Analyst, August 1995, Vol. 120 205 1

Thermal Lens Spectrometry A Review

Richard D. Snook and Roger D. Lowe Department of Instrumentation and Analytical Science, University of Manchester Institute of Science and Technology, P. 0. Box 88, Manchester, UK M60 1 Q D

This review considers the technique of thermal lens spectrometry and its applications to chemical measurements in solid, liquid and gaseous phases. Practical applications, theoretical treatments and instrumental developments are considered in terms of their analytical use and potential.

Keywords: Thermal lens spectrometry; chemical measurement; gas, solid and liquid; review

Thermal Lens Spectrometry Thermal lens spectrometry (TLS)1-4 is one of a family of photothermal techniques that can be used for physical and chemical analysis. These techniques also include photo- acoustic spectrometry, optothermal radiometry and photo- thermal beam deflection spectrometry. All rely upon absorp- tion of optical radiation by the sample and subsequent non-radiative relaxation to yield a measurable quantity of heat which can provide details of the optothermal properties as well as absorption properties of the sample or minor components in the sample.

In the thermal lens technique the sample is illuminated using radiation from a T& or Gaussian intensity profile laser beam. Some of the radiation is absorbed by the sample or by chromophores within the sample. Excited states formed in this way may either lose energy radiatively, e.g. , fluorescence or phosphorescence or by non-radiative routes, e.g. , internal conversion or by interaction with other molecules in the sample which results in the generation of heat. These are often competing mechanisms with photochemical processes as well. However in nearly all situations where the quantum efficiency of fluorescence is less than, e.g., 0.95 then some heat is evolved. Even if the quantum efficiency for fluorescence was unity then some heat would be evolved as a consequence of the Stokes’ shift. The flow of heat from the region illuminated by the laser results in a thermal gradient that is proportional to the beam intensity profile in the sample which may be a solution, solid or gas. Heating is stronger at the centre of the beam profile than in the wings so the thermal gradient in turn establishes a refractive index gradient. The coefficient of refractive index with temperature, dnldT, varies for different materials but is normally negative for gases and liquids and positive for solids. In the case of gases and liquids the refractive index gradient established by absorption and subsequent heating of the solution in effect presents a graded index lens to the beam. As the beam passes through the solution it progressively diverges and the degree of divergence depends upon the power of the laser beam and the absorption coefficient of the sample. From this thumbnail sketch it is easy to see how the thermal lens effect can be used as an indirect method to determine absorbance and hence its potential as an analytical spectrometric technique.

For most analytical applications the preferred mode of operation is continuous wave (c.w.) and therefore the

theoretical treatment given below relates to that mode. However there are reports of the use of pulsed lasers as an excitation source (mostly in gas-phase work) and these are discussed individually in the text. It should be remembered that in both cases when a dual beam system is used the probe laser is always of C.W. type.

Similarly there are several reports of time-resolved c.w.- TLS in which the C.W. beam is periodically interrupted. This mode of operation enables the history of the thermal lens to be determined as it propagates through the sample and fun- damental thermo-optical parameters of the sample to be determined, e.g., thermal diffusivity and conductivity. Per- haps this mode of operation is a good compromise between pulsed and C.W. operation for many applications, with the exception of those that require any short exposure times, e,g., absorption and luminescence lifetime studies.

It is the purpose of this review to describe the theoretical and practical aspects of TLS when applied to gaseous, liquid and solid samples and to show where the technique is analytically useful. The use of the technique for the determi- nation of absolute values of optothermal properties and absorption coefficients and quantum yields will also be discussed. Different experimental configurations and proce- dures will be appraised in terms of their analytical use.

Theoretical Basis of c.w.-TLS

The first published observation of a photothermal lens was made by Gordon et al. in 1964,4 and it can therefore be considered as the first of the photothermal phenomena to be described. The effect was observed quite by accident during their study of laser Raman scattering of pure liquids. Their experiment involved placing a 1 cm pathlength sample cell at the Brewster angle inside a helium-neon laser cavity to utilize the higher circulating intra-cavity laser power. This led to the observation of build-up and decay transients, mode changes, and relaxation oscillations, all with time constants in the order of seconds, which would suggest a thermal phenomenon. The resulting investigation of this effect5 predicted that the most important application would be for the measurement of small absorbances. Using this intra-cavity set-up, Leite et a1.6 calculated the absorption coefficients for pure liquids, from the focal length of the induced thermal lens. Values ranged from 2.3 x 10-4 cm-1 for CC14 to 5.9 x 10-4 cm-1 for CS2. Solimini’ measured the absorption coefficients of several pure organic liquids using the same technique as Leite,6 and later8 published a comprehensive report on the accuracy and sensitivity of this method for measuring small sample absorp- tion coefficients.

The biggest problem associated with the intra-cavity experi- ments was with the reproducibility of the results. This was owing to the difficulty in controlling the parameters of such an experimental set-up. The first extra-cavity thermal lens was generated by Rieckhoff,9 who describes the self-induced divergence of a C.W. He-Ne laser beam after passing through a

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2052 Analyst, August 1995, Vol. 120

sample cell with a pathlength of 98 cm, containing a series of pure solvents. However, the effect was explained in terms of non-linear absorption, without considering the possibility of weak linear absorption in a 'transparent' liquid.

Although it is easier to place the sample cell outside the laser resonator (and for most commercial lasers it is essential), the power is much lower outside the laser cavity than inside. Hu and Whinnery,'O however, recognized that the greatest divergence of the laser beam could be attained for a given lens by positioning that lens at the point of minimum radius of curvature of the beam wave fronts, i.e., at a distance of one confocal length, Z,, from the minimum beam waist, 00, of the laser. They also demonstrated that sensitive detection of the thermal lens could be made for samples positioned extra- cavity by use of a secondary lens to create a waist at one confocal length before the sample cell. The degree of divergence could then be monitored by noting the transient changes in intensity at the beam centre, using a pinhole positioned on the beam axis, in front of the photodetector.

In its simplest form a single C.W. Th& laser beam with a Gaussian intensity cross-section passes through an absorbing medium as shown in Fig. 1. Some of this laser beam energy is absorbed by the sample which subsequently produces a thermal lens.

The steady-state focal length of the induced lens given in the parabolic approximation11 of the lens is given by eqn. (1)

where k is the thermal conductivity of the sample, Pe is the laser excitation power and A is the absorbance of the sample. Thus as P,, dnldT, and A get larger then the focal length of the lens gets shorter and the beam divergence increases. The divergence of a single beam passing through the solution can be measured simply by placing a pinhole over the photodetec- tor in the far field at the centre of the diverged beam as shown in Fig. 1. As the beam energy is spread over a larger area, the photodetector signal falls. Alternatively a linear or area photodetector array may be employed to image a cross-section of the beam or the entire area.

Analysis of eqn. 1 shows that the sensitivity of the thermal lens technique is directly proportional to the excitation laser power and on the thermo-optical properties of the solvent. Thus in principle higher sensitivity can be obtained by increasing the power of the excitation laser and by choosing an appropriate solvent. Indeed trace analysis has been carried out on solutions with an absorption coefficient of 10-7 cm-l,1*J3 which is three to four orders of magnitude better than that achieved with conventional UVNIS spectropho- tometry. This enhancement is not always available, however,

Laser

Fig. 1 trometer.

Schematic diagram of a single beam thermal lens spec-

as competing energy loss mechanisms, e.g., fluorescence, photochemical reactions and convection effects are often seen. In addition in many spectrophotometric systems with high reagent blank absorption the noise associated with the excitation laser can degrade signal-to-noise ratios.

When comparing TLS in the UVNIS region with UVNIS spectrophotometry we can consider the basic equations that describe the analytical signal response. Thus in UVNIS spectrometry the absorbance, A, of a solution is given by Beer's Law

J = I0 e-A (2)

where I. is the initial intensity and A = ECZ, where E is the molar absorption coefficient (in mol-1 dm3 cm-I), c is the concentration of the solution (in mol dm-3) and 1 is the pathlength of the absorbing cell (in cm). For a weakly absorbing solution the relative change in signal, AI, can be written as

A I = I o A

or SA = Alllo = A (3)

In TLS the thermal gradient established after optical absorp- tion and thermal relaxation of the sample results in a change in intensity at the beam centre owing to the induced beam divergence thus the time dependent I(t) signal 14 can be written as

where t, is a characteristic time constant of the order of 0.01-0.1 s and STL is the relative change in signal measured at t = 0 and t >> tc and

AJ P, (dnld7')A s,=-= ( 5 )

J h k where P, is the power of the excitation laser (in W), dnldT is the refractive index temperature coefficient, hp is the wavelength of the probe laser (or excitation laser in a single-beam system) and k is the thermal conductivity of the solvent. The collection of terms is often referred to as the enhancement factor (E) over absorbance techniques, i. e.,

(i .e. , S n = EA compared with SA = A in the absorbance case. Generally non-polar solvents (e.g. , benzene, carbon tet-

rachloride) are the best media for sensitive thermal lens measurements owing to their high values of dnldT and low k values. For benzene dnldTis -6.4 x 10-4 K-1 and k is 14.42 x 10-4 W cm-1 K-1, whereas for water, the most useful and widely encountered solvent, these values are -0.8 x 10-4 K-1 and 59.45 x 10-4 W cm-1 K-1, respectively. In terms of thermal lens spectrometry water is not an ideal solvent therefore a typical value of E for water is 0.22 mW-1 using the Ar ion line at 514.5 nm. Thus to achieve a ten-fold theoretical enhancement in sensitivity over U V M S spectrometry would require an excitation beam power of 45 mW.

The parabolic approximation summarized above makes several assumptions that are justifiable for single-beam experiments or for two-beam experiments which utilize a pump laser for excitation and a different lower-powered laser to probe the thermal lens formed by the pump laser in which the probe laser is arranged to be coaxial with the pump laser in

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the absorption cell (Fig. 2). It is assumed that no appreciable convection takes place in the cell and that radial heat conduction dominates until a steady-state temperature gra- dient is established under these conditions. It is also assumed that the probe beam diameter does not exceed the pump beam diameter in the sample cell interaction volume and therefore the Gaussian beam near its axis can be approximated to a parabola. This approximation in fact holds until r, the radial distance from the beam centre equals the beam radius 00,

defined as the position where the intensity has fallen to l/e2 of its peak value at the beam centre. When r = 00, (r/w = 1) 87% of the light energy is included in this radius and the resultant lens as defined in eqn. 1 shows little spherical aberration. The parabolic model is not completely quantitative however. The remaining 13% of energy that lies outside r = 00 causes aberrant effects, especially in the wings of the beam profile. Sheldon et aZ.15 were the first to consider the aberrant nature of the thermally-induced lens. Rather than defining an expression for the focal length of the induced lens these authors used diffraction theory to find the intensity at the beam centre in the far-field after it had passed through the sample. Evaluation of the appropriate diffraction integrals leads to an expression for the relative change in the beam centre intensity.

where is a geometrical factor such that when 0 = fl the cell is located at fi times the confocal distance in front or behind the beam waist. At this position Sheldon concluded that the thermal lens effect is optimized. In this expression 0 is proportional to

P, dnld T A hk

The parabolic and aberrant lens models were both derived for single-beam situations and are therefore only useful in single-beam experiments or coaxial two-beam experiments in which the probe beam and pump beam radii are the same in the sample cell. In practice greater sensitivity can be achieved using two-beam configurations in which the focal points (or beam waists) of the pump and probe beam are displaced. Fang and Swofford16 postulated that mismatched waists in a two-beam system (i.e., probe and pump beam waists non- coincident) would offer enhanced sensitivity but failed to carry out any systematic study into the potential of such a geometry. Berhoud et al. ,I7 however, undertook such an investigation and derived a theoretical, though semiquantitative, model to describe experimental data produced by a mode-mismatched investigation. In practice the result of these studies is that maximum sensitivity is also obtained in the two-beam config- uration when the excitation or pump beam is focused in the

Pump Laser

Fig. 2 Schematic diagram of a dual beam thermal lens spectrometer.

sample and the beam waist of the probe beam is arranged to be at a distance of fi 2, before that point, where 2, is the confocal distance given as X W O , ~ ~ ~ and where 0 0 , ~ is the lie2 radius of the probe beam and hp is the wavelength of the probe beam.

