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DISSERTATION
EARLY STAGES OF POLYMER CRYSTALIZATION
STUDIED BY DIELECTRIC SPECTROSCOPY
DISSERTATION
zur
Erlangung des akademischen Grades
doctor rerum naturalium (Dr. rer. nat.)
der Mathematisch-Naturwissenschaftlichen Fakultät
der
UNIVERSITÄT ROSTOCK
Vorgelegt von
Ragab M. Soliman
Geboren am 24.12.1966 in Kairo Stadt
Ägypten
Rostock, Dezember 2004
Gutachter: Prof. Dr. Christoph Schick, Universität Rostock, Institut für Physik PD Dr. Andreas Schönhals Bundesanstalt für Materialforschung und -prüfung, Fachgruppe IV.3, Berlin PD Dr. Ingo Alig Deutsches Kunststoff Institut, Abteilung Physik, Darmstadt Tag der Verteidigung: 21.04. 2005
Zusammenfassung . i
Zusammenfassung
Polymere sind bei Temperaturen unterhalb der Schmelztemperatur Tm nicht im
thermodynamischen Gleichgewicht. Es verändern sich daher mit der Zeit ihre
Eigenschaften in Richtung des thermodynamischen Gleichgewichtes. Dieser Prozess ist
eine strukturelle Relaxation. In vielen Fällen kristallisieren die Polymere dabei. Der
Prozess der Polymerkristallisation wird seit seiner Entdeckung kontrovers diskutiert.
Trotzdem gibt es einige grundlegende Fragen, die noch völlig offen sind. Eine davon ist,
ob das Herausbilden von Polymerkristallen ein ein- oder mehrstufiger Prozess ist. Vor
allem in den traditionellen Theorien wird von einem einstufigen Prozess ausgegangen.
Neuere experimentelle Befunde zeigen aber, dass diese Theorien den Übergang von der
verknäulten Polymerschmelze zum teilkristallinen Festkörper nicht richtig beschreiben.
In einem neueren Modell von Strobl aus dem Jahre 2000 [43] wird der gesamte
Kristallisationsprozess als Mehrstufenprozess aufgefasst, wobei das Polymer einige
spezifische und allgemeingültige Stufen durchläuft. Dabei wird als erster Schritt das
Herausbilden einer metastabilen Struktur mit geringer Vorordnung angenommen, die
danach einen Stabilisierungsprozess zur Kristalllamelle durchläuft.
Auf der Basis dieses Modells wurde in der vorliegenden Arbeit versucht
experimentelle Hinweise zu finden, die Vorstellungen über die Bildung vorgeordneter
Strukturen in der Polymerschmelze als Initialschritt der Polymerkristallisation
unterstützen. Als Modellsystem diente PCL als typisches kristallisierendes Polymer, dass
keine Lamellenverdickung während der Sekundärkristallisation zeigt [87, 88]. Auch die
Kristallisationskinetik ist bei Temperaturen kurz unterhalb der Schmelztemperatur von
etwa 70°C langsam genug, um einzelne, angenommene Zwischenschritte bei der
Kristallisation zeitlich auflösen zu können.
Die meisten in der Literatur diskutierten experimentellen Befunde basieren auf
Beugungsexperimenten. Die Interpretationen werden jedoch oft spekulativ, da geringe
Unterschiede in der Elektronendichte zwischen der verknäulten Schmelze und den
vorgeordneten Bereichen mit wenig Ordnung schwer aufzulösen sind. Im Gegensatz dazu
prüfen Relaxationsexperimente nicht die Strukturunterschiede, sondern
Beweglichkeitsunterschiede. Während der Kristallisation wird das kristallisierende
Zusammenfassung . ii
Material vom flüssigen in den festen Zustand überführt. Demzufolge werden dabei für
die Flüssigkeit typische Bewegungen eingefroren und tragen nicht weiter zum Messsignal
bei. Für die angenommen vorgeordneten Bereiche werden aufgrund der
Konformationsänderungen ebenfalls Änderungen in der Beweglichkeit erwartet.
In der vorliegenden Arbeit werden zwei verschiedenartige Experimente vorgestellt. In
den so genannten Scanexperimenten werden die Verläufe von Realteil (ε′) und
Imaginärteil (ε′′) der dielektrischen Permittivität beim Kristallisieren und Schmelzen
beim Kühlen bzw. Heizen untersucht. Des Weiteren werden isotherme
Kristallisationsexperimente vorgestellt, die eine detaillierte, zeitaufgelöste Untersuchung
des Kristallisationsprozesses bei verschiedenen Temperaturen ermöglichen.
Sowohl bei den Scanexperimenten, als auch bei den isothermen Experimenten
zeigen sich im Verlauf des Realteils der dielektrischen Permittivität bei niedrigen
Frequenzen starke Änderungen lange bevor Kristallinität mittels DSC nachgewiesen
werden kann. Diese experimentellen Befunde können im Rahmen eines Modells, bei dem
die Entstehung vorgeordneter Strukturen angenommen wird, erklärt werden. Da Beiträge
von typischen Relaxationsprozessen ausgeschlossen werden können, können die Verläufe
von ε′ vor der eigentlichen Kristallbildung als Grenzflächenpolaristionsprozess
interpretiert werden (Maxwell- Wagner- Sillars- Prozess oder Elektrodenpolarisation).
Die Abnahme von großräumigen Ladungsträgerbewegungen (Abnahme der
Elektrodenpolarisation) lange bevor Kristallinität mittels DSC nachweisbar ist unterstützt
das Modell von großräumigen vorgeordneten Bereichen. Die gleichen Strukturen
induzieren einen zusätzlichen Maxwell- Wagner- Sillars- Prozess, der in bestimmten
Frequenzbereichen einen frühen Anstieg von ε′ zur Folge hat. Simultane dielektrische
und Röntgenbeugungsuntersuchungen am ESRF bestätigen diese Ergebnisse und
unterstützen Vorstellungen von vorgeordneten Srukturen die sich im weiteren
Kristallisationsprozess zu Kristallinen Bereichen stablisieren.
Contents . iii
Contents
Page NO
1 Introduction
1
1.1 Introduction 1
1.2 Literature survey and problems description 2
1.3 Aim of work
6
2 Theoretical Considerations 7
2.1 Introduction to polymer crystallization 7
2.2 Dielectric relaxation spectroscopy 9
2.2.1 Relaxation phenomena 11
2.2.2 Polarization mechanism 11
2.2.2.1 Maxwell Wagner Sillars polarization
12
3 Materials and Methods 14
3.1 Experimental Techniques 14
3.1.1 Dielectric spectroscopy technique 14
3.1.1.1 Samples preparation for dielectric measurements 16
3.1.1.2 The dielectric measurement 17
3.1.1.3 Dielectric data analysis 19
3.1.2 Differential scanning calorimetry technique 20
3.1.3 Simultaneous SAXS/ DRS Techniques 21
3.1.3.1 New sample Cell 21
3.1.3.2 Simultaneous SAXS/DRS measurements
21
3.2 Materials 23
3.2.1 Poly (ε-caprolactone) 23
3.2.2 Polyoxymethylene 24
3.2.3 Isotactic polypropylene 24
3.2.4 Poly (ethylene terephthalate) 25
Contents . iv
3.2.5 Polyethylene 25
3.2.6 Isotactic Polystyrene 25
3.3 Performance Test 26
3.4 Temperature calibration of dielectric spectroscopy cell
27
4. Results 30
4.1 Dielectric spectroscopy measurements during temperature
scans.
30
4.1.1 Poly (ε- caprolactone) 30
4.1.1.1 Contribution from charge carriers polarizations to the dielectric
permittivity
33
4.1.2 Polyoxymethylene 34
4.1.3 isotactic Polypropylene 35
4.1.4 Poly (ethylene terephthalate) 37
4.1.5 Polyethylene 38
4.2 Dielectric spectroscopy measurements from isothermal
experiments
39
4.2.1 Poly (ε- caprolactone) 39
4.2.1.1 Arrhenius diagram and α, β and γ modes in PCL 42
4.2.1.2 Frequency and time dependence of ε′ and ε′′ during
isothermal crystallization
43
4.2.1.3 Reduction of electrode polarization 46
4.2.1.4 Time dependence Comparison of the permittivity with
the non-crystalline fraction obtained from DSC experiment
49
4.2.1.5 Temperature dependence of the peak observed in ε′ 52
4.2.1.6 Simultaneous SAXS/ DRS experiment
54
4.2.2 Isothermal measurements for polyoxymethylene 57
4.2.2.1 Frequency and time dependence of ε′ and ε′′ during isothermal
crystallization of POM
57
Contents . v
4.2.2.2 Time dependence comparison of the permittivity with the
non-crystalline fraction obtained from DSC experiment
59
4.2.3 Isothermal measurements for isotactic polypropylene 61
4.2.3.1 Frequency and time dependence of ε′ and ε′′ during isothermal
crystallization of iPP
61
4.2.3.2 Temperature dependence of the peak observed in ε′ 62
4.2.3.3 Time dependence comparison of ε′, tan δ and χc at crystallization of iPP from different techniques
64
4.2.4 Isothermal measurements for Poly (ethylene terephthalate) 65
4.2.4.1 Frequency and time dependence of ε′ and ε′′ during
isothermal crystallization.
66
4.2.5 Isothermal measurements for isotactic polystyrene 67
4.2.5.1 Frequency and time dependence of ε′ and ε′′ during
isothermal crystallization
67
5. Discussion 69
5.1 The pre-ordered structure formed at crystallization of PCL 69
5.1.1 Discussion of pre-ordered structure by dielectric relaxation
experiments
69
5.1.2 Discussion of pre -ordered structure by simultaneous SAXS/
DRS experiments
74
5.2 Discussion of the dielectric relaxation experiments for isotactic
polypropylene, poly (ethylene terephthalate), polyethylene and
isotactic polystyrene
74
6. Conclusion 76
7. Summary 77
8. References 79
Appendix
Introduction . 1
1. Introduction 1.1 Introduction A fundamental understanding of the molecular relaxation processes of amorphous
polymers upon crystallization has been the subject of many studies [1-4]. The importance
of these studies arises from the fact that the physical properties of polymers alter as
temperature increases through the glass transition. Young’s modulus decreases, whereas
heat capacity and the thermal- expansion coefficient all increase as temperature increases
above glass- transition temperature (Tg). The decrease in density (increase in free
volume) at Tg causes the optical index of refraction to decrease. Crystallinity is often
introduced to provide thermal stability and minimize these property changes experienced
at Tg. In bulk polymers, introducing crystallinity strongly affects the physical properties
of the amorphous phase and, consequently, the relaxation behavior occurring at Tg [5-12].
For example, in poly (vinylidene fluoride) and poly (ethylene terephthalate) (PET), the
dielectric loss spectra broadened with increasing crystallinity [13-16]. This broadening of
loss curves was attributed to the restrictions to the mobility of polymer chains in the
amorphous layer because of the existence of crystalline layers. Many polymers are able to
form nano - crystalline structures. In contrary to low molecular weight substances, the
crystallization process always ends up with a semi crystalline morphology. This is the
result of the complicated chain structure. Nevertheless, the molecular processes during
the formation of the semi crystalline morphology are not completely understood. Even
the early stages of polymer crystallization are discussed in the literature controversially.
1.2 Literature survey and problems description
Crystallization in polymer systems which transfers the entangled melt into a semi-
crystalline state is a process of primary importance and has been studied since polymer
crystals were first mentioned by Staudinger in 1927 [17]. Over the years, the whole
spectra of available experimental methods were used to study the process of morphology
development in polymers. Since the beginning of the 60th, the Hoffmann-Lauritzen theory
and several modifications and extensions of it dominate the discussion in the scientific
community [18-20]. These theories assume the transition from the entangled polymer
Introduction . 2
melt to the crystal as a single step which occurs directly at the growth front. But there is
increasing evidence that these theories do not describe the process correctly. Especially
the observation of ordered structures at very early times forced the development of new
theories and models [21-29]. All these theories assume a multi step process from the
entangled melt via different metastable structures to the final polymer crystal. Often only
the first or initiating step, as the key step for the whole process, is discussed and
described. This step is assumed as spinodal decomposition [30-40] or as nucleation
followed by growth [41, 42].
In 2000, Strobl [43] introduced a model for polymer crystallization, which covers
the whole process with a few specific steps. These steps are considered to be universal for
polymer crystallization. Because of the great importance of these steps in our work,
particularly of the first step, related the early stages of crystallization, Strobl’s model for
one growing lamella is mentioned in details as shown in figure (1.1). The first step is
assumed to be the formation of a metastable pre-ordered structure in the super cooled
melt (its nature is mentioned in section 2.1). This structure should be in thermodynamic
equilibrium with the surrounding melt and should undergo different annealing stages to a
stable lamella step by step. As the last step a stabilization process of the lamellae is
assumed. Evidence for that comes from scattering experiments [44] and techniques
probing properties like shear modulus or melting temperature rather than morphology
directly [45].
Figure 1.1: Strobl’s model for polymer crystallization
Introduction . 3
In parallel to the development of new theories and models, specific experiments were
performed to demonstrate the existence of pre-ordered structures at the beginning of the
crystallization process. Most of the experimental techniques used are scattering
techniques [24, 28, 46-48] which test small density differences between the assumed
precursors of the crystals and the surrounding melt. Because of the low density contrast,
most of these studies have been limited to the observation of crystal growth processes and
little information exists about how nucleation proceeds from the disordered amorphous
state. This means there remain a lot of open questions regarding the interpretation of the
data. Interpretation is only possible if a certain structural model is assumed. Therefore, up
to now it was not possible to prove explicitly the existence of pre-ordered structures. Also
with AFM, which allows following the growth of a lamella in situ [49], it seems to be
difficult to resolve the development of the first ordered structures because of low
contrast.
Evidence for pre-ordered structures comes from time resolved FT-IR
spectroscopy, which does not require three-dimensional order. These spectra are
determined by regular packing of the folded chain into the crystal lattice as well as by
intermolecular conformational changes. For example, Li et al. [50] report a time shift
between the appearance of the characteristic peaks for first conformational changes and
of the characteristic FT-IR peaks of the crystalline phase in poly (bisphenol A-co-decane
ether). Nevertheless, the assumption of the formation of a mesomorphic structure as the
first step in Strobl's model is yet not experimentally justified. This is mainly due to
insignificant contrast for scattering and microscopic techniques commonly used to study
early stages of polymer crystallization.
