclusion rule, 30
Nernst glower, 107noise equivalent power, 113non-aqueous solutions, 133normal coordinate, 20normal frequency, 23normal modes, 23normal vibrations, 17, 23, 80, 97normalized detectivity, 113
object space; 291order, 43order-disorder transition, 244organic light emitting diodes, 214organic thin films, 195orientation measurements, 202overfitting, 293overtones, 21, 33, 37
parallel-polarized light, 145partial least squares, 290, 294particle theory, 1penetration depth, 137pentafluorophenylacrylate, 197pentafluorophenylmethacrylate, 197period of the motion, 3perpendicular-polarized light, 144phase transitions, 260phospholipids, infrared spectra of a
model compound for, 260phosphonic acids, 166photoacoustic signal, 155photoacoustic spectroscopy (PAS),
131photoacoustic techniques, 196photoconductive effect, 111photoelectromagnetic effect, 111
photoemissive effect, 111photoinitiator, 218photoisomerization, 220photon, 6photon detectors, 109,111photosynthesis, 255photovoltaic cells, 236photovoltaic effect, 111Planck's constant, 6point groups, 53polarizability, 79polarized light, 144poly(acrylic acid), 166poly(ethylene glycol), 230poly(ethylene oxide), 201poly(methacrylic acid), 166poly(methylmethacrylate), 165, 201poly(propylene oxide), 197poly(vinylphenol), 201polyacrylonitrile, 166polyatomic molecules, 29, 97polyethylene, 206polymer blends, 225polymer characterization, 195polymeric sulphonic acids, 166polystyrene microspheres, 223polyurethanes, 168predictor variables, 288principal axis, 43principal component analysis, 290,
292prisms and accessories for ATR
spectroscopy, 139product operation, 57proper rotation axis, 43proportionality constant, 286propyl ester phosphazene, 166protein dynamics, 255proteins, infrared spectra of, 255Pseudomonas chlororaphis, 263pyroelectric devices, 236pyroelectric effect, 110pyrolysis products, 182
354
quantitative analysis, 285quantum, 6quantum mechanics, 19
random coil structure, 256Rayleigh radiation, 79reducible representations, 70redundant aperturing, 189reflection absorption, 131, 143, 238,
241refractive index, 2, 133registration advantage, 120response variables, 288retardation, 119retinals, 255rocking vibrations, 30, 239rotation reflection axis, 47
Schottky noise, 112Schrodinger's equation, 27scissoring, 30,239score plots, 293secondary structure, 142selection rule, 19SFC/FTIR, 182silicone, 159similarity transform, 65simple harmonic, 2size distribution, 151spectrometer, 12spectroscopic imaging instrument, 222spectrum, 1specular reflectance, 285Staphylococcus aureus, 263step-scan dynamic FT-IR, 209step-Scan FT-IR, 125step-scan impulse-response
experiments, 210Stokes lines, 79stretching vibration, 23, 138structural absorbance, 204styrene-butadiene block copolymer
blends, 165
subcell packing, 241supercritical fluid chromatography,
182surfactant, 184, 197symmetric stretching, 239symmetric stretching vibrations, 29symmetry elements, 42symmetry of a molecule, 20symmetry operations, 42symmetry plane, 47synchronous correlation spectra, 321,
324synchronous modulation, 125, 207
target projection plots, 306target projections, 300tetrachloroethylacrylate, 197TGA/FT-IR, 158thermal conductivity, 156thermal detectors, 109, 110thermogravimetric analysis, 302thermoplastics, 163thermopneumatic effect, 110thermovoltaic effect, 110thin films, 236time-domain experiments, 125time-resolved experiments, 125time-resolved infrared spectroscopy,
255total internal reflectance, 285trans conformation, 248transferrin receptor, 258transition moment, 82,204translation, 15transmittance, 21,131transmitted radiation, 12trans-zigzag structure, 240triaminotriazine derivatives, 250trisacrylates, 215twisting vibrations, 30two-dimensional correlation
spectroscopy, 256, 318
355
univariate technique, 285
variable space, 291vinylidene fluoride copolymers, 196vinylidene fluoride-trifluorethylene,
201vitrinite, 296
wagging vibrations, 30, 241water molecules, 255
wave theory, 1,6wavelength, 5wavenumber, 5, 286weathered sealants, 159window materials, 133
x-ray diffraction, 319
zirconium oxide, 218
356