Shen et aZ.18 have recently developed a quantitative model for mode-mismatched thermal lens spectrometry that can be used for steady-state measurements and time-resolved studies19 as well as mode-matched experiments. In the model a typical mode-mismatched scheme is used as shown in Fig. 3. Here the position of the pump beam waist is designated as the origin of the optical axis, 2. A sample of length Z is placed at a distance Z1 from the origin and the detector placed at Z1 + 2 2 from the origin. The waist of the probe beam is w9, and the radius of the probe beam and excitation beam in the cell are wlp and we, respectively. In this model it is assumed that the cell dimensions are large compared with w, such that the sample can be considered as infinite; that the absorbed power is low; no convection effects are induced and that dn/dT remain constant over the temperature rise induced.

In this model, using diffraction theory18 a diffraction integral is derived that describes the intensity of the probe beam centre after a phase shift is imposed upon the beam centre by the induced refractive index gradient. The integral is solved using analytical approximations to derive the steady- state thermal lens signal, S given as

Where the degree of mode-mismatching m, is given by

V is the ratio of distance from the cell to the probe beam waist over the confocal distance Z,, i.e.,

The time-resolved thermal lens signal can also be derived as

Z(t) =

The time-resolved model is valuable because it gives a convenient method for the measurement of thermal diffusiv- ity, D, of the sample via the characteristic time constant where

(oO)2 tc = - 40

Dotactor Plr.ne

Probe

Fig. b--zzz 3 Schematic diagram of the geometric position of the beam

waist in a mode mismatched thermal lens spectrometer.

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Indeed, D has been determined successfully using this method in samples as diverse as glass19 and skin.20

Most models of the thermal lens describing its effect upon the propagation of the probe beam assume that the sample is infinitely thick and of infinite radius at the position of the excitation beam waist. Thus the surrounding medium of a sample is not considered to influence heat flow away from the probed region in the sample. When dealing with small samples or thin samples or both this assumption cannot be made and the steady-state model fails unless the contribution of the walls is considered as shown by Wu and Dovichi21 who developed a Fresnel diffraction theory for steady-state thermal lens measurements in thin films. Building on this work Shen et al. developed a time-resolved model in which the minimum radius and thickness22 conditions of a sample for time resolved measurements with respect to probe/pump diameter ratio (mode-mismatched ratios) were derived. The derived minima were verified experimentally using short pathlength cells of 100 and 200 pm thickness. Thus the time-resolved method was used to accurately determine absorbance and thermo-optical properties in these samples. The model predicts that the minimum radius can be as small as 25 pm and the minimum thickness can be as small as 20 pm. Measurements are made by fitting eqn. 12 to the experimentally observed rising portion of the thermal lens profile to determine the appropriate parameter in eqn. 12. Provided that measurements are made in a time t less than 10 x tc the equation holds. In effect measurements are made before equilibrium conditions are established in a timescale where the surrounding medium has no effect upon heat-flow boundary conditions, i.e., the heat has not arrived at the boundary.

Trace Determination and Characterization of Gases by TLS It was first observed in 1964,23 that a radial temperature gradient in a gas could be used as a thermal lens. Grabiner et a1.,24 designed a collinear dual-beam arrangement with a Q-switched C02 laser (9.6 or 10.6 pm), and a 1 mW CW He-Ne probe laser, to examine the density changes caused by heating that arose from vibrational relaxation processes in a gas at low pressures. They observed translational cooling in CH3F, and calculated an approximate lower limit of 200 ms-1 for the rate of this cooling process. In an extension to this work,25 using the same experimental set-up, they carried out a series of experiments to measure vibrational relaxation phenomena in a variety of gases, including CD4, OCS, and SO2. They suggested that the excellent sensitivity of the thermal lens technique could prove to be valuable for the detection of trace concentrations of absorbing species in atmospheric samples. Also, as the temporal behaviour of the thermal lens would not be important in this kind of experi- ment, the infrared pump laser could be modulated, and phase-sensitive detection of the probe laser light would give significantly enhanced sensitivity. This work and that of Nieman and Colson,26 where TLS was used in a study of the electronic excited states of trans-butadiene and SO2, implies that TLS is useful in the determination of characteristics of molecules in the gaseous phase. However, these studies have only hinted at the analytical sensitivity of the thermal lens method for trace species determination. In a study by Mori et a1.,27 calculated enhancement factors for pulsed and C.W. laser excitation of gaseous samples were verified using experimental data, and the trace determination of NO2 was carried out. Using a pulsed dye laser, they achieved a detection limit of 1.74 X 10-5 mol dm-3. Their results showed that a C.W. laser is a less efficient exciting source for gaseous samples, when compared with a pulsed laser of equivalent power. However, a conventional commercially available C.W. laser has a much higher average power output, and detection

limits of 1.09 X 10-7 mol dm-3 of NO2 have been attained using an argon ion laser (700 mW; 488 nm).28 Following the observations published by Mori et al., Long and Bialkowski29 constructed a thermal lens spectrometer using a pulsed C 0 2 infrared laser, for the quantitative determination of CF2C12. The results of their studies were extrapolated to give an atmospheric pressure detection limit of less than 8.26 x 10-9 mol dm-3. Though more importantly, they showed that infrared absorptions of ClO-7 (atm cm)-l, previously inac- cessible to conventional IR spectrometers, can be measured using TLS.

Glatt et al.30 studied the spatial behaviour of the thermal lens induced by irradiation of SF6 with a pulsed C 0 2 laser. They used an optical technique called moire deflectometry31 to monitor the transient thermal lens signal by mapping the ray deflections. The signal measured by this technique is proportional to the gradient of the refractive index. Their results show that this technique gives better signal-to-noise ratios compared with the widely used pinhole method, and that the thermally induced lens is significantly broader than the profile of the pump laser. In 1985 Nickolaisen and Bialkowski,32 studied the behaviour of a pulsed C 0 2 infrared laser, thermal lens signal in flowing gas samples. Using this method, they showed that the flow rate of gas does not significantly degrade the amplitude of the signal up to flow rates of 100 ml min-1. Therefore the minimum amount of CF2CI2 that should be detectable is 8.26 X 10-9 mol dm-3, as found in ref. 33, though no experimental data was given in support. The authors state that their results were susceptible to poor precision, with a quoted relative precision of 4%. The source of this imprecision was identified as mode variations in the excitation laser beam. Although difficult to quantify, such variations could result in effective pointing noise. When using noisy light sources, such as lasers, a relative precision of 4% is quite acceptable.

Most inorganic and some organic molecules such as ammonia and hydrocarbons do not readily absorb in the visible or ultraviolet region, so infrared sources are essential for their determination. The C02 laser is line tuneable from 9 to 11 pm so a bar graph spectrum can be measured, but a completely tunable infrared laser is needed to record the whole spectrum. Kawasaki et a1.,34 constructed a simple Raman cell for frequency conversion from visible dye laser emission to infrared radiation. They used this tunable infrared laser to record the thermal lens spectrum of ammonia in the gaseous phase.

TLS for the Determination of Trace Analytes in the Liquid Phase

The first study of the application of the thermal lens technique to trace solute determination was in 1979. Dovichi and Harris35 used low power, discrete wavelength C.W. lasers (e.g., He-Ne, He-Cd, Ar+) to construct a sensitive, but non- selective thermal lens spectrometer. In their work, they chose to study the determination of Cu2+, which forms an EDTA complex with a molar absorption coefficient of 47 mol-1 dm3 cm-1 at 632.8 nm. Since the choice of solvent for an experiment governs the enhancement E , which can be attained for a particular laser power, they investigated the effect of different mixtures of acetone and water upon the detection limit. Their results show that as the thermal conductivity decreases, and the value of dnldT increases with increasing acetone concentrations, the limit of detection improves, and the observed enhancement rose from 0.22 for pure water, to 2.0 for a 3 + 1 acetone-water mixture, Dovichi and Harris extrapolated their results to give a predicted limit of detection for a 1 W laser, of -10-10 mol dm-3.

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In TLS, the lower limit of detection is often dominated by the background absorbance of the sample matrix or the solvent. Any analytical application of this technique, would benefit from an experimental arrangement by which the difference in absorbance between a blank reference, and an unknown sample could be directly determined. Hu and WhinnerylO first observed the anti-symmetric dependence of the thermal lens effect on the position of the induced thermal lens relative to a waist in a Gaussian beam, though they made no comment upon its significance. In 1980 Dovichi and Harris36 recognized the importance of this dependence, and constructed a differential thermal lens spectrometer. If the value of dn/dT for the sample is negative, then a diverging lens will ensue if the sample is placed beyond a waist in the beam. If the same sample is positioned an equal distance before the waist, a converging lens will result. Therefore, when two cells, filled with identical weakly absorbing samples, are placed symmetrically about a beam waist, a cancellation of -99% of the thermal lens signal is observed. In this manner, the signal due to the sample matrix or the solvent, can be optically substracted from that of the sample automatically, if one cell filled with a blank sample, is placed 31/22, before the beam waist, and the sample cell is placed 31/22, beyond the beam waist. Using this experimental arrangement, an improvement in the detection limits of more than an order of magnitude was reported.36

Using a similar experimental set-up, Dovichi and Harris37 realised that an increase in the speed of measurement could be achieved by recording the time-dependent build-up of the signal rather than just the initial and final amplitudes. An additional benefit to be gained by repeated measurements is the averaging out of short-term source fluctuations.