In contrary to scattering and microscopic methods, where information is gained
from the small contrast between the pre-ordered structure and the surrounding super
cooled melt, relaxation experiments are probing motions in the sample. During
crystallization, material is transformed from the liquid to the solid state. Consequently,
motions (fluctuations) typical for a liquid become impossible and do not longer
contribute to the measured signal. Quantities like heat capacity, shear modulus or
dielectric permittivity therefore allow studying crystallization. The occurrence of
cooperative motions (cooperatively rearranging regions (CRR), dynamic heterogeneities)
Introduction . 4
which are the reason for the liquid like heat capacity, for example, is probed by relaxation
experiments [51, 52]. There is no need for any density contrast to observe differences
regarding mobility within the amorphous phase of a semi crystalline polymer by means
of relaxation measurements. This allows as an example a more detailed description of the
semi-crystalline morphology within a so called "three phase model". It is possible to
distinguish between the mobile amorphous, the rigid amorphous and the crystalline
fraction and to follow their development during crystallization [53]. Because no density
contrast is needed, relaxation experiments are sensitive tools to study early stages of
polymer crystallization too. Winter et al. [54] performed shear spectroscopy experiments
and showed for different polymers, that one can treat early stages of polymer
crystallization like a gel formation. They discussed the formation of a network of
mechanical force propagation paths as the first step of the crystallization process prior to
crystal formation. Unfortunately, the relation between mechanical properties and sample
morphology is very complex because of unknown details of force propagation in semi
crystalline polymers [55].
For dielectric experiments the situation is different. Here the fluctuations of
dipoles and charge carriers are tested only. In contrary to mechanical experiments, no
network for perturbation propagation is necessary. The propagation of the electrical field
is easy to realize, therefore the possible frequency range for the perturbation is much
broader than for other dynamic experiments. With a combination of different devices one
can cover a frequency range between 10-6 to 1012 Hz and higher [52]. For the
investigation of relaxation processes and conductivity, dielectric spectroscopy is a
frequently used method. To detect changes in morphology often the so called α-relaxation
(dynamic glass transition) is followed in time or temperature [56-66]. It is assumed that,
first of all, the step in the real part of dielectric permittivity is directly related to the
fraction of material taking part in the relaxation process studied. The intensity of the α-
relaxation (glass transition) is known to depend on the liquid fraction only. Therefore the
transformation of liquid material into crystalline and rigid amorphous can be followed
[67, 68]. Additional information is available from the shift in relaxation time and the
shape of the loss peak [68, 69]. On the other hand, the intensity of local relaxation
processes like the ß-relaxation in PET depends on the non-crystalline fraction only and
Introduction . 5
allows following crystallinity directly [68]. Often not only changes in the relaxation
strength but also changes in the relaxation time distribution are observed. The relaxation
peak in the imaginary part of dielectric permittivity shifts during crystallization of
homopolymers generally to lower frequencies and becomes broader [60, 68, 70].
Extensive studies in this field were performed by Ezquerra et al. who also combined
dielectric spectroscopy with X-ray scattering for simultaneous measurements [58, 59,
67]. But due to the complex behavior of the alpha relaxation and the crystallization
process it is difficult to interpret the data.
The cooperative motions representative for the liquid behavior of the melt and
detected by the α -relaxation occur on length scales of some nanometers [51, 52]. As long
as pre-ordering does not yield significant changes in mobility on such length scales, there
is basically no way to obtain information on pre- ordering from dielectric spectroscopy in
the α-relaxation range. Consequently, only a few dielectric studies devoted to the early
stages of polymer crystallization are available in the literature [57, 64]. The information
available so far does not give conclusive information about possible pre-ordering in
polymers. Another unfavorable prerequisite for such type of experiments is the necessity
to crystallize the sample at temperatures, where the alpha process can be followed in the
frequency window of the dielectric device. This is usually possible at temperatures just
above the thermal glass transition. For polymers, one is therefore often limited to
investigate cold crystallization. Cooling the sample through the maximum of the growth
rate without forming crystals is often not an easy task for fast crystallizing polymers.
Therefore, sample variety is limited. There is another important disadvantage of cold
crystallization, so that if the cooling through the maximum of crystallization rate is
possible without detectable crystallization, the influence of the cooling process on
nucleation and the following crystallization process is well known but not completely
understood. Aging below the glass transition temperature of the amorphous polymer may
influence crystallization [71], too. Consequently, for investigation of the early stages of
polymer crystallization, one has to take into account possible influences due to cooling
and storage. Crystallizing from the glassy state generally yields smaller crystals and a
larger number of spherulites, etc. Therefore, it seems to be better to study crystallization
at high temperatures near the melting temperature. Then the initial state of the sample, the
Introduction . 6
entangled equilibrated melt, is the same for all experiments and will not significantly
change at cooling from the melt to the crystallization temperature. While at cold
crystallization, the dielectric response is mainly determined by the α-relaxation at higher
temperatures, charge carrier relaxations and conductivity may dominate the signal.
1.3 Aim of work This work aims to investigate the dielectric processes which are affected by
crystallization, in particular at the early stages of crystallization from the melt. At first,
we were planning to study all possible processes (dipole relaxation and charge carrier
processes) taking place in the sample. However, during the work we found out that dipole
relaxation processes were only affected by the main crystallization processes. On the
other hand, charge carriers processes (Maxwell Wagner Sillars or electrode polarization)
were significantly influenced by the early stages of polymer crystallization which we are
interested in. Accordingly, explanation and interpretation of data is completely based on
the behavior of charge carrier relaxations.
The study was applied on poly (ε – caprolactone) (PCL) as a model system. In
addition, other semi-crystalline polymers were briefly studied namely, POM, iPP, PE,
PET, iPS. Based on above, dielectric spectroscopy (DS) technique was used in this study,
which is well known in the field of material physics. In addition, differential scanning
calorimetry (DSC) was used to investigate crystallinity, crystallization and melting
temperature of the materials used. Also, a combination between Small- Angle X-ray
Scattering (SAXS) and DS technique was used to get simultaneously information about
the structure and dynamics of the ordered and disordered regions in polymers.
Theoretical considerations . 7
2. Theoretical considerations
Since we are interested in studying the crystallization process taking place in polymeric
materials by means of the dielectric spectroscopy, a short introduction to polymer and its
crystallization was recommended. Then, some interesting concepts related to dielectric
spectroscopy are also important to mention.
2.1 Introduction to polymer crystallization Polymers are large class of materials and they consist of a large number of small
molecules called “monomers” that can be linked together to form a very long chain. The
word macromolecule comes from the origin 'makros', which mean large and 'molecula'
which mean small mass. If the long-chains pack regularly, side-by-side, they tend to form
crystalline polymers. In addition, a real polymeric solid is usually a mixture of crystalline
and amorphous phases called semi-crystalline polymer (i.e. its physical structure is
heterogeneous); see figure (2.1c). Semi-crystalline polymers are not in thermodynamic
equilibrium. Crystalline and non-crystalline regions (amorphous) must therefore be
interconnected: any single macromolecule passes through both phases. The two phases of
semi-crystalline polymers are therefore not separate entities; they cannot be separated by
physical means.
Polymers, in which the molecules and segments are completely disordered in the
solid state, they are said to be amorphous. This are generally found in a random coil
conformation and have a disordered chain structure. In contrast, for that are completely
ordered, they are said to be crystalline. The process at which the structural material
transformed from the amorphous to crystalline state is defined as the crystallization. For
most polymers, the crystallization can take place in the temperature range between their
own glass transition and melting temperatures.
Long chain polymer molecules have topological constraints that don’t allow them
to crystallize when cooled from the liquid (melt) in the same way as more simple
molecules. So, in crystalline ceramics or metals, a crystalline solid comprises repeating
unit cells that contain each of the component atoms in the material. Each unit cell is
Theoretical considerations . 8
composed of one or more molecular units. In a polymer this is not possible; the molecules
are chains containing potentially millions of formula units. Therefore, crystallization in
polymer systems from the melt is a complex process. This complication can be somehow
demonstrated as shown in figure (2.1).
For the polymer melt, the polymer chains overlap and look like spaghetti as
shown in figure (2.1a). Therefore, most polymer chains don’t stretch out fully as shown
in figure (2.1b). Instead, they fold back on themselves after going straight for a short
distance and form the lamellar crystallites; see the crystalline phase in figure (2.1c).
Structure parameters like the volume fraction of the crystallites or their thickness are
kinetically controlled and change with the crystallization conditions. Usually crystallites
get thicker when the temperature of crystallization is increased. This is always
accompanied by a decrease in the rate of crystallization described by an exponential law.
Mobile amorphous(melt)
(b)
(a)
Different annealing stages
Mesomorphic structure
The lamellae crystalline structure
(d)
Stretching out
(c)
Amorphous phase
Amorphous phase
Crystalline phase
Mobile amorphous(melt)
(b)
(a)
Different annealing stages
Mesomorphic structure
The lamellae crystalline structure
(d)
Stretching out
(c)
Amorphous phase
Amorphous phase
Crystalline phase
(c)
Amorphous phase
Amorphous phase
Crystalline phase
Figure 2.1: Polymer chains in the melt (a) Stretching of chains (b), formation of
crystalline lamella (c) and formation of pre-ordered structure (d).
The transformation from the polymer melt into the final lamellar crystallite does
not take place directly in one step process, but in fact, it always starts with a nucleation
Theoretical considerations . 9
step (see the mesomorphic layer in figure 2.1d) at the very beginning of crystallization
which is then followed by a growth of the crystallite, it occurs in two dimensions often in
a continuous manner, as a cooperative process taking place in the whole layer at once. As
seen in figure (2.1d), stretching of polymers chains in the mesomorphic layer is not
perfect, i.e. the chains, although basically helical, include many conformational defects.
The density in the layer is slightly above that of the isotropic melt, away from the value
in the crystal. There exists a minimum thickness for the layer in order to be stable in the
surrounding melt, and it is found at the boundary, i.e. the lateral surfaces in contact with
the melt. The thickening process requires a continuous rearrangement of the chain
sequences in the zone composed of folds and loops near to the layer surfaces. With
increasing layer thickness, its inner immobility decreases.
The mobile dipoles which are freely and randomly distributed in the polymer melt
changes with crystallinity. Consequently, the dielectric permittivity which is related to
polarization of the dipoles, decreases with increasing crystallinity. Also, at the early
stages of polymer crystallization we are interested in, mobility of the polymer chains
decrease even if the crystalline structure was not definitely formed. Therefore, some
concepts related to dielectric permittivity and polarization should be taken into our
consideration.
2.2 Dielectric relaxation spectroscopy The dielectric material is a substance that resists the electric field from passing through
it, in addition to its ability to support an electrostatic field while dissipating minimal
energy in the form of heat. Most the dielectric materials are solid such as ceramic, mica,
glass, plastics, and the oxides of various metals. The degree to which a medium resists
the flow of electric charge, defined as the ratio of the electric displacement to the electric
field strength. It is more common to use the relative dielectric permittivity. In addition,
dielectric permittivity is given in literature with different names as dielectric constant,
real part of dielectric permittivity and storage energy. For our study we used expression
real part of dielectric permittivity.
Dielectric Relaxation Spectroscopy (DRS) probes the interaction of a
macroscopic sample with a time-dependent electric field. The resulting polarization
Theoretical considerations . 10
either expressed by the frequency-dependent complex permittivityε * and conductivity or
as an impedance spectrum, characterizes amplitude and timescale (via the relaxation time
τ) of the charge-density fluctuations within the sample. Such fluctuations generally arise
from the reorientation of the permanent dipole moments of individual molecules or from
the rotation of dipolar moieties in flexible molecules, like polymers. Other possible
mechanisms include the transport of ions or the appearance of interfacial charges in
heterogeneous systems. The timescale of these fluctuations depends on the sample and on
the relevant relaxation mechanism. Relaxation times range from several picoseconds in
low-viscosity liquids to hours in glasses, probably marking DRS as the technique with the
most extensive coverage of dynamical processes.
From studying the interaction of electromagnetic radiation with matter, the complex
dielectric permittivity ε* can be obtained from Maxwell’s equations as:
ED
oεε =*
(2.1)
Where 0ε is the dielectric permittivity of vacuum ( 0ε = 8.854 × 10-12 F m-1) and
D is the dielectric displacement. ε* is frequency (or time) dependent if time dependent
process occurs within the sample. In general, time dependent processes within a material
lead to a phase shift between the external electric field E (t) and the resulting dielectric
displacement D (t). Beside the time dependence of ε*, it also depends on temperature.
Moreover, ε * (ω,T) in its dependence of frequency and temperature can be split off into
real part ε′ (ω,T) and imaginary part ε′′ (ω,T) of the dielectric permittivity [72], see
equation (2.2). Both experimental magnitudes are available by capacity measurement of a
condenser filled with sample.
( ) ( ) ( )TiTT ,,, ωεωεωε ′′−′=∗ (2.2)
Where ω is the angular frequency with ω = fπ2 , i = 1−
This function describes - within the regime of linear response – the interaction of
electromagnetic fields with matter and reflects by that the underling molecular
mechanisms.
Theoretical considerations . 11
2.2.1 Relaxation Phenomena
Relaxation is a classical phenomena and it is about a process by which the system goes
from non-equilibrium state to equilibrium state. Relaxation processes have different
names according to their origin thus we have thermal relaxation, dielectric relaxation or
dipole relaxation and structural relaxation.
2.2.2 Polarization mechanism
When an electric field is applied across the faces of a parallel plate capacitor containing a
dielectric, the atomic and molecular charges in the dielectric are displaced from their
equilibrium positions and it is said the material is polarized. However, polarization
mechanism is essentially a statistical effect and therefore, it is not possible to observe the
orientation of the individual moments. For the present work, when an electric field in the
range of 10-2 to 107 Hz is applied to molecules of the samples used, the dielectric
dispersion and absorption phenomena that occur in this vast frequency range are due to:
(i) Dipole relaxation arising from the reorientation motions of molecular dipoles
(ii) The separation of charges at interfaces which gives rise to an additional
contribution to the polarization. This is always accompanied by an increase in the
dielectric permittivity at low frequencies.
Charge carriers can be blocked at the internal dielectric boundary layers
(Maxwell/ Wagner/Sillars-polarization) on a mesoscopic scale (see figure 2.2), and / or
at the external electrodes contacting the sample (electrode polarization) on a
macroscopic scale (some details were mentioned in section 4.2.1.3). Additionally, in case
of electrode polarization, the charge carriers may be separated over a considerable
distance and therefore, its contribution to ε′′ can be by orders of magnitude larger than
the dielectric response due to molecular fluctuations. For the proposed work here,
interpretation and explanation of the most important results related to the early stages of
polymer crystallization based on the behavior of Maxwell/ Wagner/Sillars-polarization.
Therefore, some details should be given for this process.
Theoretical considerations . 12
2.2.2.1 Maxwell/ Wagner/ Sillars (MWS) polarization MWS polarization is due the building-up of charges at the interface between components
in heterogeneous systems. This polarization is known as interfacial, space charge or
MWS [73, 74]. MWS polarization processes are investigated for inhomogeneous
materials like biological materials, phase separated polymers, blends, crystalline or liquid
crystalline polymers.
LD
++++++ ++ +
+ + + + + + + + + +
- - - - - - - - - -
+
-~
LD
D1Sample
-------+ - ε2 , σr2
ε1 , σr1
- --
+
D2
LD
++++++ ++ +
+ + + + + + + + + +
- - - - - - - - - -
+
-~
LD
D1Sample
-------+ - ε2 , σr2
ε1 , σr1
- ---
++
D2
(a)
G1= σ1 A/D1
G2 = σ2 A/D2
C1 = ε1 A/D1
C2 = ε2 A/D2
(b)
Figure 2.2: (a) two dielectric layers in series. ( 1ε , 2ε ) and ( 1rσ , 2rσ ) are the
corresponding dielectric permittivities and conductivities. (b) Equivalent circuit where A
is the diameter of the electrodes. (D1, D2)) and (G1, G2) are the thickness and
conductance of the two layers.
MWS-model and its equivalent circuit which are sketched in figure (2.2) is a very
simple model used to describe an inhomogeneous structure by considering a double layer
Theoretical considerations . 13
arrangement where each layer is characterized by its permittivity iε and its
conductivity riσ . Accordingly, the pre-ordered structure and its surrounding melt can be
represented also as a double layer. The first layer represents the melt (amorphous) and is
characterized by its permittivity 1ε and conductivity 1rσ . While the second layer formed at
the very beginning of crystallization is characterized by its permittivity 2ε and
conductivity 2rσ .
The signs represented by (-) and (+) demonstrate how charge carriers can be
blocked by the additional internal surfaces formed at the early stages of crystallization. If
it is considered the thickness of the first and the second layer is the same, then D1 = D2,
the relaxation time MWτ of the interfacial polarization is given by:
21
21
rroMW σσ
εεετ++
= (2.3)
From equation (2.3) the relaxation time scales inversely proportional to the conductivity
of the system. This quite simple example demonstrates that the dielectric response of an
inhomogeneous medium can be frequency dependent although none of the individual
components has frequency dependent dielectric properties. The frequency dependence
can be similar to an orientational polarization.
Materials and methods . 14
3. Materials and methods
3.1 Experimental techniques In order to get complete information about the crystallization process taking place in
polymeric materials, three different important techniques were used namely:
1- Dielectric relaxation spectroscopy (DRS) technique:
DRS are powerful and experimental tools which have dramatically developed in the last
two decades. It covers the spectral range of frequencies from 10-6 to 1012 Hz and
therefore enables all researchers to investigate the relaxation processes taking place in the
material. Accordingly, it was chosen as one of the most important techniques used in this
study because of its sensitivity to any weak changes in structure and dynamics.
2- Differential scanning calorimetry (DSC) technique:
Morphologies of polymer samples under studying were investigated by DSC. Therefore,
it enables us to investigate crystallinity, crystallization temperature and melting
temperature.
3- Simultaneous SAXS / DRS technique:
A combination between a small angle X-ray scattering and dielectric spectroscopy
technique was done to provide us with simultaneous information about morphologies and
dynamics of poly (ε-caprolactone) (PCL).
3.1.1 Dielectric Spectroscopy technique
In modern dielectric spectrometers, the complete measurement procedure including
control of devices and evaluation of the data is automatically performed by computer
control. Nevertheless, the quality and the accuracy of the results strongly depend on the
proper preparation of the sample. In the present study, two dielectric spectrometers were
used for measuring the impedance and complex dielectric permittivity of materials,
namely:
Broadband dielectric spectrometer (BDS 4000): it is capable of measuring in the
frequency range (10-2 Hz-107 Hz) and the temperature range (113-773 K). In the present
study, most of the dielectric relaxation experiments were performed by this device. The
device with its supported liquid nitrogen cryostat and cell was schematically drawn as
Materials and methods . 15
shown in figure (3.1). The time for one frequency sweep was about 30 minutes. As seen
in this figure, the system used in the measuring dielectric data is Alpha dielectric material
analyzer which is connected directly to the measuring cell.
GENV1V2
QUATRO
CH.1
CH.3
CH.4
CH.2
A1A2A3A4A5A6A7
A8CRYOSYSTEM
GAS-HEATERA
V
FUSE
DEWAR
FUSE
MAINS
LOAD
01
MAINS
ON/OFF
01
ON/OFF
VACUMEmbr
BROADBAND DIELECTRIC SPECTROMETER
To Alpha activesample cell connector
on the mainframerear
Liquid Nitrogen Evaporator
Dewar
Dewar Temperature Sensor
GEN V1 V2
PT100
Sample Temp. Sensor
Cryostat BDS1100
Sample
PressureSensor
Gas Temp. Sensor
Active sample Cell Of BDC
Gas Heater
Vaporizing Module BDS 1320
High Resol. Dielec. Analyzer
GENV1V2
QUATRO
CH.1
CH.3
CH.4
CH.2
A1A2A3A4A5A6A7
A8CRYOSYSTEM
GAS-HEATERA
V
FUSE
DEWAR
FUSE
MAINS
LOAD
01
011
MAINS
ON/OFF
011
ON/OFF
VACUMEmbr
BROADBAND DIELECTRIC SPECTROMETER
To Alpha activesample cell connector
on the mainframerear
Liquid Nitrogen Evaporator
Dewar
Dewar Temperature Sensor
GEN V1 V2
PT100
Sample Temp. Sensor
Cryostat BDS1100
Sample
PressureSensor
Gas Temp. Sensor
Active sample Cell Of BDC
Gas Heater
Vaporizing Module BDS 1320
High Resol. Dielec. Analyzer
Figure 3.1: Broadband Dielectric Spectrometer used in measuring and connected to the
Dewar and Sample Cell BDS 1200 (or Active Sample Cell).
Materials and methods . 16
Hewlett-Packard Impedance analyzer (HP 4284A): it measures in a frequency regime
between 20 and 106 Hz. The time for one frequency sweep was about 1 minute.
In addition, both devices are equipped with a Quatro cryosystem for temperature control
and WinDETA software version 4.1 to control the systems. For each single measuring
point, real and imaginary parts of dielectric permittivity as well as time, temperature and
frequency were recorded. The controlling and measuring software were provided by
Novocontrol, GmbH, Germany. The measuring method is described in Appendix [1].
3.1.1.1 Samples preparation for dielectric measurements
For dielectric measurements, the sample material should not be prepared directly between
the contacts of the sample cell. Instead, the sample should be prepared as thin film
between two-copper disk shaped electrodes, see figure 3.2 (b). The studied materials
were first melted above the melting temperature on one of the electrodes then the spacers
were added to the sample, then the other electrode was added and then the whole system
(i.e., the sample and the two electrodes) was quenched to room temperature.
Thickness of sample was checked by using special micrometer screw. The obtained
sample thickness is 0.15 mm for thin samples while thick samples were prepared between
1 and 5 mm. Spacers were added to the samples in order to control sample thickness
during measurements in the melt. Additionally, the spacers used should have high
melting temperatures compared to samples under investigation, such as glass or silica.
Poly (ether ether ketone) (PEEK) is a polymer has a high melting temperature (367 °C)
and therefore it would also be used as spacer for polymers with low melting temperatures
(PCL, PE).
For thin samples having ionic conductivity, mobile ions can migrate within the
sample material, hence giving rise to potential differences at the electrode surfaces. As a
result, the dielectric relaxation process associated to electrode polarization can be
obtained. In order to investigate the influence of possible relaxation processes taking
place in the sample by crystallization, the contribution from electrode polarization to the
measuring signal was firstly reduced. This can be done by separating the measured
sample from the metal electrodes with thin layer of plastic such Teflon, Kapton or Mica.
Thickness of the separating materials used was approximately 0.01 mm (see Fig. 3.2a).
Materials and methods . 17
Also, thick sample with approximately 5 mm in thicknesses was used to reduce the
electrode polarization (see Fig. 3.2b). Although the two methods were experimentally
performed, results of the later one were more successful in the present study (see details
in section 4.2.1.3).
External electrodes
Glass spacers
Mica
PCL sample
External electrodes
Glass spacers
Mica
PCL sample
(a)
External electrodes
Screws
Glass spacers
Teflon
PCL Sample
External electrodes
Screws
Glass spacers
Teflon
PCL Sample
(b)
Figure 3.2: (a) Separating the sample from metal electrodes by using Mica.
(b) Preparation of the dielectric thick sample used through the measurements.
3.1.1.2 The dielectric measurement
When an electric field is applied to a condenser filled with a material under test, the
capacitance C* of the condenser increases due to polarization of the sample. The complex
dielectric permittivity and its relation with the capacitance can be given as:
Materials and methods . 18
( ) ( ) ( ) ( )oC
Cωειω,Τεωε ω∗∗ =′′−′= (3.1)
Where Co is the capacitance of the empty condenser. Using a sinusoidal electric field
E*(ω) = Eo exp (iωt) and at field strengths within linear response, the complex dielectric
permittivity can be derived by measuring the complex impedance Z*(ω) of the sample.
( ) ( )( ) ( ) oo CZiEi
Jωεωωωωε
ω∗∗
∗∗ ==
1 (3.2)
Where J*(ω) is the complex current density. The complex impedance of the sample can
be extracted by using either bridges or analyzers. Heir we presented the extracting by
using the analyzer as shown in figure (3.3).
≈
*sI
*sZ
*1U
*2UR
Vector voltageanalyzer Ch II
Vector voltageanalyzer Ch I
SampleSample capacitor
Generator
≈
*sI
*sZ
*1U
*2UR
Vector voltageanalyzer Ch II
Vector voltageanalyzer Ch I
SampleSample capacitor
Generator
Figure 3.3: Scheme of a Fourier correlation analyzer
As seen in the figure that a sine wave voltage U1 (t) with frequency ω/2π is applied
to the sample by a generator, covering the frequency range from 10-2 Hz to 107 Hz. The
resistor R converts the sample current Is(t) into a voltage U2 (t). U1(t) and U2 (t) are
analyzed with respect to the amplitudes and phases of their harmonic Fourier base waves
Materials and methods . 19
)(*1 ωU and by two phase sensitive sine wave correlators. Then, the complex sample
impedance is calculated from the measured data by:
)(*2 ωU
*sZ
( ) ( )( )
( )( ) ⎟
⎟⎠
⎞⎜⎜⎝
⎛−==
∗
∗
∗
∗∗ 1
2
1
ω
ω
ω
ω
UU
RI
UωZ
s
ss
(3.3)
Where and are the sample voltage and current. )(ω∗sU )(ω∗
sI
3.1.1.3 Dielectric data analysis
The dielectric relaxation spectra were fitted by using model Havriliak and Negami
equation [75]. This was only done for PCL to check the influence of the relaxation
processes α, β and γ. This not necessarily means that we are interested in study the dipole
relaxations taking place in the sample, but only to study the charge carrier processes
which are affected by crystallization, in particular at the early stages of polymer
crystallization.
The measuring system gives the relation between frequency (f), the real (ε′) and
the imaginary (ε′′) parts of the complex dielectric permittivity and the dielectric loss
tangent (tanδ). The data is drawn on ORIGIN software which is given by the Microcal
Company. Then, ε′′ curves were fitted by the same software using the fitting equation “3
processes Havriliak-Negami equation”. In addition, a term of the conductivity
contribution was added to the model to account for the dc- conductivity. The fitting
procedure was done on the basis of the (Marquardt fitting procedures). The fitted
equation was of the form:
( )( )[ ] o
s
n
i i
i ii
ωii εω
σ
ωτ
εεε βα+
+
Δ+= ∑
=∞
∗
1 1 (3.4)
It is clear from equation (3.4) that for each relaxation process, separated the HN-
evaluation provides four characteristic parameters as follows:
Materials and methods . 20
The relaxation time: iτ determines the position of each process in the time-or
frequency – scale.
The dielectric relaxation strength: iεΔ corresponds to the product of the number
density of dipoles of reoriented units with its mean effective dipolar moment. It means
the step in ε′ or, equivalently, the area below ε′′ peak.
Shape parameters: iα and iβ are shape parameters of the relaxation process, which
represent the distribution of the relaxation times with the meanings: iα is the width of the
relaxation process (width of the distribution of relaxation times) and iβ the asymmetry
of this process.
Conductivity term: o
sεωσ this term is related to dc-conductivity.
3.1.2 Differential scanning calorimeter measurements DSC is commonly used to measure specific heats, heats of fusion and enthalpic changes
associated with physical and chemical transitions. Therefore, melting and crystallization
enthalpies were measured for our samples. Moreover, DSC is used to study and
characterize many materials such as adhesives, coals, foods, glasses, metals, rubbers,
semiconductors, polymers and so on. Accordingly, DSC scan experiments were
performed at a rate of 1 K min-1 on cooling and heating with a Perkin - Elmer DSC 6.
Samples of 2 mg were placed without pan on a thin aluminum foil of about 2 mg at the
sensor to reduce thermal lag as much as possible. Crystallinity as function of
crystallization time was obtained from DSC scan experiments with heating rate 1 K min-1
utilizing a Perkin-Elmer Pyris 1 DSC and a Setaram DSC 121. PCL sample mass was
about 10 mg in the Perkin Elmer DSC Pyris 1 and 168 mg in the Setaram DSC 121. PCL
sample was heated to the melt at 70 °C after each crystallization step and the heat of
fusion was determined by simple integration of the relatively sharp melting peak. Heat of
fusion of the 100% crystalline PCL was assumed as 153.5 J/g [76]. The measurement was
repeated for other times and other temperatures as needed. PCL is thermally very stable.
No changes after several crystallization-melting cycles were detected.
Materials and methods . 21
3.1.3 Simultaneous SAXS/ DRS experiment Instead of calorimetric experiments which give only an indirect link to the morphology,
the comparison of dielectric experiments with scattering experiments, which give access
to morphology, is more directly. Accordingly, a simultaneous small angle X-ray
scattering (SAXS) and dielectric relaxation spectroscopy (DRS) experiments were
performed to study crystallization of PCL (see figure 3.4).
For different devices, a lot of experimental differences like temperature
distribution, surface material of the sample holder, sample geometry, and sample
preparation may affect the crystallization process and the formation of precursors,
respectively. The comparison between such (comparable experiments) becomes therefore
often doubtful. In order to avoid all these problems, a simultaneous measurement of
different quantities related to dynamics and morphology is favorable. Therefore a new
sample cell [107] was designed, which allows simultaneous X-ray scattering and
dielectric experiments during crystallization.
3.1.3.1 New sample Cell (1)
The sample cell consists of two parallel plates from Teflon (2) in the shape of egg. The
distance between the Teflon plates which determines the sample thickness, between 0 and
2 mm is controlled by three screws. Two brass electrodes of 20 mm in diameter (3) are
incorporated in Teflon plates. The electrodes are provided by two pins (4) for the
Hewlett-Packard Impedance analyzer connection. A hole of 6 mm is made in the center
of each brass plate through which X-ray beam passes into the sample. This hole is
covered by a thin layer of mica window, which does not significantly affect the scattering
signal and prevents sample from flowing out of the electrodes. The solid sample fills the
whole space between Teflon plates and therefore is prepared in the same egg-shape. The
whole cell is placed in a copper block, which consists of two parts (1).
3.1.3.2 Simultaneous SAXS/DRS measurements
As can be seen from figure (3.4), measurements were carried out in an operating room,
while controlling and recording the data were done by two individual computers (10, 11)
located in other room called watching room. This was done for protection from X-ray.
Materials and methods . 22
Video camera (13) is located somewhere inside the operating room and connected to a
monitor present in the watching room, for watching all events inside the operating room.