Following the work of Dovichi and Harris,35 where en- hancement factors of between 0.22 and 2.0 were obtained, Imasaka et a1.38 used a higher power argon ion laser to increase the enhancement factor, for the determination of Fe2+ with 4,7-diphenyl-1 ,lo-phenanthroline disulfonic acid. Using a collinear dual-beam set-up they achieved observed enhance- ments of 7.3, and detection limits of 3 x 10-7 mol dm-3. To prevent the pump radiation from falling upon the photodetec- tor, the argon ion laser beam (514.5 nm) was completely absorbed by a liquid filter (K2Cr207; 7.84 X 10-2 mol dm-3). Such a concentrated solution of potassium dichromate would undoubtedly absorb all the pump radiation, but such absorp- tion would lead to substantial heating of the filter solution, with the formation of a second thermal lens, and strong convection currents. This would in turn affect the propagation of the probe beam, and lead to spurious results. Absorptive filters for blocking the pump laser light at the detector should not be used, only thin-film interference filters, available for all the common C.W. laser lines, should be utilized. Employing an improved experimental set-up, though still using the liquid filter, Miyaishi et a1.39 applied TLS to the determination of Fez+ with 4,7-diphenyl-1 ,lo-phenanthroline disulfonic acid in aqueous solution, and in chloroform by ion-pair extraction with trioctylmethylammonium chloride. Owing to the differ- ent solvent parameters, the limits of detection and enhance- ment factors were 2 X 10-9 mol dm-3, E = 70 in water; and 2 X 10-10 mol dm-3, E = 1200 in chloroform, with a pump laser power of 800 mW. Further to this work Miyaishi et a1.,40

developed a thermal lens spectrometer with image detection of the probe laser. Using a similar experimental arrangement, and the same reagents as in their previous work, they used a photodiode array as a detector to image the probe beam profile as the thermal lens forms, and decays. Using this system, detection limits comparable with other spectroscopic method based on AA and ICP-AES, were achieved.

In the work of Haushalter and Morris,41 the thermal lens technique was used to monitor the reaction of the enzyme-

catalysed oxidation of dopamine by polyphenyloxidase. Owing to the poor separation of the broad absorption bands of dopamine and other related catecholamines such as L-dopa, norepinephrine, and epinephrine, which all undergo similar catalysed oxidations, it is almost impossible to distinguish between them using any solution-phase molecular absorption technique, including TLS. However, their results showed that under some conditions it is possible to differentiate between them by monitoring the individual reaction rates. They used TLS to follow the reaction, and from the initial rates they were able to construct a calibration graph.

Mori et al. ,42 investigated the determination of Cu2+ with porphyrin compounds as colour reagents, which have sharp Soret bands (A,,, = 420 nm) with molar absorption coeffi- cients in excess of 105. They constructed a collinear pulsed dual-beam system, using a nitrogen pumped dye laser. The pulsed excitation source is useful not only for selective excitation of the sample because of its tunability, but also for the sensitive detection of the sample because of its large enhancement factor. Furthermore, the thermal lens signal rises quickly from its constant background level, it can then be subtracted precisely and therefore very small signals can be detected. They suggested that as in the gas phase, pulsed lasers may provide better detection limits than C.W. lasers.

In photothermal refraction or cross-beam TLS, a cylindrical lens-like optical element is formed within a sample, which is then probed at right angles with a second laser. Since the technique only measures sample absorbance at the intersec- tion of the two beams, this method should produce measure- ments with excellent spatial resolution. Using this technique for the determination of iron with 1,lO-phenanthroline in a mixed water-methanol solvent, Nolan et a1.43 attained a concentration detection limit of 3 x 10-7 mol dm-3 within a 2.5 X 1011 dm3 probed volume. They suggest that the technique would be useful for applications where small volume samples need to be analysed, such as in capillary flow injection and capillary column high-performance liquid chro- matography (HPLC).

During the last decade, a sensitive method has been required for the determination of phosphorus, since eutrophi- cation of lake water causes an environmental problem. Near-infrared spectrophotometry based on the Heteropoly Blue method is the most frequently used.44 At nanomolar levels this method suffers from poor sensitivity, therefore preconcentration from a large sample volume is presently nece~sary.~S Fujiwara et al. reported the thermal lens spec- trometric determination of phosphorus in sea-water using a C.W. dye laser pumped by an argon ion laser as a light source.46 Their method was useful for the determination of a sample at trace levels (detection limit, 1.61 x 10-10 mol dm-3), but the method was impractical for routine ‘in the field’ analysis, due to the large size, and expense of the lasers involved. Moreover, the wavelength of the pump laser (660 nm) does not exactly coincide with the absorption maximum of the Heteropoly Blue complex (700-900 nm). Nakanishi et al.47 constructed a compact thermal lens spectrometer using a near-infrared semiconductor laser (832.9 nm) and applied it to the trace analysis of phosphorus at sub-micromolar levels. They reported detection limits of 7.10 x 10-8 and 2.26 x 10-8 mol dm-3 for single- and dual-beam methods, respectively. When the samples were measured after solvent extraction into 2-butanol, the detection limit was improved to 6.45 x 10-9 mol dm-3 for both experimental arrangements. They con- cluded that the minimum detectable quantity was mainly limited by blank absorption.

In the method proposed for the determination of phos- phorus in sea-water by Fujiwara et al. ,* any effect of the saline background on the thermal lens signal was neglected. The sample matrix cannot be ignored in thermal lens measure-

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ments however. Phillips et a1.M reports the matrix effects on the thermal lens signal arising in the spectrophotometric determination of phosphorus in saline solutions, and the results of their efforts to reduce this effect. Their results show a definite enhancement in the thermal lens signal upon the addition of sodium chloride. They found that the main reason for this difference in 8 was due to variations in the thermo- optical parameters of aqueous and saline solutions. No significant variation for the value of tc, the characteristic time constant of the system, was noted: They concluded that in these situations where the interfering matrix cannot be precisely compensated for or effectively separated from the analyte species, TLS analysis requires preparation of a calibration graph in a matrix approximating the environmen- tal sample.

Grishko et al. ,49 compared single-beam, differential single- beam, and dual-beam thermal lens measurements for the determination of phosphorus. The phosphorus is determined as the molybdophosphate-auramine ion pair that is extracted into 2-methylpropan-1-01-hexane (1 + 2). They found that one important drawback of the differential thermal lens system is that measurement of the absorbance of an unknown solution against a single blank was imprecise because of blank fluctuations. This can be overcome by taking a series of blank measurements to give an average response. The dual-beam method was found, as one would expect, to be far more sensitive than the single-beam system. Finally they applied their dual-beam system to the layer-by-layer determination of phosphorus in semiconductor silicon wafers.

Knowledge of the behaviour of actinide ions in ground- waters is imperative for the assessment of the safety of nuclear waste deposits in rock formations. Speciation of these elements is also a major interest for the understanding of their physico-chemical behaviour at trace levels. In 1983, Berthoud et al.33 presented some preliminary results obtained with pulsed dye laser excitation of uranium in pure water solutions. Uranium was chosen due to the similarity in its behaviour with the other actinides, and because it does not need measures for radio-protection. The minimum detectable absorption coeffi- cient was 3 x 10-5 cm-1, and the limit of detection for uranium was 4 x 10-6 mol dm-3. Following this work they carried out a more thorough investigation.50 Using a series of laser dyes, a thermal lens spectrum was obtained at concentra- tion levels far below those obtained using conventional spectrophotometry , thereby allowing the study of the complex chemical equilibria involved in such systems. Using their improved experimental arrangement, they decreased the minimum measurable absorption coefficient to 5 X 10-7 cm-1. Finally,sl they reported on the thermal lens spectrometric investigation of the conversion of neodymium and hexavalent uranium free ions, to complete complexation in carbonate solutions. They also assessed the advantages and disadvan- tages of TLS for chemical speciation studies.

Following the construction of a differential single-beam thermal lens spectrometer,36 Berthoud et al.52 investigated the feasibility of constructing a differential dual-beam thermal lens spectrometer. They describe a systematic study of the influence of the beam geometric positions, and a study of the effect of varying both the beam waist and sample cell position upon the amplitude and sign of the thermal lens signal. They also presented a qualitative theoretical model, involving beam sizes in the cell, which showed that Gaussian beam diffraction phenomena play a major role in TLS when the size of the lens created is smaller than the probe beam. They show that the thermal lens method can be used either in optimum conditions with mismatched waists, or in the less sensitive differential arrangement with matched waists. In the latter scheme the detection sensitivity is limited only by the spatial and intensity fluctuations of the probe beam, generally <2%, rather than by

the background absorbance. In their following publication,53 they use a differential dual-beam thermal lens set-up for the determination of the lanthanides. Their optimized instrumen- tation allowed compensation of 95-98% for the background solvent effects, and analytical determinations of two lanthan- ide ions, Nd3+ and Pr3+, gave detection limits in the range 10-6 mol dm-3.

The common brown colouration of freshwater is associated with dissolved organic matter (DOM). It has long been recognized that these materials play an important role in the speciation of trace metals in water,54 because of their ligand sites for metal binding. Recently it has been shown that light absorption by DOM can initiate a variety of photochemical process,55 some of which are detrimental to the environment. The major problem associated with the investigation of DOM arises because the chromophores of interest are generally associated with particulates, and therefore absorbance needs to be distinguished from scattering. Filtration to eliminate scattering particles is not possible, since this process may eliminate an important part of the light absorbing material sought, therefore Power and Langford,56 proposed to use TLS for this application. Although their results show that TLS has the necessary sensitivity for the detection of low levels of DOM, their discussion of the effect of scattering is not complete. They comment on the fact that particles reduce the beam power available to form the thermal lens, but they fail to mention the noise created when particulate matter, carried by convection currents, passes into and out of the beam. This effect alone could create unacceptably large random varia- tions in the thermal lens signal.

Fujiwara et a1.57 describe a single-beam thermal lens system for the determination of the nitrite ion. The colour develop- ment was based on the diazo-coupling reaction between N02-, N-(naphthy1)-ethylenediamine dihydrochloride, and sulfanylamide. They used the 514.5 nm Ar+ laser line to create and probe the induced thermal lens. This single-laser system has the advantage of simple alignment of optics. Three different solvents were used and a comparison of three different pathlength cells was made. Using a 1 cm pathlength cell and a solvent of a 1 + 1 mixture of acetone-water, the minimum detectable concentration was 2 X 10-10 dm-3. This value was limited by the colour development in the blank solution. This detection limit was two orders of magnitude less than that achieved using a commercially available spectropho- tometer.

The potential of formaldehyde as a human health hazard has generated a need for its quantitative determination.58 Formaldehyde polymers are used in the fabrication of wood products, and home insulation, and are known to emit low concentrations of formaldehyde into the surrounding atmo- sphere .59@J Alfheim and Langford61 suggest a modified National Institute of Occupational Safety and Health (NI0SH)Q method to improve its sensitivity from 3.33 X 10-64.67 x 10-5 mol dm-3, to the micromolar range. They compared two experimental set-ups, a single-beam laser system with a single photodiode detector, and a dual-beam laser arrangement with a diode array detector. In both cases, the excitation laser was an argon ion pumped dye laser operating at 600 nm. Using standard solutions prepared by dissolving sodium formaldehyde bisulfite in ultrapure water, detection limits of twice the standard deviation of the blank were calculated to be 2.2 x 10-6 and 5.6 X 10-7 mol dm-3, respectively, using the two experimental systems. Gas chro- matography (GC) and HPLC methods have been reported to use from 30 to 500 dm3 of air per sample,63>64 and have sampling times ranging from one65 to several hours.& However, owing to the far superior sensitivity of TLS, with detection limits of 5.6 x 10-7 mol dm-3, it would require only 8 dm3 of air at standard temperature and pressure (STP) to

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detect formaldehyde in the 3.33 X 10-7 mol dm-3 range, assuming 95% collection efficiency.58 With improved signal processing and extra effort in standardization, a detection limit of 1.5 x 10-8 mol dm-3 could be achieved, which would reduce the volume of sample air to less than 1 dm3 to detect levels of less than 1.67 x 10-7 mol dm-3.