For dielectric spectroscopy experiment, HP 4284 A (details mentioned before)
was used. For each single measuring point, the real and imaginary parts of dielectric
permittivity as well as time, temperature and frequency were recorded.
For X-ray scattering experiment, time-resolved SAXS experiments used to
study the morphology during crystallization were performed on the DUBBLE beam line
BM26D of the European Synchrotron Radiation Facilities (ESRF), Grenoble- France
[77]. X-rays with a wavelength of 1.0 Å were used. The exposure time for each frame of
the time-resolved measurements was 30 s. SAXS patterns were recorded using a gas
filled multiwire two-dimensional (2D) detector [78] with a sample-to-detector distance of
2.5 m. A vacuum chamber (12) is placed between the sample and SAXS detector to
reduce air scattering and absorption. The experimental data were corrected for detector
response and normalized.
+ V - V
4
7
6
DRS
+ V
53°C
10
PC
1
8
5
12
2 SAXS Operating
Room
Watching Room
Wall
HP - 4284 A Device
X-raySource
4
9
PC
11
13
14 15
Sample
3
Figure 3.4: SAXS / DRS experimental set up on BM26D Double beam line at the ESRF,
Grenoble - France.
Materials and methods . 23
The new sample cell (1) is connected to HP 4284 A (9) and adjusted between the X-ray
beam (7) and the quadrant SAXS detector (8) to be ready for simultaneous
measurements. SAXS experiment was performed by focusing a low divergence X-ray
beam onto a sample and observed a coherent scattering pattern that arises from electron
density inhomogeneities within the sample.
For heating the sample, some heater foils (5) located on the outside of both
copper parts, connected to power supply (15) and fixed by additional copper plates were
used. The temperature of the copper block is measured by a thermoresistor PT100, which
is fixed in a hole at the copper block (6). The temperature of the PT100 was controlled by
an Eurotherm 816 temperature controller (14), which also works in the framework of the
WinDETA software. The sample temperature is assumed to be the same, especially for
the long isothermal experiments. Accordingly, PCL sample was heated to the melt at
70 °C and then held at this temperature for 5 minutes to erase previous history of the
sample. When the sample cooled from the melt to the crystallization temperature at 53 °C
and then SAXS and DRS measurements were applied simultaneously.
3.2 Materials
The selected materials for this study are conventional semi-crystalline polymers like
polyoxymethylene, isotactic polypropylene, poly (ethylene terephthalate), polyethylene
and isotactic polystyrene. These materials provide a wide range of systems with different
mobilities and different mechanisms of relaxation. Especially interesting is the selection
of poly (ε-caprolactone) to be a model system during this study. Most of these materials
were powders except for some of them were granules.
3.2.1 Poly (ε-caprolactone) (PCL)
The linear aliphatic poly (ε-caprolactone) is provided from Fluka with a molecular weight
average of 10,000 g/mol. We took a typical crystalline polymer, PCL as a model system
because its crystalline growth rate is suitable slow at temperatures near the melt and also
its melting temperature is low (around 70 °C). PCL is one of the most important samples
showing no lamella thickening during isothermal crystallization [79, 80]. PCL is a
biodegradable thermoplastic polymer and its chemical structure is:
[(CH2)5 COO)]n
Materials and methods . 24
The material was provided as white granules, so it was first heated to the melting
temperature 70 °C between two electrodes on a hot plate, and then the sample was
quenched to room temperature, to be ready for dielectric measurements.
Because of the thermal stability of PCL, the dielectric spectroscopy measurements were
carried out under dry air atmosphere instead of using liquid nitrogen for a nitrogen
atmosphere.
3.2.2 Polyoxymethylene (POM)
The material was provided as white granules from BASF (Ultraform N2320 003). Its
melting temperature is around 167 °C (CAMPUS DATABASE-BASF). POM has high
chain flexibility and its the chemical structure is:
–[CH2-O]n – Thermal decomposition occurs relatively easily when the POM sample is melted and kept
at high temperature for a long time. This occurs even when an inert gas is flowing around
the sample. To avoid these problems, the sample was melted at 200 °C for 25-30 min as
regarding by Hama et al. [81] and then quenched to room temperature to be ready for
dielectric measurements.
3.2.3 Isotactic polypropylene (iPP)
Vestolen P7000 is provided from DSM Polyolefin. The material was provided as white
granules, so it was first melted at 200 °C between two electrodes on a hot plate and then
the sample was quenched to room temperature to be ready for dielectric measurements.
Polypropylene which used is isotactic. This means that all the methyl groups are on the
same side of the chain; its chemical structure is given as:
Isotactic polypropylene, like polyethylene, belongs to polymers which have a regular
chain structure. Crystallization rate of iPP is fast but its crystallization rate is less than
that for PE.
Materials and methods . 25
3.2.4 Polyethylene terephthalate (PET)
The PET 5445 used in this study is provided – from Kodac Company. This material is a
thermoset polymer, so it has a high melting temperature 290 °C. PET is the most
common thermoplastic polyester, this polymer is often called just "polyester" and its
chemical structure is:
The material was provided as sheets, so it was first heated to the melting temperature at
290 °C between two electrodes on a hot plate and then the sample was quenched to room
temperature to be ready for dielectric measurements. PET was chosen for this study,
because its crystal growth rate of PET is slow enough to allow for investigation of the
real- time behavior during the crystallization process.
3.2.5 Polyethylene (PE)
Lupolen 6011 provided from BASF AG Company. The material was provided as white
granules, so it first was melted at 140 °C between two electrodes on a hot plate and then
the sample was quenched to room temperature to be ready for dielectric measurements.
It has a very simple structure, and its chemical structure is given as:
Polyethylene belongs to polymers which have a regular chain structure; it can easily form
crystalline structure. In addition, it is well known that polyethylene has much faster
crystallization rate than most other polymers. Also, polyethylene is probably the polymer
you see most in daily life.
3.2.6 Isotactic polystyrene (iPS)
Isotactic (90 %) polystyrene powder purchased from Scientific Polymer Products. Sp2
(www.scientificpolymer.com) with a molecular weight of 400,000 g/mol. The chemical
structure of polystyrene is given as:
Materials and methods . 26
The material was provided as powder, so it first heated to the melting temperature at
230 °C between two electrodes on a hot plate and then the sample was quenched to room
temperature to be ready for dielectric measurements.
3.3 Performance test In order to verify the performance and accuracy of the instrument, the reference labeled
(accessory kit BDC- S) should be measured from time to time in order to reproduce the
original plot shown in figure (3.5). To achieve this goal, the reference was mounted
between the two electrodes of the sample cell and then capacitance (Cp) and the loss
tangent (tan δ =ε′′ /ε′ ) were measured as a function of frequency at room temperature.
As a result, two Debye relaxations processes with relaxation frequencies at 4.5 Hz and at
24300 Hz can be obtained.
10-3 10-2 10-1 100 101 102 103 104 105 106 107 1080.00E+000
2.00E-010
4.00E-010
6.00E-010
8.00E-010
1.00E-009
1.20E-009
0.01
0.1
1
CP' i
n F
f in Hz
Cp' [F] Tan δ
Tan δ
Figure 3.5: The performance test experiment of the Broadband Dielectric Spectrometer.
The capacitance Cp′ in Farad and tan δ curves are shown for the reference as a function
of frequency.
Materials and methods . 27
3.4 Temperature calibration of dielectric spectrometer cell The temperature plays an important role for studying polymer crystallization. Therefore
testing the measuring accuracy of the sample cell connected to Broadband Dielectric
spectroscopy (BDS) seems to be more important too. For calibration, four substances
with well defined melting temperatures were used. Ice besides Indium, Tin and Lead with
their melting temperatures were given in Table [3-1].
The calibration method based on determining the temperature difference ∆T
between the real melting points of these materials and their measured values indicating
by the sample cell (see equation 3.5). This can be done by following the dramatic change
in the capacitance of these materials as a function of temperature (see figure 3.7). These
materials should be blocked by using insulating materials such as Mica or any plastic to
avoid electrodes of the cell from contacting (see figure 3.6).
Table [3-1]
Materials Trea in °C Tmeas in °C ∆T in °C
Ice, H2O
The materials used for
calibration and their 0 -1.63 1.63
Indium, In
melting temperatures
difference ∆T °C 156.61 153.68 2.93
Tin, Sn 231.88 228.56 3.32
Lead, Pb
327.47 323 4.47
In order to achieve this goal, the blocked materials were put in the sample cell, and then
heating program was applied according to the kind of each material used (see figure 3.8).
For each program, the materials were first pre-heated (without using heating rate) from
the room temperature to temperatures below the melt, and then the materials were heated
gradually to temperatures above the melt. Figure (3.7) shows how ∆T can be determined
by using Tin. At first, Tin was heated to 220 °C and then held at this temperature for
600 s, then followed by heating to 224 °C with heating rate 1 K min-1 and then heated to
230 for every 1 K with heating rate 0.1 K min-1, see figure 3.8 (b).
Materials and methods . 28
-
+ Electrode
Electrode
Sample Two blocking Layers from PEN or Mica
Figure 3.6: Preparation method of Ice (H2O), Indium (In), Tin (Sn) and Lead (Pb) for
thermal calibration of the Sample Cell of BDS Instrument.
It is clear that as the temperature increases, capacitance Cp of the Tin increases
and then increases dramatically at temperature 228.56 °C. That indicates the measured
melting temperature of Tin by using the sample cell. Moreover, the temperature
difference can be simply obtained by the following relation:
measrea TTT −=Δ (3.5)
Where Trea represents the real melting temperature of the Tin which 231.88 0 °C and
Tmeas represents the measured melting temperature by the sample cell.
218 220 222 224 226 228 230 232 2346.00E-012
8.00E-012
1.00E-011
1.20E-011
1.40E-011
1.60E-011
1.80E-011
CP
in F
T in °C
Tmeas = 228.56 °C
Sn
Figure 3.7: The Temperature dependence of capacitance of the two parallel plates of the
sample cell in the presence of Tin (Sn). The vertical line indicates the measured
temperature at which Tin melts.
Materials and methods . 29
151 °C
150 °C
R.T.R.T. R.T.
160 °C
1K/min
600 s
600 s600 s
152 °C 225 °C
220 °C
230 °C
315 °C
325 °C
150 °C
R.T.R.T. R.T.
224 °C1 K/min
0.1 K/min
0.1 K/min
600 s
1 K/min 1 K/min
1 K/min
600 s
323 °C
323..2 °C300 s
300 s
151 °C
160 °C
1K/min
600 s
600 s600 s
152 °C 225 °C
220 °C
230 °C
315 °C
325 °C
224 °C1 K/min
0.1 K/min
0.1 K/min
600 s
1 K/min 1 K/min
1 K/min
600 s
323 °C
323..2 °C300 s
300 s
(a) (b) (b)
Figure 3.8: The heating program which was applied on Indium (a), Tin (b) and Lead (c).
Figure (3.9) shows the thermal temperature difference ∆T as a function of temperature for
all calibration materials used. It is clear that ∆T increases with increasing temperature and
therefore this difference should be taken into our consideration before starting to measure
by using such cell sample.
-50 0 50 100 150 200 250 300 350
1.5
2.0
2.5
3.0
3.5
4.0
4.5
T rea-T
mea
s in
°C
Tm in °C
H2O
InSn
PbY= 1.58409 + 0.0084 X
Fig. 3.9: Thermal calibration data of the sample cell which was detected by measuring
the melting points of Indium, Tin and Lead. The data represented by the squared symbols
were fitted by linear equation. Linear fitting gives ∆T = 1.58409+0.0084 Tm.
Results 30
4. Results
In recent years, early stages of polymer crystallization have attracted the attention of the
materials researchers with increasing interest for obtaining complete information about
the whole crystallization process.
Dielectric spectroscopy was used in this work to investigate the relaxation and
polarization processes and how they change during evolution of crystallization. The
obtained results can be divided into two parts. In the first part, the influence of
crystallization and melting on real and imaginary parts of the dielectric permittivity was
firstly checked during temperature scan experiments with constant cooling or heating
rate. While, in the second part the influence of crystallization at different constant
annealing temperatures on dielectric permittivity was tested.
The most important results presented here were related to demonstrate the early stages of
polymer crystallization of poly (ε-caprolactone). Besides, some relaxation experiments
were carried out for other polymers namely, polyoxymethylene, isotactic polypropylene,
poly (ethylene terephthalate), polyethylene and isotactic polystyrene in order to give
comparable results with that obtained for PCL.
4.1 Dielectric spectroscopy measurements during temperature scans Scan experiments are very important to perform, to define when and at which
temperature the crystallization and melting of the polymer sample start. Moreover, these
experiments show how real part ε′ and imaginary part ε′′ of the complex dielectric
permittivity are influenced by crystallization and melting.
4.1.1 Scan measurements for poly (ε- caprolactone)
In figure (4.1a), real ε′ and imaginary ε′′ parts of the dielectric permittivity at 20 Hz and
10 kHz as well as the specific heat flow from a DSC experiment for PCL are shown for
cooling at 1 K min-1, followed by heating at 1 K min-1. ε′ and ε′′ coincide in the melt for
each frequency on cooling and on heating between 60 °C and 70 °C. Therefore, the
identical state can be assumed before crystallization and after melting. In addition, the
Results 31
experiment was repeated several times to check reproducibility and stability of the
sample. Two scan experiments with the same time-temperature-profile are shown in
figure (4.1a) in part A and part B. However, the two independent experiments coincide
and yield the same crystallization kinetics. This was also checked for all following
isothermal experiments. No differences in the behavior of the dielectric permittivity were
observed for equal experimental conditions.
468
101214 A A
468
101214
10 kHz
20 Hz
ε'
10-1
100
101
102 B 20 Hz
10 kHz
ε''
35 40 45 50 55 60 65 70-0.5
0.0
0.5
TCexotherm
C
T in °C(a)
HF
in W
g-1
10 kHz
20 Hz
ε'10-2
10-1
100
101 D 20 Hz
10 kHzta
nδ
35 40 45 50 55 60 65 70-0.5
0.0
0.5
TC
C
T in °C(b)
HF
in W
g-1
exotherm
Figure 4.1: (a) Real part ε′ (A) and imaginary part ε′′ (B) of the dielectric permittivity
ε*(ω) = ε′ (ω) – iε′′(ω) at cooling of PCL followed by heating at rate 1 K min –1 (two
independent measurements) at 20 Hz and 10 kHz. Specific heat flow HF (C) from a DSC
experiment at the same scanning rates. Then, ε′′ (B) in (a) is replaced by loss tangent
tan δ and shown in Fig. (4.1b).The vertical dotted line at 55 °C indicates the
crystallization temperature for the isothermal crystallization experiments shown below.
Sample thickness is 0.15 mm.
At crystallization, a decrease and at melting, an increase of the dielectric
permittivity is expected because of the changing number of mobile dipoles and charge
carriers contributing to the signal. The imaginary part ε′′ shows the expected
dependencies at crystallization and melting for all frequencies studied (only two are
Results 32
shown). The real part ε′ at high frequencies (10 kHz) also exhibits the expected behavior.
But the curves at 20 Hz are unexpected. At crystallization and at melting a peak in ε′ is
observed. Interestingly, at cooling the peak onset appears at approximately 4 K higher
temperature compared to the first changes detected in the heat flow rate (HF) or in ε′′ or
in ε′ (at high frequencies), see vertical line at 46 °C. In order to complete our study forε′′,
especially for PCL, the results are represented by tan δ to obtain more information about
the relaxation processes in PCL sample, see part (D) in figure (4.1b). It is clear from this
figure that tan δ decreases on crystallization and shows the expected behavior at high
frequencies (10 kHz), while it decreases earlier at low frequencies (20 Hz) and shows the
unexpected behavior.
The differences in the absolute values of the permittivity in figure (4.1) result
from the frequency dependence of charge carrier relaxations. As lower the frequency as
higher is their contribution to the dielectric permittivity. The increase in ε′ at low
frequencies is commonly interpreted as an interfacial process (Maxwell/Wagner/Sillars or
electrode polarization). Accordingly, the peak seen in ε′ at 20 Hz at crystallization and
melting of PCL may be related to such processes because of the formation and
disappearance of interfaces during the course of crystallization and melting, respectively.
Maxwell/Wagner/Sillars (MWS) and electrode polarizations are not relaxation processes
due to molecular fluctuations. MWS is due to the separation of charge carriers at inner
dielectric boundary layers on a mesoscopic length scale (details mentioned in
Section.2.2.2.1). Electrode polarization is due to separation of charge carriers at the
sample electrode interface on a macroscopic scale (details come next in Section 4.2.1.3).
Results 33
4.1.1.1 Contribution from charge carriers polarizations to the dielectric
permittivity
Contribution of the electrode or MWS polarization to the dielectric permittivity at low
frequencies depends on the sample thickness, and therefore, the dielectric behaviors of
PCL sample with different thicknesses were checked. In figure (4.2), three independent
scan experiments were carried out at 10 Hz for the samples with 0.9 mm, 3 mm and
5 mm in thicknesses. It is clear from this figure that ε′ shows a peak at crystallization and
at the melt in addition, this peak becomes more pronounce by increasing the sample
thickness. The contribution from electrode polarization decreases with increasing sample
thickness and therefore the contribution from MWS polarization becomes more
responsible for the peak observed in ε′ for the thick samples.
10
15
20
25(a)
ε'
3 mm
5 mmf = 10 Hz
0.9 mm
35 40 45 50 55 60 65 70 75
101
102
103
(b)
ε''
T in °C
f = 10 Hz
Figure 4.2: Real part ε′ and imaginary part ε′′ of the dielectric permittivity at cooling of
PCL followed by heating at rate 1 K min –1 for (A) at different sample thicknesses
namely, 0.9 mm, 3 mm, and 5 mm.
Results 34
4.1.2 Scan measurements for Polyoxymethylene
To check the behavior of real part and imaginary part of the dielectric permittivity at
crystallization and melting of POM, the sample was cooled from the melt (200 °C) at
1 K min-1 then followed by heating at 1 K min-1. ε′ and ε′′ as well as the specific heat
flow from DSC can be seen in figure (4.3). This experiment was carried out at different
frequencies but the measurements were only represented here at 1, 20, 103 and 104 Hz.
100
101
102 A
ε'
1 Hz
10-1
100
101
102
103
104B
ε''20 Hz
103 Hz
104 Hz
100 120 140 160 180 200
-6
-3
0
3
exotherm
C
T in °C
HF
in W
g -1
Figure 4.3: Real part ε′ (A) and imaginary part ε′′ (B) of the dielectric permittivity
ε*(ω) = ε′ (ω) – iε′′(ω) at cooling of POM from the melt (200 °C) followed by heating at
rate 1 K min –1. Sample thickness is 0.9 mm.
In figure (4.3), ε′ at low frequencies (at 1 Hz and 20 Hz) shows an increase at
crystallization instead of expected decrease, while at high frequencies shows the expected
behavior. Interestingly, at cooling the peak onset appears at approximately 3 K higher
temperature compared to the first changes detected in the heat flow rate (part C), see
vertical line at 147 °C. Similar effect is seen for all ε′′ curves but is not understood.
During cooling POM from the melt, the imaginary part of the dielectric permittivity
shows a decrease at low and high frequencies, while it shows an increase during heating
and therefore shows the expected behavior. It can be seen also that the real and imaginary
Results 35
parts of the dielectric permittivity coincide in the melt for each frequency on cooling and
on heating between 176 °C and 200 °C. Therefore, the identical state can be assumed
before crystallization and after melting.
4.1.3 Scan measurements for isotactic polypropylene
The crystallization and melting behavior of isotactic polypropylene are closely related to
its microstructure and the external conditions when these processes occur [82-86]. This
part of work aims to study the change of real part ε′ and imaginary part ε′′ of the
dielectric permittivity as well as the heat flow from DSC for cooling of iPP from the melt
at 200 °C at 1 K min-1, followed by heating at 1 K min-1 (see Fig. 4.4).
3.2
3.6
4 A
ε'
0.1 Hz
1 Hz
10 H
10-4
10-2
100
B
ε''
105 Hz104 Hz
100 120 140 160 180 200
-0.4
0.0C
T in °C
HF
in W
g-1
exotherm
Figure 4.4: Real part ε′ (A) and imaginary part ε′′ (B) of the dielectric permittivity
ε*(ω) = ε′ (ω) – iε′′(ω) at cooling of PET from the melt (200 °C) to 100 °C followed by
heating at rate 1 K min –1. Specific heat flow HF (C) from a DSC experiment at the same
scanning rates. Sample thickness is 2.3 mm.
The dielectric spectroscopy measurements were carried out at different
frequencies, but the measurements were presented here at 0.1, 1, 10, 104 and 105 Hz. In
order to avoid iPP sample from oxidation at high temperatures, nitrogen was used instead
Results 36
of air. Although this experiment was repeated several times by using both broadband
dielectric spectroscopy (BDS 4000) and HP 4284 A devices, however it gives the same
results. In figure (4.4), at crystallization, ε′ shows a small peak for all frequencies studied,
which indicates the polarization of the sample and the charge carrier processes. In
contrast, ε′′ curves show the expected decrease at crystallization and melting. But this
behavior is clear only at 0.1 and 1 Hz. The decrease in ε′ starts simultaneously with the
first change detected in heat flow or in ε′′, that is indicated by the vertical line at 130 °C
in figure (4.4). Above 10 Hz, ε′ shows no frequency dependence on cooling and on
heating of iPP.
Results 37
4.1.4 Scan measurements for poly (ethylene terephthalate)
The influence of crystallization and melting on the dielectric permittivity was firstly
checked at cooling and heating. In figure 4.5(a) real and imaginary parts of dielectric
permittivity at 20, 900, 104, 9*104 and 9*105 Hz as well as specific heat flow from a DSC
experiment for PET are shown for cooling at 1 K min-1 then followed by heating at
1 K min-1.
Figure 4.5: Real part ε′ (A) and imaginary part ε′′ (B) of the dielectric permittivity
ε*(ω) = ε′ (ω) – iε′′(ω) at cooling of PET from the melt (290 °C) to 50 °C followed by
heating at rate 1 K min-1. Specific heat flow HF (C) from a DSC experiment at the same
scanning rates. Sample thickness is 0.15 mm.
For the dielectric measurements, Hewlett-Packard Impedance analyzer (HP
4284A) was used. It is clear that the imaginary part ε′′ shows the expected dependencies
at crystallization and melting for all frequencies studied (only five are shown). Also, at
frequencies higher than 900 Hz, the real part ε′ shows the expected dependencies. The
decrease in ε′ at crystallization (at high frequencies) is due to decreasing the number of
mobile dipoles. On the other hand, at frequencies below 900 Hz; a peak in ε′ is observed
101
102
103 A
ε'
20 Hz
900 Hz
10 KHz90 KHz
900 KHz
10-2
10-1
100
101
102
103
104
B ε''
50 100 150 200 250
-0.2
0.0
exotherm
C
T in °C
HF
in W
g -1
468
1012141618
A
900 kHz
ε'
900 Hz
B
900 kHz
900 Hz
10-1
100
101
102
ε''
220 240 260 280-1.5
-1.0
-0.5
0.0
0.5
exotherm
C
T in °C
HF
(a) (b)
Results 38
at crystallization and therefore it shows the unexpected behavior. Such increase shows a
relaxation process due to increasing number of charge carrier polarization (MWS or
electrode polarization). In figure 4.5(b), the increase in ε′ at 900 Hz starts simultaneously
with the first changes detected in the heat flow rate from DSC experiment or in ε′′ see
vertical line at 240 °C. The broad peak observed in ε′ at melting starts at much lower
temperatures as melting in the DSC. This result may be attributed to the fact that PET can
be crystallized over a wide temperature range and forms different crystals and therefore,
the broad peak observed in ε′ at 900 Hz represents the superposition of the different
melting points distribution.
4.1.5 Scan measurements for polyethylene
Changes in morphologies and dynamics of PE at crystallization and melting were
checked by performing dielectric relaxation experiment and differential scanning
calorimetry experiment, respectively. The two experiments were carried out at 1 K min-1
on cooling and on heating (see Fig. 4.6).
1.8
1.9
2.0
2.1
100 kHz
990 Hz
A
ε'
10-2
10-1
990 HzB
100 kHz
ε''
115 120 125 130 135
-1.5
-1.0
-0.5
0.0
0.5
1.0C
T in °C
HF
in W
g -1
exotherm
Figure 4.6: Real part ε′ (A) and imaginary part ε′′ (B) of the dielectric permittivity
ε*(ω) = ε′ (ω) – iε′′(ω) at cooling of PE from the melt (140 °C) to 115 °C followed by
heating at rate 1 K min –1. Specific heat flow HF (C) from a DSC experiment at the same
scanning rates. Sample thickness is 0.15 mm.
Results 39
The dielectric experiment was carried out several times by using broadband dielectric
spectroscopy (BDS 4000) and Hewlett-Packard Impedance analyzer (HP 4284A) devices.
However the measurements below 990 Hz were noisy. Therefore, only the dielectric
relaxation measurements at 990 Hz and 105 Hz are presented here.
For a comparison between dielectric and DSC data, the real and imaginary parts
of the dielectric permittivity at 990 Hz and 105 Hz were plotted as well as heat flow (see
Fig. 4.6). It is clear that ε′ shows an increase at crystallization which indicates relaxation
processes at the two frequencies studied. The increase in ε′ starts simultaneously with the
first changes detected in the heat flow rate from DSC experiment or in ε′′ (part B), see
vertical line at 123 °C. On the other hand ε′′ shows very weak maxima on cooling and on
heating. Also, both of real and imaginary parts of dielectric permittivity coincides in the
melt for each frequency on cooling and on heating between 135 °C and 140 °C and
therefore the identical state can be assumed before crystallization and after melting.
4.2 Dielectric spectroscopy measurements from isothermal experiments From scan experiments described above, at crystallization of poly (ε-caprolactone)
pronounced effects in ε′ at low frequencies are observed before changes in crystallinity
can be detected. Additionally, α-relaxation and melting and re-crystallization processes
affect dielectric permittivity in the interesting frequency range. Therefore, we have
performed more detailed experiments with PCL only.
4.2.1 Isothermal measurements for Poly (ε - caprolactone)
In addition to charge carrier processes, another possibility for an increasing real part of
the dielectric permittivity is the occurrence of the α-relaxation or local relaxation
processes (β and γ) in the frequency- temperature window of the experiment. To verify
the presence or absence of such processes, a dielectric relaxation experiment was
performed in a wide range of frequency (10-2 Hz-107 Hz), and in a temperature range
between -150 °C and 0 °C every 10°K, i.e. at temperature below and above glass
transition temperature of PCL (-70 °C).
Figure (4.7) shows the real and imaginary parts of dielectric permittivity as a
function of frequency. It is clear that at lower frequency ~ 1 Hz (see vertical line) as the
Results 40
temperature increases, the dielectric permittivity increases, which indicate separation of
charges at sample / electrode, interface. This process will be discussed as an electrode
polarization which causes increasing the real and imaginary parts of the dielectric
permittivity at low frequencies. Additionally, the relaxation processes can not be easily
recognized in spectra of ε′′. Therefore, to resolve the complex spectra of imaginary part
of the dielectric permittivity (ε′′ ), an analysis was done using the Havriliak and Negami
empirical equation plus a conductivity term (see section 3.1.1.3), as shown in figure (4.9).
5
10
15
20
- 80 °C - 70 °C
(a)
ε' - 150 °C - 140 °C - 130 °C - 120 °C - 110 °C - 100 °C - 90 °C
0 °C
-10 °C
-20 °C
10-2 10-1 100 101 102 103 104 105 106 10710-3
10-2
10-1
100
101
- 60 oC
- 50 oC
(b)
ε''
f in Hz
-30 °C
-40 °C
Figure 4.7: Frequency dependence of Real part ε′ (A) and imaginary part ε′′ (B) of the
dielectric permittivity ε*(ω) = ε′ (ω) - iε′′ (ω) at a wide range of temperature from -
150 °C to 0 °C of PCL and frequency range from 10-2 Hz to 107 Hz. Sample thickness is
0.15 mm.
Also, to observe the common relaxation processes take place in PCL in the
frequency range mentioned above, an example for fitting the spectra at -30 °C is given as
shown in figure (4.8). The contribution from dc-conductivity (s) is subtracted from the
experimental values of the imaginary part of the dielectric permittivity (ε″exp) and
therefore a pure ε′′ can be obtained.
Results 41
It has been found that PCL shows all the three relaxation processes in the temperature
range, α- process, which is a high temperature relaxation process, is commonly
considered to be connected to the amorphous phase and related to the dynamic glass
transition temperature. The β- process in such a polymer has been connected also to the
amorphous phase and is attributed to local twisting motions of the main chains in the
amorphous region [87]. The γ- processes (or β in the crystalline polymers which do not
show α- process) which is generally agreed that it has an amorphous phase origin, but
many studies consider it as it has component from a crystalline phase.
-2 0 2 4 6 8
0.00
0.02
0.04
0.06
0.08
0.10
0.12
0.14
0.16
-30°C
γ
β
α
ε''
log(f/Hz) Figure 4.8: An example for dielectric loss spectra of PCL analyzed at -30 °C. Symbols
are experimental points and the line passing through them is the Havriliak and Negami
fit curve for the 3 single processes. Three dipole relaxation processes (α, β andγ) are
separated and represented by three different curves. ε′′= ε″exp-s.
Results 42
4.2.1.1 Arrhenius diagram and α, β and γ modes
The present part of the work aims to illustrate the complex relaxation behavior of the
permittivity curves for five representative temperatures as shown in figure (4.9). It is
clear at temperatures above 0 °C; charge carrier polarizations became dominant in the ε′
curves at low frequencies. Therefore, these effects can not be neglected for further
discussion of the maximum observed at crystallization and melting for PCL. Then the
final analysis was to plot the frequencies of the loss peak maxima for the different
relaxation process in semicrystalline PCL as a function of reciprocal temperature.