Tran67 describes the development of a double-beam, dual-wavelength thermal lens spectrometer using a helium- neon laser. With the correct choice of mirror set and removal of the housing, the laser was forced to produce radiation from both ends. Such a dual-output laser would provide an excellent alternative to conventional pump and probe beam experiments. Generally the output of the He-Ne laser occurs at 632.8 nm. However there are other visible He-Ne lines, and He-Ne lasers operating at 594 and 543.5 nm have been reported.68 A most important feature of any analytical technique is its selectivity. Unfortunately, most thermal lens spectrometers operate with only one pump laser wavelength. The selectivity can be enhanced by measuring the thermal lens signal at two different pump wavelengths, thereby improving the capability of identlfying a substance in solution. Trar16~ therefore used the 632.8 and the 594 nm lines of a He-Ne laser to determine palladium(I1) using a solvent extraction proce- dure, and compared this method with the dual-output method, and the single-laser, single-wavelength double-beam method. The limit of detection for the single-laser dual- wavelength double-beam experimental scheme was 5.64 X 10-8 mol dm-3 of Pd2+ dissolved in butylacetate. Calibration graphs were linear in the range 7.14 x 10-8-1.47 x 10-5 mol dm-3. Compared with the single-laser, single-wavelength double-beam arrangement, this system provides better beam quality, employs fewer and more simple optical elements, and thus reduces the complexity due to unwanted back-reflection or background absorption.

Following this work67 Franko and Tran69 constructed a dual-wavelength pump-probe configuration thermal lens spec- trometer, which was capable of measuring thermal lens signals at two different wavelengths. Two pump beams were derived from the same argon ion laser, operating in the multi-line mode. The sample was excited at these two wavelengths alternately, and the resultant thermal lens signals were probed using a He-Ne laser. The advantages of this dual-wavelength set up included its ability to correct for solvent background absorption, and its improved selectivity. This arrangement allowed the determination of trace chemical species in the presence of interfering species at much higher Concentrations. The detection limit for praseodymium ions in the presence of 1.0 X 10-2 mol dm-3 nickel glycinate using 25 mW of pump laser power was 4.7 x 10-5 mol dm-3.

Ramis-Ramos et al.70 constructed a conventional pump- probe mode-mismatched thermal lens instrument for the determination of metals after extraction with dithizone into carbon tetrachloride. They used the 514.5 nm argon ion line with an output power of 22 mW as the pump, and a He-Ne probe laser. Dithizone is a common spectrophotometric reagent mainly used for the determination of trace quantities of lead, zinc, cadmium, mercury, silver, copper and bis- muth.71 These metal dithizonates in carbon tetrachloride all have molar absorption coefficients in the range 3 x 104-9 x 104 mol-1 dm3 cm-1. From extractions of cadmium dithizo- nate at concentrations lower than 1.78 x 10-8 mol dm-3, a limit of detection of 7.12 X 10-11 mol dm-3 was achieved for cadmium.

A novel method has been developed to enhance the sensitivity and selectivity of the thermal lens spectrometric detection of lanthanide ions.72 In this method, the rare earth ions were selectively extracted from water to a more thermo- optically favourable organic solvent, with the use of crown ethers, e.g., 18-crown-6 or 15-crown-5. This resulted in a

24-fold increase in enhancement of the thermal lens signal for the extracted ions in the organic phase. The well-defined cavities of the crown ethers restrict their complex formation, and therefore their extraction efficiencies, to only the rare earth ions, the sizes of which are compatible with their cavities. This is the origin of their selectivity. With use of 18-crown-6, up to 41% of the Er3+ ion can be extracted from water to chloroform, whereas the extraction yield for the Pr3+ ion, under the same experimental conditions, was only 28% .73*74 Using this information, TLS was used to determine the stoichiometry of the extracted ion pair complexes for several lanthanide ions and crown ethers.

Shen and Snook75 designed and constructed a dual-beam mode-mismatched thermal lens spectrometer for the determi- nation of copper in water. They used the 647.1 nm Kr+ ion laser line as the pump source, and a He-Ne probe laser. The absorption maximum for the [CU(H,O)~]~+ ion is found at 800 nm. The minimum detectable absorption coefficient at 647.1 nm was 4.1 x 10-7 cm-1 which corresponds to a concentration of 5 x 10-8 mol dm-3 of Cu2+. At the sample cell the pump beam radius was calculated to be 4.63 x 10-3, this resulted in absolute detection limits of 2.14 x 10-13 g of Cu2+.

Rojas et al.76 developed a dual-beam thermal lens optical fibre spectrometer. The aim of their work was to construct an instrument capable of measuring sensitive thermal lens spectra at a location remote from the dye laser system, particularly in an environmentally-controlled glove box for actinide chemistry studies, process stream monitoring, and ultimately remote environmental analysis. An argon-ion pumped-dye laser beam was delivered to a sample cell through optical fibres. Core diameters of 100, 200, and 400 ym were compared by assessing the enhancement factors of the induced lenses. The thermal lens signal was detected with a He-Ne laser guided to a photodiode by an optical fibre of 200 pm core diameter. Using an aqueous solution of Nd3+, they found that the theoretical thermal lens enhancement factors, showed good agreement with the experimental values. A detection limit of 7 x 10-6 mol dm-3 and an enhancement factor of 0.9 were obtained for an incident power of 25 mW.

Imasaka et al.77 designed, and constructed a dual-beam thermal lens spectrometer for the determination of iron(r1) using 2-nitroso-5-diethylaminophenol as the spectrophoto- metric reagent. They used a semiconductor laser, which is an attractive light source for TLS because they are inexpensive, have a relatively large output power (exceeding 10 mW), which is regulated by a feedback control, and the noise level can be reduced to approximately 0.003% .78 Near-infrared semiconductors lasers have previously been used in TLS for the determination of phosphorous.& However the importance of collimating optics, when using semiconductor lasers, and the significance of the selection of solvent for use in the near-infrared region were not discussed. These problems were addressed by Imasaka et al. 77 A microscope objective lens was found to provide the highest collection efficiency and there- fore the largest enhancement factor of the lenses studied. Most common solvents used, are relatively transparent in the visible region. Though in the near-infrared region ( ~ 7 8 0 nm) a number begin to absorb appreciably, and therefore create a significant background signal in TLS that is very sensitive to small absorbances. A series of experiments showed that chloroform provides the best compromise, as it has sufficient polarity as to allow efficient liquid-liquid extraction to occur, it has a relatively low background, and has good thermo- optical properties for thermal lens measurements.

A most important problem in analytical chemistry involves the determination of trace concentrations of physiologically active substances. Theophylline is used in medical practice as a stimulant of the central nervous system, and heart. Only a few techniques are available for the determination of theophyl-

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line. HPLC with conductometric detection is the most promising of the techniques available ,79 but this technique requires a relatively high concentration of theophylline in the sample, and involves a complex and difficult isolation proce- dure. Therefore Abroskin et a1.80 developed a thermal lens spectroscopic method for the determination of theophylline in mollusc cytoplasm. They used a conventional dual-beam system with an argon ion pumped laser (A = 488 nm), and a He-Ne probe laser. The detection limit using this experimen- tal arrangement was 1.67 x 10-9 mol dm-3, which corre- sponds to an absorbance of 8.2 x 10-6.

Measurement of Absolute Absorption Coefficients Using TLS The assumption that the signal generated by a thermal lens spectrometric experiment is proportional to the absolute absorption coefficient was made in most of the initial publications on this technique.18~19.22.81 Whinnerysl assumed that the thermal energy absorbed from a laser beam passing through a nearly transparent material allowed the measure- ment of the absorption coefficient with sensitivities of <lo-5 cm-l. Twarowski and Kligers2 then claimed to have measured the two-photon absorption spectrum of benzene with a pulsed nitrogen laser pumped dye head in the range 360-530 nm using a series of laser dyes. Good agreement with theory was found for the time dependence of the signals, and the dependence of the signals upon the incident laser power, though in their experiments for obtaining two-photon absorption spectra, they assumed that the quantum yield for radiationless de-excitation processes was independent of excitation wavelength. Carter and Harris83 again assumed a direct proportional dependence of the thermal lens signal with the absolute absorption coefficient of the solute. In their work they were considering the trade-off between detection volume and sensitivity, which is related to the divergence of the focused beam. Their results show that the detection limits for the smaller sample volume (pathlength 0.1 cm) reflect greater precision and a larger sensitivity compared with the greater sample volume (pathlength 1.0 cm). The absolute detection limits based on the sample mass in the interaction volume, reflect differences in sample pathlength and volumes as well as precision and sensitivity of the measurement. The smaller volume measurement reduced the minimum detectable sam- ple by a factor of 20. Weimer and Dovichi84 used a multichannel crossed-beam thermal lens spectrometer to make absolute absorbance measurements with pulsed laser excitation. The observed change in intensity due to the formation of the lens can be given as:

A1 = const E C(dnld7) P E (14) where const is a constant that depends upon the solvent and focusing parameters used. However, the pump laser energy decreases with distance into the sample due to Beer’s absorbance so that AZ can be given in terms of the pump laser energy incident upon the sample, PEO8?

AZ = const E C (dnldT)PEo 10-EBC (15) where B is the distance from the entrance of the sample cell to the measurement region. Most thermal lens measurements use samples that are highly transparent so that this exponential decrease in signal with distance into the cell is negligible. Weimer and Dovichi84 made the point that because this decrease in signal with distance follows directly from the definition of absorbance, a measurement of the decrease in signal amplitude with distance into the sample, may be used as an absolute determination of absorbance without the need for either measurement of a blank or construction of a calibration graph. Thus TLS has been reported to have been used to measure the absolute absorbance of a range of

samples. 18~19,2231-84&87 Terazima et a1.M report , however, that the absorbance of a sample cannot be measured precisely by this technique without knowledge of the sample, because the thermal lens signal depends upon the nature of the particular analyte species. The sample absorbance can be obtained if the absolute energy of the incident excitation light, and the absorbed energy by the solute can be measured. The energy of the incident light can simply be measured using a conventional light meter, assuming that losses due to scatter- ing at the cell wall interfaces are accounted for. The absorbed energy can, in principle, be measured by TLS because the thermal lens signal intensity is related to the absorbed energy. However, since the thermal lens signal intensity depends upon so many factors besides the absorbed energy,89 it is very difficult, if not impossible to obtain the absorbed energy directly from the thermal lens signal intensity. Therefore, the energy released from a sample is estimated by comparing the thermal lens signal intensity with that of a reference sample of known absorbance.8@7. This method can only be applied when the experimental set-up is identical for both the reference and the sample measurements, the differences in thermal properties between the reference and the sample are negligible, all the light energy absorbed by the analyte is released by radiationless transitions, and since the thermal lens signal intensity of the sample is compared with that of the reference solution containing a different solute, the thermal lens signal should not depend on the nature of the solute.

The experimental conditions can be arranged to satisfy the first condition, and the second condition can be satisfied by using dilute solutions. The contribution of emission and photochemical reactions can be corrected for if the quantum yields of the processes and reaction enthalpies are known. TLS can only detect the gradient of the refractive index in a small monitoring volume. Therefore, even if all the light energy is converted to heat in the whole sample, it does not necessarily mean the last condition is satisfied. Terazima et a1.88 report that this condition is not true for many organic species, i .e., the thermal lens signal intensity is dependent upon the particular solute. They investigated several possible solute-dependent parameters that could affect the thermal lens signal intensity, and found that the solute effects on the thermal properties of the solvent, the transient and multipho- ton absorptions, scattering processes, and energy dissipation as a pressure wave were insignificant. They proposed that the energy was dissipated as vibrational energy, which suggests that TLS could not detect all the energy released by the analyte species. They suggest that another parameter should be added to the theory of TLS to account for this solute dependency.

Thermal Lens Spectrometric Detection in Flowing Streams Dovichi and Harris90 were the first to consider using TLS for detection in flowing samples. A quantitative model of thermal lens behaviour in a flowing sample is considerably more complex than that simply for static samples. However, several general predictions can be made without carrying out this complex procedure. As flow in a medium of constant refractive index does not affect beam propagation,gl the initial intensity is independent of flow rate. At times greater than zero, turbulent and bulk flow act as an additional thermal transport mechanism, which has two results. First the increased rate of thermal transport produces a steady-state signal more rapidly, and second, the steady-state intensity change is smaller than that observed from a static, thermal diffusion-limited case. Flowing samples will also generally produce a decrease in the observed enhancement, E . Compli-

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cations could arise if the flow severely distorts the radial symmetry of the temperature distribution, which could lead to an aberrant far-field beam profile.

Flow Injection (FI)

Sample processing in flow injection manifolds is a means of minimizing the risks associated with sample preparation, and transfer to sensitive detectors.92.93 The advantages of FI in trace level determinations arise from the fact that all sample processing can be carried out in a closed inert manifold before detection. Also, the continuous flow of liquid carrier in the manifold rinses previous samples from the system, reducing carry-over, and allowing blank measurements to be made between each sample. The consumption of costly ultrapure reagents is also reduced when compared with conventional sample handling. Sample injection volumes of 10-100 mm3 are commonly used as compared with 1-3 cm3 of sample needed when using a conventional sample cuvette.

While FI solves several problems associated with trace analysis, it generates several restrictions upon the detector. The response time of the instrument must be short to monitor the changes induced as the samples pass through the detection zone. TLS is, therefore, an ideal detection technique for FI. One advantage is that a focused laser beam provides a diffraction-limited spot size, which is compatible with the small dead-volume flow cells currently being used. Also, the response time of the instrumentation is sufficiently fast to cope with the intrinsic demands of FI.

Yang and Hairre1194 were the first workers to combine thermal lens spectrometric detection with FI. They used a single-laser crossed-beam (crossing angle =lo) configuration to monitor the signal generated by a solution of Bromophenol Blue in ethanol. Using a range of flow rates between 0.1 and 1.0 cm3 min-1, the optimum flow rate was found to be 0.3 cm3 min-1. At 1.0 cm3 min-1 the signal dropped to about a third of its maximum level, and the solvent background noise increased by a factor of -2. The reproducibility of the peak heights for five consecutively injected samples at a concentra- tion of 8.0 x 10-6 mol dm-3 was 2.7% (sr) , and the detection limit was 2.5 x 10-7 mol dm-3. The major sources of noise have been identified as turbulence in the flow cell and flow pulsations.90~95 The turbulence can be alleviated by using a better designed, smaller dead-volume flow cell. Smaller volume flow cells would also reduce the peak width, allowing a higher sampling frequency. Pulsations in the flow stem from the pumping system employed, and can be eliminated by using pulse dampeners or surgeless pumps.

Leach and Harris% carried out real-time thermal lens measurements with application to FI. A krypton or argon ion laser was used to construct a single-beam thermal lens spectrometer. An FI star97 system was used in their work. All transfer lines were 0.5 mm id Teflon tubing, and sample injection loops were always 100 mm3. The performance of the thermal lens detection technique was evaluated using both aqueous and organic carrier streams, and iron was determined as its 1 ,lo-phenanthroline complex in methanol-water (50 + 50). This gave detection limits of 6.4 x 10-9 mol dm-3. An advantage of FI compared with conventional sample handling was observed when they constructed a calibration graph for the dye, Solvent Green in carbon tetrachloride. For static samples, the signal decreased with exposure to the laser radiation, probably because of photodegradation of the analyte after contact with the intense optical power (>1 kW cm-2). This steady decrease in signal was not evident in a flowing sample stream, at a flow rate of 0.57 x 10-3 dm3 min-1.

Measurements in supercritical fluids by thermo-optical techniques have been described.98 The sensitivities of these

thermal lens measurements were monitored at temperatures and pressures around the critical temperature. Although the values obtained corresponded closely with the theoretical predictions, no information about the resultant detection limit was obtained due to the batch style sample handling used. Therefore Leach and Hams99 developed a flow-based sample handling system for measurements in supercritical C02, based on FI injections of 2.0 x 10-5 dm3 of azulene solutions ranging in concentration from 2.5 x 10-6 to 2.5 x 10-5 mol dm-3, and this gave absorbance detection limits of Amin = 2.4 x 10-7, which shows an improvement of approximately 20 times compared with using CC14 as the solvent.100

Jansen and Harris101 constructed a single-laser, double- beam configuration thermal lens spectrometer for real-time monitoring of flow injection peaks. They observed a signifi- cant blank contribution to the measured response in the amplitude and peak shape for the lower concentration samples (12 in CC14). Based on its asymmetric shape, the blank contribution probably arose from refractive index gradients in the sample zone due to slight differences in composition or temperature between the injected solvent and carrier. The blank response was nearly constant however giving linear calibration graphs and a detection limit, based on the reproducibility of the blank, of Amin = 1.7 x 10-5, which was larger than the detection limit derived from the baseline noise,

Simono-Alfonso et al. have studied the use of mixing reactors in FI using thermal lens spectrophotometric detec- tion.102 They concluded that the major source of background noise can be caused by incomplete mixing of merging solutions. The mixing noise arose mostly from changes in probe beam direction produced by refraction through ir- regular liquid-liquid interfaces. These authors suggested that the peak irreproducibility obtained using thermal lens detec- tion could be used as a measure of the efficiency of mixing in the reactor and finally concluded that the mixing noise would largely limit any advantages that thermal lens detection has with respect to very low detection limits.

Amin = 5.5 X 10-6.

Liquid Chromatography

Laser spectrofluorimetry is a sensitive detection technique for HPLC.103 Where the analytes fluoresce, or where fluorescent tags can be easily attached, laser spectrofluorimetry provides sub-picogram detection limits in a simple, reliable system. However, few molecules have a sufficiently high fluorescence quantum yield, and therefore a search was carried out to find other sensitive laser-based spectroscopic detectors for non- luminescent molecules.

Leach and Harris104 were the first to apply thermal lens spectrometric detection to liquid chromatography (LC). They constructed a single-beam system with a laser wavelength of 458 nm, and an output power of 190 mW. Using standard solutions of the positional isomers of nitroaniline in methanol- water (50 + 50), pumped at a rate of 1 cm3 min-1, thermal lens generated chromatograms were produced. The limit of detection, which was derived from the standard deviation of the baseline, was 1.5 x 10-5 cm-1.

Buffett and Morris95 then went on to construct a dual-beam thermal lens spectrometer for LC detection. Analytes derived from nitroaniline were used, and lower detection limits than those of Leach and Harris104 were achieved. This was probably due to lower noise levels attained compared with the single-beam detector. The dual-beam configuration is suitable for use with pulsed lasers, which would make it more useful in the UV region, as there are no commercially available C.W. lasers that operate below 300 nm. A combined thermal lens-fluorescence detection system is feasible, and would allow simultaneous detection of luminescent and non-iumines-

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cent analyte species. In further work,105 they showed that their dual-beam thermal lens spectrometer could be applied to sub-cubic millimetre detection volumes and that with pump laser powers below 10 mW, results comparable with those using higher powers were achieved. The detector response was linear from the detection limit Amin = (2-4) x 10-6 to at least A = 1 x 10-3.

It has been reported that open tubular LC (OTLC) using columns with inner diameters of less than 10 pm, and employing detectors with high sensitivity, and low cubic micrometre volumes, will yield a better performance than packed columns.106-108 However, there. was still a need to develop detectors that satisfy the extremely low volume and high sensitivity requirements of OTLC. Sepaniak et al. 109 designed a single-beam thermal lens spectrometer and carried out some preliminary experiments to demonstrate the feasibil- ity of thermal lens detection for OTLC. Initial attempts at on-column thermal lens detection were unsuccessful due to a severe distortion of the Gaussian laser-beam profile after passing through the column. However, better profiles were obtained using square flow cells. The major problem encoun- tered, concerned the thermo-optical properties of the solvent and their effect on the size of the enhancement factor, E. Solvents with a low polarity generally have properties that result in the largest enhancement. However, the bonded reversed-phase OTLC columns they used require very polar mobile phases. A calibration graph for o-nitroaniline gave an absolute limit of detection of 3.0 x 10-1' g (S/N = 2), and a linear regression coefficient of 0.994 from the limit of detection to 1.2 x 10-9 g injected.

Since the lower limit of detection of this technique is often dominated by the background absorbance of the solvent, a differential technique36 was developed by which the difference in the thermal lens signals between reference and unknown samples could be directly determined. Water, which forms part or all of most LC solvent systems, is relatively opaque and the absorption coefficient is about 1.5 x 10-4 cm-1 at 450 nm. However, the absorption coefficient increases to about 5 x 10-3 cm-1 at 250 nm and to 3 x 10-2 cm-1 at 200 nm.110 Therefore, Pang and Morris111 developed a single-beam differential thermal lens LC detector. They modified the previously published apparatus, and compared their results with those produced using a conventional single-beam system. In their differential arrangement the solvent signal was reduced from about 0.07 to about 0.0025 pA. Although the photocurrent was reduced from about 220 to 170 yA, the thermal lens response increased from 0.075 to 0.155 PA. Simultaneously the noise was reduced from about 0.004 to about 0.002 yA.

Nickolaisen and Bailkowskil12 constructed a pulsed, dual- laser thermal lens spectrometer. The pump radiation was provided by a nitrogen laser operating at 337.1 nm, which delivered about 20 pJ of energy to the sample in a 10 ns pulse, and a He-Ne laser was used as the probe. The analyte used for this flow study was 2-mercaptopyridine. They found that this system was superior to C.W. systems for flowing samples. It has the advantage of a signal size that is relatively insensitive to flow rate, a rapid rate of data acquisition, relative immunity to thermal convection effects due to a low duty cycle, a low average pump power, and an enhancement factor that is greater than that of a comparable C.W. technique. The major disadvantage was the poor precision due to the pulsed laser pointing noise, and mode variations.