5
10
15
20
25
30
55 oC
-150 oC-100 oC-50oC
0 oCA
ε'
10-2 10-1 100 101 102 103 104 105 106 107
10-2
10-1
100
55oC
-100 oC
-150 oC
-50oC
0 oC
B
ε''
f in Hz Figure 4.9: Frequency dependence of the real part ε′ (A) and imaginary part ε′′ (B) of
the dielectric permittivity of PCL at different temperatures (-150 °C, -100 °C, -50 °C,
0 °C, 55 °C). The thin lines in B represent fit-curves taking into account one or two
Havriliak - Negami functions and a conductivity term [75] at –50 °C, 0 °C and 55 °C.
The short vertical dashes indicate the position of the maximum of the fit curves which are
shown in the Arrhenius - diagram (See figure 4.10).
Results 43
3 4 5 6 7 8
-2
0
2
4
6
8
γ-relaxation
β-relaxation
α-relaxationlo
g(f/H
z)
1000K/T Figure 4.10: Arrhenius diagram for PCL from isothermal dielectric experiments; lines
from [87]; symbols this work. The points represent the frequency of the dielectric loss
maximum for the fit functions according to Havriliak and Negami [75], see figure (4.9).
The vertical bar indicates the frequency-temperature-range to study isothermal
crystallization.
Figure (4.10) shows that at crystallization temperature between 40 °C and 55 °C, the
maximum position of all other relaxation processes (dipole relaxation processes) is above
1 MHz. Therefore, for PCL the observed maximum at 20 Hz is not due to one of the
relaxation processes.
4.2.1.2 Frequency and time dependence of ε′ and ε′′ during isothermal
crystallization
The present part of the work aims to obtain more detailed information about the whole
crystallization process and possible reasons for the maximum observed in ε′ at
crystallization of PCL. In order to achieve this goal, isothermal crystallization
experiments were performed at temperatures with slow crystallization kinetics. This is
usually the case near the melting temperature. For isothermal crystallization of PCL the
crystallization process is reasonable slow at temperature above 50 °C. We used a
temperature of 55 °C for our detailed studies. This temperature is indicated as the dashed
line in figure (4.1). At this temperature the experiments in the frequency range between
Results 44
10-2 Hz and 1 MHz are not influenced by the alpha relaxation. But as shown in
figure (4.9) curve at 55 °C, charge carrier processes and conductivity influence the real
and imaginary parts of the dielectric permittivity of PCL sample at frequencies below
103 Hz and 105 Hz, respectively. The frequency dependency of permittivity of the
supercooled melt and its development during isothermal crystallization can be seen from
figure (4.11). PCL sample was cooled from the melt at 70 °C to the crystallization
temperature at 1 K min-1. Frequency sweeps were successively repeated every 2,100 s.
101
102
103
104
105
66,000 s55,400 s
45,000 s34,500 s20,000 s9,000 s
A
104,000 s
3,400 s
ε'
10-2 10-1 100 101 102 103 104 105 106 10710-2
10-1
100
101
102
103
104
105
106
B
104,000 s
3,400 s
ε''
f in Hz
101
102
103
20,000 s
9,000 s
A
104,000 s
3,400 s
ε'
100 101 102 103 104
B
104,000 s
3,400 s
10-1
100
101
102
103
104
ε''
f in Hz
(a) (b)
Figure 4.11: Frequency dependence of the real part ε′ (A) and imaginary part ε′′ (B) of
the dielectric permittivity during isothermal crystallization of PCL at 55 °C at different
times. The right graph (b) shows in detail the frequency range between 1 Hz and
10,000 Hz for measurements after 3400, 9000, 20000, and 104000 s. Sample thickness is
0.15 mm.
At 55 °C and before crystallization sets in, ε′ is frequency independent at frequencies
above 40 Hz. During the isothermal experiment the frequency dependence does not
change until 10,000 s. But the curve observed at 20,000 s is significantly different
Results 45
compared to the earlier curves at frequencies above 10 Hz (see Fig. 4.11 b). At the lowest
frequencies, this is the result of decreasing electrode polarization, whereas in the
frequency range between 10 and 103 Hz, a new process which is introduced during main
crystallization is observed.
For more detailed discussion of the time dependences of ε′ and ε′′, the data
presented in figure (4.11) are shown in figure (4.12) as a function of time for the different
frequencies. It is clear that ε′ and ε′′ show a continuous decrease with time at very low
and high frequencies. But at intermediate frequencies between 2.5 Hz and 250 Hz, a
maximum in ε′ occurs again. The very large values of ε′ at low frequencies in
figures (4.11) and (4.12) are due to charge carrier processes. Because the high values
appear from the very beginning of the isothermal experiment, when the sample is in the
isotropic liquid state, electrode polarization rather than MWS polarization [73, 74] seems
to be the reason for the observed large values.
101
102
103
104
105 A
10 MHz
0.02 Hz
0.4 Hz0.16 Hz0.06 Hz
6 Hz2.5 Hz1 Hz
16 Hz
ε'
103 104 10510-2
10-1
100
101
102
103
104
105 B
10 MHz0.2 MHz
1.6 kHz
16 Hz
0.01 Hz
ε''
t in s Figure 4.12: Time dependence of the real part ε′ (A) and imaginary part ε′′ (B) of the
dielectric permittivity during isothermal crystallization of PCL at 55 °C at different
frequencies between 10-2 Hz and 107 Hz. Real part as well as imaginary part decreases at
all times with increasing frequency. Sample thickness is 0.15 mm.
Results 46
4.2.1.3 Reduction of electrode polarization
Electrode polarization is simply defined as a blocking of charges at the sample/electrode
interface and influences the dielectric properties of the sample at low frequencies.
Accordingly, an application of blocking layers [88-90] between sample and electrodes
permits to avoid contribution from electrode polarization, and thus, the very large values
seen in ε′ and ε′′ can be reduced. Ions are blocked from the external circuit and current in
the external circuit is induced entirely through capacitive coupling. This approach has
been formerly used for the thermally stimulated current measurements [91] and also
proposed for the DRS investigation of the aqueous electrolytes [92].
Therefore, separating of conductive electrodes from PCL sample was firstly done
by using thin, non dispersive layer such as Teflon, Kapton or Mica. The preparation way
was described in section 3.1.1.1. Based on above, isothermal relaxation experiment was
carried out for a Mica-PCL sandwich at 53 °C and at different crystallization time as
shown in figure (4.13). As shown in figure 4.13 (a), as the frequencies decreases below
300 Hz (see vertical line), the dielectric permittivity ε′ increases, whereas ε′′ shows a
maximum (Fig. 4.13 b). The increase in ε′ at low frequency may be attributed to MWS
polarization due to the differences in permittivities and conductivities of the PCL sample
and the insulating material used, i.e. heterogeneous system is formed (see section
2.2.2.1). It is clear that as the crystallization proceeds with time, the peak observed in ε′′
shifts to the lower frequency and somehow broadness and therefore, MWS relaxation is
strongly affected by crystallization. Obviously, the large values appeared in ε′ and ε′′
related to electrode polarization are reduced by using an insulating material at the
sample/electrode interface in comparison with that obtained for PCL sample only.
However, the appearance of MWS polarization makes the interpretation of data
speculative. Therefore, we tried another way by measuring samples with a reduced
electrode surface to volume ratio. That’s why we have measured a sample with 20 mm
diameter and 5 mm thickness.
Results 47
10-2 10-1 100 101 102 103 1041.8
2.1
2.4
2.7
3.0
3.3
3.6
3.9
4.2
f in Hz(a)
900 s 13600 s 34000 s 46000 s 56000 s 69000 s 78000 s 91000 s 100000 s 113000 s 132000 s 149000 s
ε'
A
900 s
149000 s
10-2 10-1 100 101 102 103
0.0
0.3
0.6
0.9
1.2
1.5 900 s 13600 s 34000 s 46000 s 56000 s 69000 s 78000 s 91000 s 100000 s 113000 s 132000 s 149000 s
ε''
f in Hz(b)
B
149000 s
900 s
Figure 4.13: Frequency dependence of real part ε′ (a) and imaginary part ε′′ (b) of the
dielectric permittivity during isothermal crystallization of PCL at 53 °C in the presence
of thin layer from Mica at the sample/electrode interface. The numbers given in the figure
are the annealing times in seconds. Sample thickness is 0.17 mm.
The results for an isothermal crystallization experiment at 52 °C are shown in
figures (4.14) and (4.15). It is clear that the values of ε′ at low frequencies are drastically
reduced. This proves that electrode polarization is the reason for the high values seen
in figures (4.11) and (4.12) for the thin sample. On the other hand, the maximum in ε′ is
Results 48
now seen in all curves for frequencies below 10 Hz in figure (4.14). Even at the lowest
frequency of 0.01 Hz the maximum is well pronounced.
0
130
260
390
520 A
85,000 s
9,000 s
30,000 s35,000 s
150,000 s
60,000 s
45,000 s
17,000 s
ε'
10-2 10-1 100 101 102 103 104 105 10610-2
10-1
100
101
102
103
104
105 B
150,000 s
9,000 s
ε''
f in Hz Figure 4.14: Frequency dependence of the real part ε′ (A) and imaginary part ε′′ (B) of
the dielectric permittivity during isothermal crystallization of PCL at 52 °C at different
times. Sample thickness is 5 mm.
For thick PCL sample, the increase of ε′ starts despite the lower crystallization
temperature after longer annealing times compared with the thin samples. This means
that the whole crystallization process shows a slower kinetic instead of the expected
faster kinetic because of the lower temperature. So, crystallization kinetics seems to
depend on sample thickness. This effect is often observed when crystallization begins at
the surfaces of the sample and proceeds later in the bulk. A similar effect was observed
for the crystallization kinetics in the DSC. The thin sample measured in the Perkin Elmer
DSC 6 crystallized much faster than a ca. 5 mm diameter cylindrically sample measured
in the Setaram DSC 121. Nevertheless, the occurrence of the maximum at low
frequencies for the thick sample and the comparable maximum values of ε′ in the
medium frequency range show that electrode polarization or some changes in the
Results 49
polymer morphology close to the surface at the early stages of crystallization (trans
crystallinity [93]) can not be the reason for the observed maximum in ε′.
101
102
A
0.37 Hz
ε'
103 104 105
10-1
101
103
105 B
1.6 MHz
1.64Hz
10 kHz
270 Hz25 Hz
0.11 Hz
0.02 Hz
0.01 Hz
ε''
t in s Figure 4.15: Time dependence of real part ε′ (A) and imaginary part ε′′ (B) of the
dielectric permittivity during isothermal crystallization of PCL at 52°C at different
frequencies between 0.01 Hz and 1.6*106 Hz. Sample thicknesses is 5 mm.
4.2.1.4 Time dependence comparison of the dielectric permittivity with
the non-crystalline fraction obtained from DSC experiments
This part of work aims to give more quantitative discussion of the curves shown in
figures (4.12), (4.15), and therefore the time dependence of permittivity with the time
dependence of the non-crystalline fraction obtained from DSC experiments during the
course of isothermal crystallization of PCL were compared as shown in figures (4.16),
(4.17). From DSC scans of comparable thick PCL samples to the melt (70 °C) after
annealing at the crystallization temperature we obtained crystallinity from cχ = ΔH/ΔHo
where ΔH equals the measured heat of fusion and ΔHo equals the heat of fusion of the
infinite large crystal at the melting temperature. ΔHo = 153.5 J g-1 is given from ATHAS
[76]. The non-crystalline fraction was obtained from ncχ = 1 - cχ . For seek of clarity
Results 50
permittivity and non-crystalline fractions are scaled such way that in the melt (short
times) and in the semicrystalline sample (at the end of the measurement) both curves
coincide.
5
6
A106 Hz
ε'
-20
0
20
40
60
16 Hz
B
ε'
0.0
0.5
1.0
10-2 HzC
ε'/10
5
0.04
0.06
D106 Hz
ε''
0.6
0.8
1.0
χnc
0.6
0.8
1.0
χnc
0.6
0.8
1.0
χnc
0.6
0.8
1.0
χnc
0
200
400 16 HzE
ε''
103 104 105
0
2x105
4x105 F10-2 Hz
t in s
ε''
0.6
0.8
1.0
χnc
0.6
0.8
1.0
χnc
Figure 4.16: Time dependence of the real part ε′ (A-C) and imaginary part ε′′ (D-F) of
the dielectric permittivity during isothermal crystallization of PCL at 55°C at frequency
106 Hz (A and D), 16 Hz (B and E) and 10-2 Hz (C and F). The squares represent the
amount of amorphous material after different times of isothermal crystallization obtained
from DSC experiments. Sample thickness is 0.15 mm.
Results 51
6.6
7.2
7.8
8.4 A
106 Hz
ε'-220
-110
0
110
220
330
440
B
2.5*10-2 Hz
ε'
0.01
0.02
C
106 Hzε''
103 104 1050
5x104
1x105
D
t in s
2.5*10-2 Hz
ε''
0.6
0.8
1.0
χnc
0.6
0.8
1.0
χnc
0.6
0.8
1.0
χnc
0.6
0.8
1.0
χnc
Figure 4.17: Time dependence of the real part ε′ (A and B) and imaginary part ε′′ (C and
D) of the dielectric permittivity during isothermal crystallization of PCL at 52°C at
frequency 106 Hz (A and C) and 2.5*10-2 Hz (B and D). The squares represent the
amount of amorphous material after different times of isothermal crystallization obtained
from DSC experiments. Sample thickness is 5 mm.
The decrease in the non-crystalline fraction starts after the induction period of
crystallization at about 20,000 s, see points in figures (4.16) and (4.17). At high
frequencies, ε′ and ε′′ follow the non-crystalline fraction during the whole course of
crystallization. This is clear from the 106 Hz curve which is shown as an example. Such
behavior is expected from the decreasing number of mobile dipoles and limited charge
carrier mobility with increasing crystallinity. From above, it can be concluded that in
both devices, dielectric spectrometer and calorimeter, crystallization kinetics is the same.
Beside the unexpected maximum at intermediate frequencies the curves at low
frequencies deviate significantly from the decrease of the non-crystalline fraction, 10-2 Hz
is shown as an example in figure (4.16) and 2.5*10-2 Hz in figure (4.17). Especially ε′
Results 52
starts to decrease for the thin sample much earlier than the non-crystalline fraction. At
such low frequencies ε′ is mainly determined by electrode polarization for the thin
sample. The early decrease of ε′ shows that charge carrier mobility is reduced due to
some structure formation different from crystal formation (main crystallization).
Next, we compare the dielectric permittivity with the non-crystalline fraction at
frequencies between 2.5 Hz and 250 Hz (thin sample) and below 100 Hz (thick sample)
where the maximum in ε′ occurs, see figures (4.12) and (4.15). The maximum in ε′ is
observed between 30,000 s and 40,000 s (thin sample) and at about 40,000 s (thick
sample). It is clear that the increase in ε′ starts already at about 6,000 s. This is again long
before the non-crystalline fraction from DSC starts to decrease. The value of the
dielectric permittivity after crystallization is for these frequencies higher than the value in
the melt before crystallization.