Most authors freely comment upon the advantages of using lasers, much less emphasis is, however, placed upon the disadvantages of using lasers for analytical measurements. The most important, is the poor intensity stability of lasers. The output intensity of a laser depends exponentially on the gain of the laser medium which is excited by similar

mechanisms as in conventional light sources. While the measured signal can be increased in laser experiments, noise also increases when lasers are used. Although there may be a net gain in the signal-to-noise ratio, a clear advantage may not be adequately shown. Common C.W. lasers with sufficient powers for TLS have inherent instabilities of 1%, which is about two orders of magnitude worse than well-regulated conventional light sources. Power stabilization circuits or a reference photodiode can reduce fluctuations to 0.1% .35 Alternatively, a second laser with better intensity stability (He-Ne lasers) can be used to probe the thermal lens generated by a more powerful, but less stable pump laser;41J13 although difficulties arise in the alignment of the beams in the probe region, especially when small sample volumes are used. It has been shown in dual-beam laser experiments that effective intensity stabilities in the 10-4 114,115 to 10-6 116 range can be achieved if high frequency modulation is used. Skogerboe and Yeung117 constructed a single-beam thermal lens spectrometer suitable for micro-bore LC detection. A baseline stability of 1 x 10-4, and lock-in detection was achieved using a reference beam and high frequency modula- tion (150 kHz). Limits of detection of 3 x 10-12 g of benzopurpurin 4B using 90 mW of pump radiation were reported. These limits of detection were defined by the pointing stability of the laser relative to the pinhole in front of the photodiode.

Nolan et aZ.118 described a low volume, high sensitivity detector using the crossed-beam thermal lens set-up for 0.25 mm id slurry-packed LC. This experimental arrangement has been used previously for amino acid determination with a commercial 1 mm id chromatography column.119 They repor- ted detection limits of sub-picomole quantities of amino acids injected. Nolan et aZ. also120 constructed a dual-beam system using a He-Cd pump and a He-Ne probe laser. They demonstrated this arrangement by the separation of a series of 2,4-dinitrophenylhydrazine derivatives of ketones. Absolute detection limits, three standard deviations above the back- ground, were 1.2 x 10-13 mol for acetone and 6.0 x 10-13 mol for adamantanone injected. Assuming a 2 x 10-12 dm3 probe volume the material present within the detection volume at the detection limit was about 3 x 10-19 mol.

The use of thermal lens detection in micrometre diameter capillary tubes has also been explored by Bornhop and Dovichil21 with the aim of providing superior detection limits in capillary electrophoresis, and ultimately protein sequenc- ing.122 In the paper by Waldron and Dovichif22 detection limits of 3 orders of magnitude better than conventional liquid chromatographic detection are reported for the determination of phenylthiohydantoin-amino acids of the type derivatized in protein sequencing. This is an important area of application that could dramatically improve the capabilities of sequencing proteins via the Edman degradation.

Measurement of Fundamental Parameters Using TLS

Quantum Yields

Hu and Whinnerylo were the first to point out that TLS could be used to measure the fluorescence quantum yield of organic dyes. The total power absorbed by the dye solution can be measured spectrophotometrically , and then the power that is converted into heat is measured by TLS. Assuming no other de-excitation process exists, the difference in power can be said to have escaped via fluorescence emission. A simple expression can thus be written:

where Qf is the fluorescence quantum yield, he is the

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wavelength of the excitation beam, hf is the average fluores- cence wavelength derived from the power spectrum of the fluorescence emission, (Yth is the absorption coefficient measured by the thermal lens method, and O C ~ ~ that measured by the spectrophotometric method. Although successfully demonstrating this method, no details were presented. Con- ventional luminescence yield measurements, involve two steps. First a luminescence standard must be measured, which is difficult, resulting in values from different laboratories usually disagreeing. Second, a particular measurement requires comparison of an unknown with a standard. There- fore careful attention must be given to corrections for differences in solvent, temperature, and so on. Brannon and Magde87 showed that the thermal lens technique significantly reduced the uncertainties in both problems outlined above. They showed this by carrying out the measurement of the absolute fluorescence quantum yield of sodium fluorescein. At concentrations below 10-5 mol dm-3 in 0.1 mol dm-3 sodium hydroxide they found that Qf = 0.95 k 0.03.

Lesiecki and Drake123 used this approach with some modifications, for the determination of the quantum yields of Rhodamine 6G and Fluorol555 in solution and in poly(methy1 methacrylate) (PMMA). They established the validity of this technique by comparing their results with those accepted as accurate for a series of dyes. They found the technique to be superior in accuracy compared with conventional techniques, and they predicted that it would become a viable method for the measurement of absolute quantum yields. A device known as a planar luminescent solar concentrator (PLSC) has been the object of considerable experimental effort. 124,125 Essen- tially solar radiation is absorbed by a dye, re-emitted, and trapped by total internal reflection providing a photon flux gain at the output edge of the concentrator. Their results for Fluorol 555 in PMMA suggest that its high quantum yield (0.88), and low probability of self absorption would make it a viable example for such a PLSC.

Terazima and Azumi12”128 carried out a series of investiga- tions to measure the quantum yield of triplet formation and the triplet lifetime of several different species in the liquid and solid phase, using a time-resolved thermal lens method. First126 they found the quantum yields of triplet formation of phthalazine to be 0.49 in benzene and 0.44 in ethanol. They determined the triplet lifetime of phthalazine in benzene at room temperature to be 2.7 ps, and then went on127 to measure the quantum yield of inter-system crossing for solid-phase pyridazine at 60 K. A value of 0.66 was obtained, and they suggested that the triplet lifetime of pyridazine at room temperature was shorter than 100 ns. Finally,128 they measured the quantum yield of triplet formation and the triplet lifetime of pyridine, for the first time in the liquid phase, using a two-photon excited time-resolved thermal lens method. This method is especially useful for molecules where the phosphorescence and/or fluorescence is very weak. They determined the triplet lifetime to be 1.0 ps, which correlates well with that obtained in the gas phase. The quantum yield of triplet formation was found to be 0.9.

Shen and Snookl29 determined a precise value for the quantum yield of sodium fluorescein in 0.1 mol dm-3 NaOH at concentrations below 1 X 10-5 mol dm-3. They used a quenched sample of sodium fluorescein as the reference. This solves the problems that occur when using a different non-luminescent material as a reference. The result grained in this work was 0.92 k 0.03.

Terazima and Azumil30 used a time-resolved thermal lens method to measure the triplet formation of transient species. They determined the quantum efficiency of inter-system crossing in the photo-induced keto-enol tautomerism reaction of 7-hydroxyquinole. The lifetime for the keto form was 9 ps in ethanol, and a quantum efficiency of 0.09 was determined.

Following the work of Terazima et a1.,88 who reported the limitations of TLS for the measurement of absolute absorption coefficients, Chartier et al. 131 investigated the limitations of this technique for the measurement of absolute fluorescence quantum yields. Their results agreed with those of Terazima, that large errors in absolute values could be introduced if the solute dependency of the signal was not considered. Although the results obtained using the method of Chartier et al. 131 did not correlate with those of Shen and Sn00k,129 the discrepancy was probably due to the fact that the lasers used were operating in a different excitation mode, Shen and Snook used a C.W. pump laser as opposed to the pulsed laser used by Chartier et al. With C.W. laser illumination the measurement is made when the thermal lens has reached a steady state. In pulsed laser experiments this is not so, and the results obtained may be dependent on the pulse duration.

A similar formalism to that used by Brannon and Magdeg7 and Shen and Snook129 was used by Degen et al. 132 to measure absolute quantum yields of transition metal complexes. Thus the quantum yields for the fluroescence of [ R ~ ( b i p y ) ~ ] X ~ , where X = C1 or C104, were measured to be @ = 0.31 and 0.79, respectively, showing that the quantum yield for such bipyridyl salts strongly depends upon the counter ion. The accuracy of the method was established using a standard methanol solution of Cresyl Violet (5.9 x 10-5 mol dm-3) which gave the accepted value of @ = 0.52 and also a solid sample of poly(methy1 methacrylate) which gave a value of @ = 0.99 (expected value 1.0). The study also showed that the quantum efficiency of the ruthenium salts was independent of complex concentration in the range 1 x 10-4-2.5 x 10-5 mol dm-3.

These methods can therefore provide accurate and absolute quantum yields without recourse to calibration via lumines- cence standards, provided that all other energy loss mechan- isms apart from the thermal lens mechanism are accounted for, e.g. , photodissociation.

Indeed the quantum yield of photodissociation of iodine has been studied by Lebedkin and Klimov133 using a time-resolved two-beam thermal lens technique. Photo-excitation of iodine in solution does not result in luminescence but photodisso- ciates in a photochemically reversible reaction with almost no products. Both photodissociation and recombination have been studied. The quantum yield for photodissociation in hexane and benzene was shown to increase as the wavelength of the excitation radiation decreases in the range 4 = 0.1-0.6 over a wavelength range of 700 to 300 nm owing to the involvement of different electronic states of the iodine molecule at different wavelengths.

The effect of tetracycline on the sensitization of europium fluorescence in a micellar solution has been studied by Georges and Ghazarianl34 as a method for the determination of tetracycline. Pulsed TLS was used in this study to determine the efficiency of intramolecular energy transfer and of the resulting luminescence efficiency again demonstrating the ease with which quantum efficiencies can be obtained.

Heats of Reaction, Energetics and Kinetic Studies Time resolved TLS has been successfully employed to study heats of reaction, energetics and reactivity of photocyclisation of diphenylamine which highlights the potential for TLS in fundamental studies of reaction kinetics and energetics. In this study Suzuki et a1.135 used a pulsed XeCl excimer laser (308 nm; 100 mJ pulse-1) with a pulse duration of 20 ns as a light source and an IR diode laser (780 nm; 30 mW) as a probe laser. Since the time-resolved method detects time-dependent heat emitted through radiationless transitions metastable and excited state information can be obtained which is not obtainable by other techniques such as flash photolysis. This

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twice-resolved TLS signal in the 1-10 ps region yielded a time profile from which the rate constants for the decay of diphenylamine and the growth of ground state dihydrocarbaz- ole (resulting cyclization) could be determined. The heat emitted was also quantitatively determined by comparing the ratio of energy released as heat to absorbed photon energy. This was achieved by comparison with data obtained from a standard of pyridazine where this ratio is known to be 1.0. Using these data and absorbance data these authors were able to determine the required values of A H and the relative energetics of the triplet and singlet states of dihydrocarbazole.

A recent study of the SF6 and SF6-Ar mixturesl36 has shown an interesting effect in which a transient focusing effect is observed prior to de-focusing of the beam. This is observed in the first few microseconds after pulse illumination of the gas mixture with a transversely excited atmosphere-C02 laser pulse and is attributed to time-dependence of the refractive index caused by the onset of a Gaussian profile of either polarizability or density. Thus an increase in electronic polarizability due to vibrational excitation and changes in molecular dimensions. Similarly a transient increase in density along the laser path is also possible, a phenomenon known as laser-induced osmosis. The density profiles develop in the timescale of microseconds and proceed at a rate close to the sound velocity in SF6 or its mixtures at the appropriate temperature. Clearly this effect has implications when inter- preting time-resolved thermal lens signals in the gas phase.

Novel Applications of TLS

The analysis of chiral drugs has increasingly become an important subject in science and in technology. Of the 1327 (in about 1990) synthetic drugs currently marketed world-wide, 528 are chiral and can exist as two or more optical isomers.137 The pharmaceutical industry therefore needs an effective analytical and preparative separation method for a variety of enantiomeric compounds. Liquid chromatography seems the technique of choice because of its efficiency, speed, wide applicability and reproducibility. As the LC separation of enantiomers becomes more universal, the demand for detec- tors that provide information on the chirality of the eluted species increases. An ideal detector would produce a complete circular dichroism (CD) spectrum of the eluted solute with the same sensitivity and speed as a standard UV chromatographic detector. The conventional CD spectropolarimeter has a minimum detectable value of only about 10-4 of an absor- bance unit.138 There is, therefore, a need to develop an ultra-sensitive chromatographic chiral detector that can deter- mine the CD of chiral effluents. Tran and Xu139 and Synovec and Yeung116 developed thermal lens circular dichroism spectropolarimeters (TL-CDSs) . These instruments are based on the measurement of the difference in the amount of heat generated in an illuminated chiral sample as a consequence of its absorption of the left-handed circularly polarized light (LCPL), and right-handed circularly polarized light (RCPL). The sensitivity of the apparatus was greater than conventional transmission measurements. The use of lasers as excitation and probe sources enable the CD measurement of samples with very small volumes. The detection limit for the optically active [C0(en)~]3+1~- complex was 1.14 X 10-9 mol dm-3. A modified version of this apparatus was then used as a detector for enantiomeric species140 using HPLC separation. Absolute detection limits of 7.2 ng were found by using a 10 X 10-6 dm3 flow cell, with a 5 mm pathlength and 6 mW excitation laser beam power (A = 514.5 nm).

Scott et aZ.141 observed a novel effect in barium sodium niobate at its Curie temperature T, = 853 K, where the large positive refractive index change with temperature associated with the ferroelectric phase transition dnldT = +1.4 X 10-3

K-1, produces a convex thermal lens with a focal length of approximately 3 cm. This is 30 times stronger than the thermal lens effect found in fluids by Gordon et al.5 and of the opposite sign. This effect provides an accurate way of measuring dnldT very near to phase transition temperatures, which would be of interest in studies of critical phenomena associated with structural phase transitions in solids.

If coplanar pump and probe laser beams are tightly focused, and crossed at right angles, high spatial resolution measure- ments of absorbance can be made.142-144 The two beams interact only in their intersection volume, and the probe beam is de-focused out of the plane containing the two beams. The amplitude is inversely proportional to the pump beam spot size. Often a lock-in amplifier is used to de-modulate the crossed-beam thermal lens signal, and this produces a simultaneous measurement of the amplitude and phase of the signal. The amplitude is related to sample absorbance, while the phase is related to the thermal diffusivity of the sample.142 This crossed-beam thermal lens technique has produced absorbance detection limits of 8 X 10-10 within a 2.5 x 10-11 dm3 interaction volume using a 1 W argon ion pump laser. Only 60 analyte molecules were present within the interaction volume.144 Burgi and Dovichi145 used such an optical config- uration to construct a photothermal microscope that gener- ated images of thin (=lo pm) histological and biological samples by recording the thermal lens signal on a point-by- point basis as the sample was translated through the intersec- tion region of the two beams. Two images were generated, one from the amplitude and the other from the phase, showing the spatial distribution of absorbance and thermal diffusivity in the sample.

When developing new techniques, not only new analytical applications are discovered, but also unexpected associated effects, or even new phenomena, can arise. Side effects can interfere, but they can also be exploited analytically. In TLS, heating of the sample in the irradiated region produces convective movement of the liquid, which results in undesir- able noise.1467147 In contrast, an effect that can be of practical interest is the lack of a direct proportionality between the thermal lens signal and absorbance.88

Villanueva Camanas et ~1.148 describe a photolytic effect caused by the intense pump radiation used in TLS experi- ments. Photolysis of hexacyanoferrate(u1) solutions asso- ciated with transport by the radiation pressure of the Fe(OH)3 particles produced, was given as an explanation for the phenomenon observed. The effect was detected as a precipi- tate that formed on the illuminated region of the cell back wall. Quantitative application of the observed effect for the determination of hexacyanoferrate(Ir1) was found to lack reproducibility and linerarity. However, it could be used for preconcentration, e.g., to precipitate a substance on an electrode surface.

Franko and Tran149 developed a novel thermal lens spectrometer that was used for the simultaneous measurement of thermal lens signal and absorbance. This was used to determine sensitive photochemical reaction kinetics using 1,2-dimethoxy-4-nitrobenzene in 0.50 mol dm-3 KOH. The measured experimental results were in good agreement with the values predicted by the theory.150 Compared with other conventional kinetic evaluation methods, this technique provided kinetic results that were not only accurate and precise but also obtained from samples whose concentrations were about 100-times lower than work conducted using conventional methods.

Thermal Lensing in Glass and Other Solid Laser Materials

The characterization of the transmission properties of laser beams through optical gIasses,151-154 ruby, sapphire,155.156 and

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lithium niobate crystalslS7 has been extensively studied for more than two decades. The existence of undesirable thermal effects associated with the generation of laser light is a basic problem in the design, and operation of any efficient solid-state laser device. Non-linear thermo-optical properties of solid dielectric materials are also of importance in high- power laser systems, and for the development of ultra-low loss optical fibres for communication networks.158J59

The amplitude, and sign of the thermal lens signal are strongly dependent upon the temperature of the absorbing medium. This is mainly owing to large variations in the optical pathlength of the sample, with temperature, (dsldT). For liquid samples, the optical pathlength is governed solely by the temperature coefficient of the refractive index, (dnldT). The temperature coefficient of the refractive index is affected by two counteracting factors.160 An increase in the specific volume (cm3 g-1) due to thermal expansion, causes the refractive index to decrease, due to the greater inter-mol- ecular spacing. Secondly, an increase in the electronic polarizability causes the refractive index to gradually increase as the structure tends towards a more dissociated state. For solid samples however, the optical pathlength not only depends upon dnldT, but also upon dlldT, the temperature coefficient of the sample thickness.161 Data for sapphire,162 and various glasses,l63 have shown that values of dnldTcan be either positive or negative, and in magnitude can be between 10-15 x 10-6 K-1 for radiation in the visible part of the spectrum. It should also be noted that anomalous dispersion effects may modify these values considerably at both emission, and absorption wavelengths. 1 6 ~ 6 s Variations in the optical pathlength due to dNdT and dnldT will be discussed in detail in this section.

The phenomenon of thermal lensing or self-focusing of laser light beams in non-linear media was first observed in 1962.166 This observation was made when irradiating a plasma using a strong electromagnetic beam. It was shown that the strong thermal ionizing effects of the beam on the plasma, set up waveguide propagation conditions, which eliminated the natural diffractive divergence of the beam, i. e., self-focusing.

Heat dissipation is inherent in all optically pumped solid- state laser materials, because the basic laser mechanism involves radiationless transitions accompanying population inversion. Many important laser parameters such as fluores- cence line width, relaxation times, and optical quality are strongly temperature dependent, and have been considered by several investigators.167-170 In April 1964, Blume and Tittell71 considered the temperature dependency of the optical pathlength of a neodymium glass laser rod. Although no reference was made to the process of self-focusing or thermal lens formation, they describe the thermal effects associated with optical excitation which are responsible for self-focusing of laser beams. They astutely recognized that the dominant phenomena involved, upon heating any laser material, is a non-linear modification of the refractive index, and that a change in the thermal expansion coefficient was involved. They also observed an internal stress effect, which, it can be assumed, is a direct result of delivering -106 W of laser light in 500 ys to the sample.

Later that year Chiao et al.172 discussed the possibility of self-focusing of laser beams as a result of the fact that the change in the refractive index of the material has an approximately quadratic dependence on the field amplitude. This could create conditions under which the radiation becomes self-focused, and propagates in the medium within a thin filament-like channel. Because of the field of the wave itself, the refractive index is greater inside the channel than outside, and the light remains confined to the channel as a result of total internal reflection. They suggested that this change in refractive index was due to the Kerr effect

(orientation of anisotropically polarizing molecules by the field), electrostriction (compression of the dielectric by the electric field), or due to electronic polarizability. In solids, the molecular orientation is frozen, and they assumed the Kerr effect to be virtually zero. They therefore, concluded that the non-uniform refractive index change was dominated by the electronic polarizability of the medium, with a small contribu- tion by electrostrictive processes. They made no reference, however, to the contribution of thermal expansion to the self-focusing mechanism.

In the period 1965-1967, several investigators studied thermally-induced optical distortions in both ruby, and glass laser rods.173--177 They began to recognize that the dominant effect of the induced temperature non-uniformities is to generate a change in the optical pathlength, and that the optical pathlength was dependent upon both a change in the refractive index, and a physical change in the sample thickness.

A change in the optical pathlength has a direct influence on the mode structure, and the time-dependent frequency behaviour of laser oscillators. 178,179 Solid-state laser amplifiers may lose their initially high optical quality during the optical pump process, due to non-uniform change in refractive index over the cross-section of the rod. This change in refractive index was first treated theoretically by Quelle ,180 and subse- quently revised in 1967,181 to include Fermat's principle, and also a change in refractive index arising from the presence of an excited ion population. This phenomenon can be explained by the fact that the polarizability of an excited-state ion is generally different than its value in the ground state. A refractive index change can therefore result from the genera- tion of an excited-state population of ions. This effect was observed during, and shortly after the pumping period, when the population of excited-state ions is relatively high.181 Baldwin and Riedellsl then went on to quantitate the correlation between their theory, and experimentally obser- ved optical phenomena in neodymium-doped glass rods. An agreement was found to exist between the two, within experimental errors. In their experiment they found that the change in refractive index due to the polarizability of the excited-state ions was approximately equal to the refractive index change caused by thermal expansion alone. They went on to state that the pump induced optical distortions in Nd3+-doped glasses were not solely determined by tempera- ture, and temperature gradients, but were strongly influenced by the magnitude and distribution of inversion within the laser rod. However, they failed to acknowledge that the division of ions between the ground and, excited states is dominated by the temperature at which the system is operating.

In 1968, Dabby and Whinneryl52 first termed these thermo- optical effects seen in solid samples, thermal lensing. Their work on lead glass followed the observations made previ- ously ,18233 that thermal lenses had been obtained in common lead glasses, which decreased the natural laser beam divergence, demonstrating a positive value for dn/dT. They152 observed strong thermal self-focusing of an argon ion laser beam, when it was passed through a 15 cm length of lead glass. Focal lengths of <20 cm were obtained, and the beam showed the effects of spherical aberration. Above a certain laser- power threshold, beam trapping was evident, where the beam was confined to a thin filament-like channel within the glass. This channel was estimated to have a radius of 4 0 ym.

The majority of the previously published work151J80J81 has been carried out using isotropic laser rods. In 1970, Foster and Osterink154 developed a mathematical model for thermally- induced optical effects in cubic, crystalline laser rods. They paid particular attention to a (111) orientated C.W. pumped Nd:YAG laser rod. Their results showed that thermal bifocusing, and birefringence greatly reduced the output

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obtainable in the TE% mode, polarized from a high power (=4 kW) Nd:YAG laser. They went on to suggest that the TE& mode, and polarized output could be improved using cooling techniques with Cartesian coordinate symmetry, to avoid the cylindrical symmetry problems.

In 1971, Sparkeslm considered the differences in the thermo-optical properties between covalent and ionic crystals, when used as windows in high-power laser systems. It was found in general, that ionic crystals have a negative value for dnldT, and covalent crystals have a positive value. The over-all distortion was generally found to be smaller for ionic crystals, than for covalent crystals as a result of the partial cancellation of the thickness, and refractive index terms, and the typically smaller values of dnldT for ionic crystals. It was also found that the degree of induced birefringence was greater for ionic materials than covalent ones. Finally, expressions were derived for the thermally-induced optical distortions in terms of the measurable parameters refractive index, dnldT, strain optical coefficients, and the thermal expansion coefficient.