Finally, it is clear from figures 4.16E and 4.17D that the behavior of ε′′ is
qualitatively the same as for the low frequency shown in figure 4.16F. According to the
starting decrease of the non-crystalline fraction with time, additional information about
crystallization of PCL can be given.
4.2.1.5 Temperature dependence of the peak observed in ε′
To check possible temperature dependencies of the observed peak in ε′, the
measurements were repeated for the thin sample at different temperatures. To be able to
follow faster crystallization, the frequency range was limited, 20 Hz to 900 kHz.
Frequency sweeps were repeated successively every 30 s utilizing the HP 4284A. In
figure (4.18), the dielectric permittivity during isothermal crystallization at different
temperatures between 49 °C and 58 °C at frequency 20 Hz and 900 kHz is shown for the
thin sample. The shift of the crystallization process to shorter times at lower temperatures
results from the increase of the crystallization rate with decreasing temperature. Whereas
ε′ measured at 900 kHz behaves always proportional to the decrease of the non-
crystalline fraction, ε′ measured at 20 Hz shows always first an increase followed by a
decrease.
The arrows in figure (4.18) indicate the starting point of the decrease of ε′ at
900 kHz. This is the beginning of crystal formation at the specific crystallization
Results 53
temperature. The increase at 20 Hz starts always significantly earlier. The maximum
values of ε′ increase with increasing crystallization temperature. The occurrence of such
pronounced maxima over time requires at least two competing processes.
103 104 105
4.5
5.0
5.5
6.0
10
20
30
40
50
60
70 58°C56°C
52°C
58°C
52°C
54°C49°C
56°C
49°C
54°C
f = 900 kHz
f = 20 Hz
ε'
t in s Fig. 4.18: Time dependencies of the real part ε′ of the complex dielectric permittivity
during isothermal crystallization of PCL at different temperatures at frequency 20 Hz
and 900 kHz. The arrows indicate the beginning of the decrease of ε′ at 900 kHz for the
different temperatures. Sample thickness is 0.15 mm.
The decrease of ε′ at longer times during main crystallization is due to decreasing
mobility of relaxing dipoles and charge carriers. The reason for the increase at shorter
times is not as clear. However, a combination between dielectric and calorimetric
experiments (mentioned above) close to the melting temperature (melt crystallization),
may give us some hints for the formation of pre-ordered regions prior to crystal formation
[106] (see details in Section 5.1.1). Nevertheless, DSC experiments give only an indirect
link to the morphology. The comparison of dielectric experiments, which test the
dynamics, with scattering experiments, which give access to morphology, is more
directly and therefore, a simultaneous experiment was performed by combining between
small angle X-ray scattering (SAXS) and dielectric relaxation spectroscopy (DRS)
techniques.
.
Results 54
4.2.1.6 Simultaneous SAXS- DRS experiments
Simultaneous measurements of different techniques such as SAXS, WAXS, DRS, DSC
permit the observation of changes in the system as a function of the reaction conditions at
different length scales, from the molecular crystalline lattice scale to the suppermolecular
or aggregate size (a few thousand of Angstrom). Therefore, in recent years, many authors
developed various devices that carried out in situ and time- resolved measurements in the
crystallization process [35, 57, 94-96]. For example, the long and short- range orders
were detected simultaneously by the SAXS and WAXS time resolved measurements. In
the process, the mobility of the polymer chain in the amorphous region as well as in the
crystalline region may change with an increase in crystallinity. Also, Fukao and
Miyamoto [97, 98] performed in situ studies of the isothermal crystallization of poly
(ethylene terephthalate) (PET) by using simultaneous time resolved measurements of the
dielectric relaxation and X-ray scattering. They concluded that the polymer chain in the
amorphous phase makes a dynamical transition from the so-called α process (dynamic
glass transition) to another relaxation process, called the α′ prior to the crystallization. In
contrary to these dielectric experiments, we performed our experiments at high
temperatures, where the dielectric signal in the frequency window of the measurement is
not influenced by the α-relaxation or other local relaxations. Such experiments allow us
to crystallize polymers at temperatures just below the melting point.
Therefore, in the present part of work, a simultaneous SAXS and DRS experiments were
performed to test changes in morphologies and dynamics of PCL at crystallization from
the melt. For such experiments, a newly sample cell [107] was designed, which allows
simultaneous X-ray scattering and dielectric experiments during crystallization. The
experiments were carried out at 53 °C which is just below the melting point to resolve all
intermediate stages at crystallization and therefore, the early stages can be followed.
The performance of the newly developed dielectric sample cell was first checked
and compared with the results from former experiments. The real part of the dielectric
permittivity ε′ as a function of crystallization time for crystallization at 53°C is shown in
figure (4. 19). As discussed before the decrease in ε′ at high frequencies can be explained
by the decrease of dipole mobility in the sample, directly related to formation of crystals.
For the low frequencies we observed as in [106] an earlier increase in ε′ followed by the
Results 55
development of a maximum. The increase starts after about 40 min at 20 Hz. These
measured curves in the new cell are exactly as in the standard sample cell provided by
Novocontrol, used for our previous studies.
10 100
10
15
20
25
30
320 Hz
2*103Hz
80 Hz
20 Hz
9*105 Hz
ε'
t in min
(A)
40 Hz
Fig. 4.19: Time dependence of real part ε′ of the complex dielectric permittivity during
isothermal crystallization of PCL at 53 °C at different frequencies between 20 Hz and
9*105 Hz.
In figure (4.20), the evolution of the SAXS peak is shown, which corresponds in
the later stage of the crystallization to the long period Lp of the semi-crystalline structure,
at a simultaneous experiment. This figure shows the real- time SAXS patterns in three
dimensional plots of intensity (I) versus time versus scattering vector q (q = 4 π sin(θ/λ).
Where θ is the half scattering angle and λ is the X-ray beam wavelength = 1.0 Å. The
evolution of a SAXS peak is caused by the formation of an alternating structure of
crystalline and amorphous layers and its periodicity that is usually observed in crystalline
polymers. The first frame; is the first curve related to intensity over scattering vector after
reaching the crystallization time, should be always subtracted from all the other curves
(frames) after the different times as the reference curve for the melt. As long as the
sample is a melt the shown intensity is “0”.
At the early stage of crystallization, the SAXS patterns are observed shortly
before 100 min. The development of the characteristic peak for a semi-crystalline
Results 56
structure at qmax of about 0.07 Å–1 is observed, which corresponds to a long period of
Lp=2π/qm of 90 Å.
Fig. 4.20: Small angle X-ray scattering (SAXS) versus scattering vector q versus holding
time for PCL isothermally crystallized at 53 °C.
10 100
10
15
20
25
30
9*105 Hz
ε'
t in min
20 Hz
(B)
1-invariant
1-4*10-8
1
Fig. 4.21: Time dependence of real part ε′ of the dielectric permittivity at 20 Hz and
9*105 Hz (lines) and "1- invariant" (squares) during isothermal crystallization of PCL at
53 °C. The horizontal line at "1-invariant"=1 is drawn as a guide for the eyes. Sample
thickness is 1.5 mm.
Results 57
For a detailed comparison of the dielectric and SAXS data, the real part of the
dielectric permittivity at 20 Hz and 9*105 Hz as well as SAXS invariant were plotted
together as a function of crystallization time (see Fig. 4.21). The SAXS invariant, which
was calculated by integrating between the experimentally accessible data limits. From our
previous studies, it is known that ε′ at high frequencies parallels the decrease of the non-
crystalline fraction. The value "1-invariant" can also be related to the decrease of the non-
crystalline fraction. As for the crystallinity data revealed from DSC in figures (4.16)
and (4.17), we scaled "1-invariant" to the dielectric permittivity at high frequencies. As
can be seen from the bottom curves of figure (4.21), both curves behave similar. First
changes during isothermal annealing are detectable after 80 min for ε′ measured at
9*105 Hz as well as for the invariant (see vertical line in figure 4.21). At this time, the
real part of the dielectric permittivity at 20 Hz has already increased significantly from 16
to 17.5. These increase starts after about 40 min (see vertical line). As mentioned before
this increase in ε′ can be explained under the assumption of at least one additional
process (detailed discussion is mentioned in section 5.1.2).
4.2.2 Isothermal measurements for Polyoxymethylene
The crystallization of POM has been investigated extensively from various points of view
[81]. But as to the time-dependent structural evolution or even the static structural change
in the crystallization process from the molten state, only limited number of papers has
been published so far. One of the reasons may come from the characteristic features of
POM sample. For example, thermal decomposition occurs relatively easier when the
POM sample melted and kept at high temperature for long time. One idea to escape this
problem, the POM sample should be heated under the optimum conditions mentioned in
section 3.2.2
4.2.2.1 Frequency and time dependence of ε′ and ε′′ during isothermal
crystallization
This part of the work aims to obtain complete information about the whole crystallization
process and possible reasons for the maximum observed in ε′ at the crystallization of
Results 58
POM. Therefore, isothermal crystallization experiments were performed at temperatures
with slow crystallization kinetics. For isothermal crystallization of POM, the
crystallization process is reasonable slow at temperature above 158 °C which is indicated
as the dashed line in figure (4.3). The crystallization temperature for POM is just below
its melting point and therefore, the dielectric signal in the frequency window of the
measurement is not influenced by the α-relaxation or other local relaxations processes. As
seen in figure (4.22a), charge carrier polarizations and conductivity may influence the
real and imaginary parts of the dielectric permittivity of POM sample at frequencies
below 5 Hz and 105 Hz, respectively. POM sample was cooled from the melt at 200 °C
(40 °C higher than its original melting point) to the crystallization temperature (158 °C)
at 1 K min-1. At 158 °C and before crystallization starts, ε′ is frequency independent at
frequencies above 15 Hz. During the isothermal experiment the frequency dependence of
the dielectric permittivity does not change until 66000s (see Fig.4.22b).
101
102
103
ε'
130 s400 s700 s1500 s4100 s8400 s17000 s28000 s66000 s
10-2 10-1 100 101 102 103 104 105 106 107 10810-2
10-1
100
101
102
103
104
105
ε''
f in Hz(a)
101
102
103 130 s700 s 66000 s
ε' 130 s
66000 s
15 Hz
10-1 100 101 102101
102
103
104
105
ε''
f in Hz(b)
Figure 4.22: Frequency dependence of real part ε′ (A) and imaginary part ε′′ (B) of the
dielectric permittivity during isothermal crystallization of POM at 158 °C at different
Results 59
times. The right graph (b) shows in detail the frequency range between 0.08 Hz and
110 Hz for measurements after 130, 700 and 66, 000 s. Sample thickness is 0.9 mm.
For more detailed discussion of the time dependences of ε′ and ε′′, the data presented in
figure (4.22) are shown in figure (4.23) as a function of time for the different frequencies.
It is clear that ε′ shows a peak at frequencies lower than 0.9 Hz, while it shows a decrease
at frequencies higher than 103 Hz. The very large values of ε′ at low frequencies in
figures (4.22) and (4.23) are due to electrode polarization as we discussed for PCL.
0
1000
2000
3000
4000
ε'
0.11 Hz
0.2 Hz
0.37 Hz
0.9 Hz
102 103 104 105
4.8
5.2
5.6
4.5*104 Hz
104 Hz
t in s(a)
3*103 Hz
102
103
104
105
ε''10 Hz
102 103 104 105
0.01
0.1
14.5*104 Hz
4*106 Hz
103 Hz
105 Hz
t in s (b)
Figure 4.23: Time dependence of real part ε′ (A) and imaginary part ε′′ (B) of the
dielectric permittivity during isothermal crystallization of POM at 158 °C at different
frequencies between 0.1 Hz and 107 Hz. Sample thicknesses is 0.9 mm.
Results 60
4.2.2.2 Time dependence comparison of the dielectric permittivity with
the non-crystalline fraction obtained from DSC experiments
This part of work aims to give more quantitative discussion of the curves shown in figure
(4.22) and therefore a combination between the dielectric and calorimetric experiments
close to the melting temperature were performed. The time dependence of the dielectric
permittivity and the non-crystalline fraction ncχ (1 - cχ ) are shown in figure (4.24).
4.5
4.6
4.7
4.8 A
105 Hz
ε'
2800
3200
3600
4000
B0.1 Hz
ε'
0.19
0.20
0.21
C105 Hz
ε''
102 103 104 105
58000600006200064000
D
t in s
0.1 Hz
ε''
0.6
0.8
1.0
χnc
0.6
0.8
1.0
χnc
0.60.81.01.21.4
χnc
0.6
0.8
1.0
χnc
Figure 4.24: Time dependence of the real part ε′ (A and B) and imaginary part ε′′ (C and
D) of the dielectric permittivity during isothermal crystallization of POM at 158°C at
frequency 105 Hz (A and C) and 0.1 Hz (B and D). The squares represent the amount of
amorphous material after different times of isothermal crystallization obtained from DSC
experiments. Sample thickness is 0.9 mm.
Crystallinity of POM is obtained from cχ = ΔH/ΔHo. Where ΔHo = 326 J g-1 is
given from ATHAS [76]. It is clear from the points in figure (4.24), that the decrease in
the non-crystalline fraction starts after the induction period of crystallization at about
Results 61
29,000 s. At this time, ε′ at 0.11 Hz has already increased from 3200 to 4000. At high
frequencies, ε′ and ε′′ follow the non-crystalline fraction during the whole course of
crystallization. This result is clear from the 105 Hz curve which is shown as an example.
Such behavior is expected from the decreasing number of mobile dipoles and limited
charge carrier mobility with increasing crystallinity. Beside the unexpected maximum in
ε′ at low frequencies, ε′′ curves deviate significantly from the decrease of the non-
crystalline fraction; 0.1 Hz is shown as an example in figure (4.24). At such low
frequencies ε′ is mainly determined by electrode polarization for the thin sample. The
early decrease of ε′ shows that charge carrier mobility is reduced due to some structure
formation different from crystal formation (main crystallization).
Comparing of the dielectric permittivity with the non-crystalline fraction at
frequencies below 0.9 Hz, where the maximum in ε′ occurs, is seen in figure (4.23). This
maximum is observed between 8000 s and 33000 s. It is clear that the increase in ε′ starts
already at about 470 s. This is again long before the non-crystalline fraction from DSC
starts to decrease. As mentioned before this earlier increase in ε′ may be explained as
some order structure formed long before crystallization.
4.2.3 Isothermal measurements for isotactic polypropylene
The crystallization and melting behavior of iPP are closely related not only to the external
conditions such as undercooling and cooling rate, but also to the chain structure
characteristics such as isotacticity distribution [99]. The perfection of crystals formed in
different conditions decreases with increasing undercooling, when the isothermal
crystallization is carried out by quickly cooling to different temperatures from the melt
[100, 101].
In order to examine the presence of pre-ordered structure at the very beginning of
crystallization, several isothermal relaxation experiments at different crystallization
temperatures were performed. For this purpose, different techniques were used.