An understanding of the fundamental mechanism of self- focusing is necessary if materials are to be developed with thermo-optical properties that are stable to high-power lasers. Until 1972, there had been a great deal of contradicting evidence as to the dominant process upon the self-focusing effect. A great deal of work had been carried out using different samples, and different experimental conditions. However, no attempt had been made to assess the significance of any of this work, and insufficient evidence had been compiled, to judge the comparative importance of electro- strictive, Ken effect, electronic polarizability , and thermal expansion processes upon the thermal lens phenomenon in solid samples.

Generally solids lack freely rotatable molecules or ions, and thus electrostriction was initially consideredl72.185.186 to be the principal cause of self-focusing when laser pulses of S l O ns were used. Kerr187 therefore, went on to develop a theory of electrostrictive self-focusing to explain the data of Stein- berg’s where 55 ns pulses from a ruby laser were used to measure the thermo-optical properties of several optical glasses. However, it was subsequently pointed 0~t,189 that in his theory, Kerrl87 found it necessary to make use of the Lorentz-Lorenz expression for the change in refractive index with density. This expression was derived for liquid samples, and gives poor agreement with experimental data when applied to solids.190

For laser pulses much shorter than 10 ns, the Kerr effect was thought to be dominant, because the electrostrictive mech- anism has insufficient time to take effect. Duguay et aZ.191 calculated the non-linear refractive index change due to the Kerr effect from measurements of the induced bire- fringence in borosilicate crown glass using picosecond laser pulses. They found that the value obtained was of sufficient magnitude to cause self-focusing, and were of the opinion that the Keer effect is the predominant mechanism for any pulse length.

The Kerr effect is defined as the orientation of molecules or ions by an incident electric field. This renders the material anisotropic, and induces birefringence, i.e., the ability to refract light differently in two directions. However, in the publication by Duguay et al.,191 and the ensuing papers by Feldman et aZ. ,189,192 the Kerr effect was assumed to arise from non-linearities in the electronic polarizabilities of the sample, and that orientational effects are negligible.

From their results of borosilicate crown glass, fused silica, and dense flint glass, Feldman et a1.1891192 also found that the redefined Kerr effect was the dominant effect when the samples were exposed to 25 ns TE& pulses from a Nd-glass laser. They also found that the effects of a change in the

thermal expansion coefficient was significant, and that the effect of the electrostrictive process was small. Their data192 suggests that the non-linear modification of the electronic polarizability increases with refractive index. As large refrac- tive index implies large charge displacements, and large charge displacements are more likely to lead to a non-linear response to the electric field, therefore to a large ‘Kerr effect’. It is known193 that flint glasses exhibit increasing polarizabil- ity, and refractive index with increasing lead content. It has also been proposed194 that although ions and molecules are held rigidly in solids, some contribution may be made to the Kerr effect, by a hindered rotation within the solid sample matrix. The relatively small Kerr effect observed for fused silica agrees with the fact that such rotatable ions are not present in fused silica, which has a tight structure with no dangling bonds. Borosiiicate crown glass however contains weakly bound alkali ions and flint glass contains lead ions, all of which could contribute to the Kerr effect through nuclear motion.

These experimental observations first made in the early 197Os, agree with the theoretical predictions made by Prod’homme in 1960.160 He stated that when the temperature coefficient of electronic polarizability, Qc, is greater than the temperature coefficient of thermal expansion, y, the value of dnldT is positive. For the materials studied by Feldman et aZ.,192 at the stated temperatures, the value of dn/dT is positive, and the dominant effect upon the optical pathlength is the increase in the electronic polarizability coefficient. When the values of Qc and y are equal, then dn/dT is equal to zero, and the refractive index, n, is at a maximum. For the situation where y is greater than Qc, the value of dn/dT is negative.

Durville and Powell195 investigated the thermal lensing characteristics of Eu3+- and Nd3+-doped phosphate glasses under resonant and non-resonant excitation conditions. They observed a significant enhancement of the thermal lens signal for resonant excitation, and also that this effect is greater for the Eu3+-doped glass than the Nd3+-doped glass. When the excitation laser beam was focused to =20 pm, a permanent change in the refractive index of the EuP5014 glass was observed. From the experimental results a value for this change of An = 1.23 x 10-5 was calculated. This value agreed with that produced in a four-wave mixing experiment carried out previously.1M This permanent change in the refractive index was attributed to a localized structural rearrangement around the Eu3+ ions caused by the high-energy local vibrational modes created by the 5D22Do relaxation process.

In 1992, Taheri et aZ.197 investigated the effects of the structure, and composition of lead glasses on the thermal lensing of pulsed-laser radiation. Using a 7 ns laser pulse at 457 nm in a tight-focus geometry, the thermal lens characteristics of a number of silicate, germanate, phosphate and borate glasses were studied. They found that the greatest influence of the network modifier ions was due to their effect on the absorption coefficient of the glasses. For the lead glasses investigated, the values of dnldT for the germanates and silicates, which have random network structures, were greater than those of borate and phosphate glasses which have ring and chain structures. Finally, in agreement with previous observations,189,191,192 the main contribution to dnldT comes from the thermally induced changes in the electronic polari- zability of the glass matrix.

They then went on to study more closely one particular lead oxide-modified silicate glass.198 Experiments were carried out using a 10 ms square pulse at 514 nm, and a 10 ns Gaussian pulse at 532 nm. Their results showed that to first order the mechanism of thermal lensing is the same on both time scales, namely the time dependent modulation of the refractive index due to thermal heating. In the millisecond time regime, they

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observed multiple focal points within the sample. This is indicative of strong thermo-optical effects. Using their geo- metric model, derived to describe the quadratic radial profile of the refractive index resulting from the laser-induced temperature profile, a value of dnldT for the chosen sample was calculated to be 1 x 10-5 K-1.

Jewel1 and Aggarwall99 investigated the effect of glass composition on the theoretical thermal lensing for ZrF4- BaF2-LaF3-A1F3-NaF (ZBLAN) heavy metal fluoride glasses. It was found that serial substitutions of, for example, HfF4 for ZrF4 had significant effects upon the refractive index, the coefficient of thermal expansion, and dnldT. The aim of the work was to investigate the possibility of producing a glass laser window, with a zero change in the optical pathlength when exposed to high laser powers. Their results showed, however, that the effects of the proposed substituents on the temperature rise upon irradiation, and the glass stability would be relatively small, and most likely insignificant at the levels of substitution required for a zero optical pathlength change.

Baesso et aZ.22 measured the absolute thermal diffusivity of soda-lime glass (70.5 mass% Si02, 17.5 mass% Na20, 10 mass% CaO, and 2 mass% FezO3) using a time-resolved thermal lens method. Using a mode-mismatched experimental configuration a value for the thermal diffusivity was calculated to be (4.9 k 0.3) x 10-3 cm2 s-1. This value was in agreement. with that found previously200 using photoacoustic spectro- scopy (PAS), on an identical sample. This method however, is advantageous when compared,with PAS as it is a non-contact measurement, and thick samples can be used.

Summary It is evident from the papers cited in this review that TLS can provide sensitive analytical measurements of absorbing spe- cies in a wide range of sample types. In addition the technique provides for measurement of certain absolute values of optothermal properties such as absorption coefficients, quan- tum efficiencies of luminescence and thermal processes as well as thermal properties of materials. The use of TLS as a diagnostic tool for these purposes is unrivalled owing to the simplicity of construction of the instrumentation, ease of use and plethora of theoretical treatments that yield similar results. A potential disadvantage of the technique is the capital and maintenance costs of acquiring and running a C.W. laser. Whilst this may not be a significant factor for diagnostic uses where no other technique is available it is a significant factor when considering the use of TLS for routine chemical analysis, e .g . , when competing against UVNIS spectropho- tometry. To incur the order of magnitude increase in cost would only be justifiable if the enhanced detection power was required, for example in capillary column detection. Even then an alternative technique, e.g. , electrochemical detection, might achieve the same result.

Clearly, for analytical purposes, the key to successful exploitation of the technique is provision of cheap, robust, tunable lasers in the visible spectrum with good beam quality. As yet diode lasers seem to offer the best hope for such a source but unfortunately these are restricted to a few discrete wavelengths in the red-end of the spectrum. Even with frequency doubling these offer very poor wavelength range. In addition the optimum powers required for TLS are not easily achieved with diode lasers and the degree of tunability around the laser wavelength is poor (50 cm-1) unlike an Ar-ion pumped-dye laser.

The quest for a widely tunable high power solid-state laser in the visible region goes on, however, and with such sources a cheap, robust and reliable thermal lens spectrometer can be envisaged. It is worth noting that Forteza et aZ.201 have already

shown the practical use of a diode array laser system albeit at reduced sensitivity.

The choice between a C.W. and a pulsed-laser excitation source depends on the timescale of events that are to be observed. For most signals dominated by formation or relaxation of the thermal lens a C.W. technique can be employed including time-resolved techniques. Most purely- analytical measurements fall into this category. The use of a pulse-laser source in these cases would only serve to degrade signal-to-noise ratio through the poor stability and pulse-to- pulse energy precision obtainable with such sources together with higher levels of mode or pointing noise .202 Pulsed-laser techniques may have advantages for thermal lens detection in flowing streams however, where C.W. techniques have been shown to be flow rate dependent owing to the transport of the heated sample region out of the probe beam.

The optimal beam configuration in the two beam coaxial mode-mismatched c. w. system in which phase-sensitive detec- tion can be exploited to increase over-all signal-to-noise ratios. The sensitivity of this technique can also be improved by increasing the ratio of probe beam-to-pump beam radius at the sample cell, but this advantage is at the expense of volumetric resolution.

In many instances, e .g . , capillary column detection, spec- tro-electrochemistry and interfacial studies, volumetric resol- ution is equally as important as a low detection limit so this may be a difficult compromise to make. It is perhaps in these areas of application, where the ability to probe small volumes of solution at the pumpprobe beam interaction region where significant new advances will be reported.

In essence we believe that TLS will be developed more as a laboratory-based diagnostic tool rather than a routine ana- lytical technique.

Appendix

A Absorbance a Absorption coefficient (cm-1) C Concentration (mol dm-3) dnldT Temperature coefficient of the refractive index (K-1)

Thermal diffusivity klCpp (cm2 s-1) Molar extinction coefficient (mol-1 dm3 cm-l) Focal length of the induced lens at t > zero (cm) Focal length of the induced lens at t = 1000t, Light intensity at time > zero Light intensity at time = zero Thermal conductivity (J s-1 cm-1 K-1) Pathlength (cm) Wavelength of the probe beam (cm) Degree of mismatching (0ld0~)2 Power of the excitation laser (W) Time (s) Time constant = 02/4D (s) Temperature (K) =Z1/Zc when 2 2 >>> 2, Distance from the beam waist to the sample cell (cm) Confocal distance = xoo2/h (cm) Probe beam radius at beam waist (cm) Probe beam radius at the cell (cm) Excitation beam radius at the cell (cm) f31/2

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Paper 4lM743F Received November 4, 1994 Accepted February 16, 1995

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