Results 62
4.2.3.1 Frequency and time dependence of ε′ and ε′′ during isothermal
crystallization
The real part ε′ and imaginary part ε′′ of the dielectric permittivity were checked at
cooling the sample from the melt at 200 °C to the crystallization temperature at 140 °C at
1 K min-1. The time dependency of ε′ and ε′′ for the supercooled melt and its
development during isothermal crystallization at 140 °C can be seen from figure (4.25). It
is clear that ε′ increases for all frequencies studied and shows a maximum at 0.01, 0.05
and 0.11 Hz. As we discussed before, ε′ should be decreased at high frequencies due to
decreasing number of mobile dipoles at crystallization and therefore the increase in ε′ at
high frequencies is poorly understood. On the other hand, ε′′ shows the expected decrease
for all frequencies studied. Interestingly, ε′ starts to increase simultaneously with the first
change detected in ε′′ at 11,000 s (see vertical line). This behavior is in agreement with
that obtained from scan experiment (see figure 4.4) and therefore we could not show the
early stages of crystallization for iPP By DRS and DSC experiments under the assumed
conditions.
3.803.853.903.954.00
6
8
10
12
14
ε'
0.01 Hz 0.05 Hz 0.11 Hz 5.50 HZ 25.0 Hz 1 MHz
A
103 104 105
10-2
10-1
100
101
102
ε''
t in s
B
Results 63
Figure 4.25: Time dependence of the real part ε′ (A) and imaginary part ε′′ (B) of the
dielectric permittivity during isothermal crystallization of iPP at 140°C at different
frequencies between 0.01 Hz and 1 M Hz. Sample thickness is 2.3 mm.
4.2.3.2 Temperature dependence of the peak observed in ε′
In order to check the temperature dependencies of the observed peak in ε′, we performed
four isothermal measurements for iPP at different temperatures namely, at 135 °C,
137.5 °C, 140 °C and 142.5 °C and then presented here at 0.01 and 106 Hz (see Fig.
4.26). Changes in the dielectric permittivity at 106 Hz are very small and therefore
normalization of their values (ε′norm) for all curves is recommended. ε′norm is given as
ε′norm = ε′ (t)/ε′ (0), where ε′ (t) is the permittivity value detected at any time and ε′ (0) is
the permittivity value at the very beginning of crystallization. This was done to get the
dielectric permittivity the same at the beginning of isothermal experiment, where tiso = 0
and therefore comparing of dielectric permittivity behavior at different temperatures
becomes easier.
3
4
5
6
7
8
9
142.5 °C
140 °C
137.5 °C
ε'
0.01 Hz
135 °C
103 104 1050.998
1.000
1.002
1.004
1.006
1.008
1.010
1.012
1.014
1.016
t in s
106 Hz
Figure 4.26: Time dependencies of real part of the dielectric permittivity (ε′) at 0.01 Hz
and 106 Hz during isothermal crystallization of iPP at different temperatures. The
Results 64
absolute values of ε′ at106 Hz are normalized and denoted as ε′norm = ε′ (t)/ε′ (0). The
arrows indicate the simultaneous changes in ε′ at low and high frequencies for specific
crystallization temperature. Sample thickness is 2.3 mm.
The shift of the crystallization process to shorter times at lower temperatures
results from the increase of the crystallization rate with decreasing temperature. The
observed peak in ε′ at high frequencies (1MHz) should be not due to charge carriers
polarization processes appeared at low frequencies but due to other process and is not
completely understood. The arrows in figure (4.26) indicate the starting point of the
increase of ε′ at 1 MHz. This is the beginning of crystal formation at the specific
crystallization temperature. The increase in ε′ at 0.01 Hz starts simultaneously with the
first change detected in the normalized dielectric permittivity at 1 MHz. The maximum
values of ε′ at 0.01 Hz and for all the presented crystallization temperatures are different.
This result may be because of changing of sample geometry.
4.2.3.3 Time dependence comparison of ε′, tanδ and χc at crystallization
of iPP from different techniques
This part of work aims to perform comparable studies on iPP obtained from different
techniques namely, DRS, DSC and Dynamic Mechanical Analysis (DMA), see figure
(4.27). As the mechanical properties of a polymer strongly depend on crystallinity,
dynamic DMA can be used suitably.
Results 65
4
6
8
103 104 105
1
10
0.0
0.1
0.2
0.3
0.4
0.5
0.6
χc
DSC
(a)
137.5 °C
140 °C
142.5 °C145 °C
ε'
DSf = 0.01 Hz
(b)
f = 0.003 Hz
tan δ
t in s
DMA
(c)
147.5 °C
Figure 4.27: Time dependence of crystallinity χc obtained from DSC experiments
(part a), the real part of dielectric permittivity (0.01 Hz) obtained from BDS (part b) as
well as tan δ obtained from DMA (0.003 Hz) experiments (part c).
In addition to study the structural changes during crystallization of iPP by using DSC, a
comparison of the mechanical and dielectric relaxation behavior can give some insight
into the molecular processes because dielectric spectroscopy is sensitive to fluctuations of
dipole moments and mechanical relaxation monitors the fluctuations of internal stresses
[102]. The device used for this study was the Advanced Rheometric Expansion System
(ARES) from Rheometric Scientific with parallel plate geometry. The diameter of the
plates and samples was 25 mm, and their thickness was between 0.5 and 1 mm. the
measured quantity is the shear stress (σ ) in response to applied shear strain (γ). From
shear stress and shear strain one can calculate the complex mechanical modulus . We
discuss tan δ which equals the real part of shear modulus G′ over the imaginary part of
shear modulus G′′ (tan δ = G′ / G′′ ) because of it changes during polymer crystallization
and is independent on changes of sample geometry. The relation between the mechanical
properties and crystallinity is very complicated. Therefore, one can not easily calculate
crystallinity from quantities measured by DMA.
∗G
Results 66
Based on above, the behavior of ε′ at 0.01 Hz measured by DRS is compared with
the crystallinity χc obtained from DSC and tan δ obtained from DMA during
crystallization of iPP at different temperature (see Fig. 4.27). Dielectric permittivity
(part B) at 140 °C (for example) starts to increase after about 4,000 s (see vertical line).
The comparison with evolution of crystallinity from DSC (part A) shows that the
increasing of ε′ (part B) and crystal formation proceeds simultaneously. Also tan δ from
mechanical experiments decreases at the same time (part C). Accordingly, the presented
results for iPP show no information can be obtained from the different techniques about
the early stages of crystallization.
4.2.4 Isothermal measurements for Poly (ethylene terephthalate)
Imai et al. [39] have already reported a new finding concerning some structural change in
the amorphous state of PET which occurs during the so-called induction period before the
start of crystallization. That structure was investigated during annealing the amorphous
PET sample at 115 °C or 40 K above the glass transition temperature by small- angle X -
ray scattering (SAXS) and wide- angle X-ray scattering (WAXS) techniques.
4.2.4.1 Frequency and time dependence of ε′ and ε′′ during isothermal
crystallization
The behavior of real ε′ and imaginary ε′′ parts of the dielectric permittivity was tested at
cooling the sample from the melt at 290 °C to the crystallization temperature at 250 °C at
1 K min-1. The time dependency of ε′ and ε′′ of the super cooled melt and its
development during isothermal crystallization can be seen from figure (4.28).
It is clear that ε′ and ε′′ show a continuous decrease after 3,000 s (see vertical
line) with time at low and high frequencies. But at intermediate frequencies between
90 Hz and 3*103 Hz an increase in ε′ is observed again. Also, changes in the behavior of
ε′ and ε′′ for all frequencies studied with time takes place simultaneously at
approximately 3,000 s (see vertical line). This behavior is in agreement with that obtained
from scan experiment (see figure 4.5) and therefore we could not show the early stages of
crystallization for PET by DRS and DSC experiments under the assumed conditions.
Results 67
101
102
A
900 kHz
35 Hz
300 Hz
90 Hz
20 Hz
ε'
102 103 10410-1
100
101
102
103B
300 kHz
30 kHz
3 kHz
300 Hz
35 Hz
ε''
t in s
Figure 4.28: Time dependence of real part ε′ (A) and imaginary part ε′′ (B) of the
dielectric permittivity during isothermal crystallization of PET at 250 °C at different
frequencies between 20 Hz and 900 kHz. Sample thickness is 0.15 mm.
4.2.5 Isothermal measurements for isotactic polystyrene
Recently, Baskaran et al [103] studied the molecular relaxation and structure of isotactic
polystyrene (iPS) films using real time- dielectric spectroscopy and simultaneous wide
and small- angle X-ray scattering. Isothermal cold crystallization at temperatures of
Tc = 140 or 170 °C resulted in a sigmoidal increase of crystallinity with crystallization
time. They reported that, for the 140 °C sample, the dielectric permittivity increased as
crystallization proceeded up to four hours of crystallization and didn’t saturate on that
time scale. Also, for the 170 °C sample, ε′ also shows an increase initially and then
saturated after one hour. From both results, crystal development of iPS causes an increase
in the dielectric permittivityε′. The dielectric permittivity is associated with the
polarizability of the entire sample. The developing crystals systematically increase the
sample polarization during cold crystallization above Tg. In contrast, for the present work,
dielectric relaxation experiments were performed at isothermal crystallization when the
sample cooled from the melt.
Results 68
4.2.5.1 Frequency and time dependence of ε′ and ε′′ during isothermal
crystallization
The behavior of real ε′ and imaginary ε′′ parts of the dielectric permittivity was tested at
cooling the sample from the melt at 230 °C to the crystallization temperature at 210 °C at
1 K min-1. Therefore, the time dependency of ε′ and ε′′ of the super cooled melt and its
development during isothermal crystallization at 210 °C can be seen from figure (4.29).
At low frequencies (lower than 1 Hz) ε′ shows first a decrease and then an
increase with time. For high frequencies, higher than 102 Hz, ε′ decreases with
crystallization time. This decrease is attributed to decreasing number of mobile dipoles
due to crystals formation (see Fig. 4.29 a). On the other hand, ε′′ shows an increase at
frequencies above 1 Hz and no change can be seen at frequencies above 102 Hz. Also, the
changes in the behavior of ε′ and ε′′ with time take place simultaneously at approximately
17,200 s (see vertical line). Accordingly, this result means no information can be
obtained from DRS measurements about the early stages of crystallization taking place in
iPS under the assumed conditions. However a small peak observed just before drastically
change in ε′ and ε′′ in the time range between 4,000 and 14,000 s (for all frequencies
studied). This small peak is seen at the very beginning of the isothermal crystallization
experiment. Accordingly, this change may be considered as an indication of some
ordered structure formed at crystallization of iPS.
Results 69
104 1052
4
6
8
50
100
150
200
250
300
104 Hz
103 Hz
ε'
t in s(a)
0.05 Hz
0.5 Hz
102 Hz
(A) 0.01 Hz
104 1050.01
0.1
1
10
100
0.1 Hz
ε''
t in s(b)
0.01 Hz
1 Hz
105 Hz
107 Hz
(B)
Figure 4.29: Time dependence of the real part ε′ (A) and imaginary part ε′′ (B) of the
dielectric permittivity during isothermal crystallization of iPS at 210 °C at different
frequencies between 0.1 Hz and 107 Hz. Sample thickness is 0.15 mm.
Discussion . 69
5. Discussion
Study of relaxation processes related to structural changes at crystallization of semi-
crystalline polymers, particularly at the early stages, seems to be of interest in polymer
physics.
Based on the results presented in Chapter 4, most of the successful results dealing with
early stages of crystallization were obtained during isothermal crystallization of poly (ε-
caprolactone). Accordingly, very much attention and detailed discussion of this part
should be taken into our consideration.
Besides, some interesting results relating structural change at the early stages of
crystallization were obtained during isothermal crystallization of poly (oxymethylene).
Additional results concerning crystallization of isotactic polypropylene, poly (ethylene
terephthalate), polyethylene and isotactic polystyrene were also interpreted and
discussed.
5.1 The pre-ordered structure formed at crystallization of PCL In this section, discussion of the results concerning the early stages of crystallization
taking place in PCL, based on two steps,
1- Discussion of the results obtained from a combination between the dielectric and
calorimetric experiments; in particular, the pronounced effects in ε′ at low
frequencies which are observed long before changes in crystallinity can be detected
[106].
2- Discussion of the pronounced effects in ε′ at low frequencies by simultaneous X-ray
scattering and dielectric experiments [107].
5.1.1 Discussion of pre-ordered structure by dielectric relaxation experiments
In order to discuss the charge carrier processes which are influenced by formation of the
pre-ordered structure at the very beginning of, we would like to answer the question:
How can we understand the early decrease and increase in ε′ at low and intermediate
Discussion . 70
frequencies, respectively, for the thin PCL sample during isothermal crystallization?
Accordingly, we divide the discussion into three parts:
(i) The high frequency range, were dipole relaxations can be followed without
contributions from charge carrier polarization and conductivity.
(ii) Contributions from electrode polarization for the thin sample at low frequencies.
(iii) For the thick samples, electrode polarization can be neglected and therefore, the
unexpected maximum in ε′ is really related to MWS polarization.
(i) The measurements during isothermal crystallization of PCL were performed at
such high temperatures that the dispersion zones of dipole relaxation processes, like α-
relaxation (dynamic glass transition) or ß- and γ - relaxation (local relaxations) are above
the frequency window of the measurements discussed here, see figure (4.10). Therefore,
all dipoles are relaxed and contribute to permittivity. At frequencies higher than 103 Hz
for ε′ and 105 Hz for ε′′ contributions from charge carriers to the dielectric permittivity
can be neglected. During crystallization, at least the dipoles, which are incorporated into
the crystalline regions, will no longer contribute to the permittivity because of the
missing mobility. With ongoing crystallization, consequently, a decrease of ε′ as well as
of ε′′ is expected and seen in figure 4.16 (A and D) and figure 4.17 (A and C). a similar
behavior can be seen during isothermal crystallization of Polyoxymethylene at
frequencies higher than 103 Hz for ε′ and 0.1 Hz for ε′′, that is shown in figure 4.24 (A
and C).
The comparison with the decreasing non-crystalline fraction during crystallization
shows a perfect agreement. This expected behavior at high frequencies is also a proof for
identical crystallization kinetics in the dielectric measuring cells and the calorimeters. For
PCL, main parameter for the identical kinetics is the same sample temperature.
Therefore, we can be sure to have same crystallization temperatures in the different
devices. Also the influence of sample thickness on crystallization kinetics is well
reproduced in dielectric and DSC measurements.
(ii) For the thin sample, electrode polarization yields the extremely high values of
permittivity at low frequencies. This was proven by measurements with a much thicker
Discussion . 71
sample, which does not show such large values. Electrode polarization is due to charge
carriers traveling between the electrodes and yielding an electric double layer at the
electrodes. These double layer increases the real and the imaginary parts of the
permittivity. For dc- conductivity, in contrast, only a contribution to ε′′ is expected. For
the isothermal crystallization experiments we observe a monotone decrease in ε′ and ε′′
see figure 4.16(C and F). The interesting point here is the very early decrease in real and
imaginary parts of the dielectric permittivity compared with the decrease of the non-
crystalline fraction in the sample. There must be a decrease of the number of charge
carriers traveling between the electrodes. For the main crystallization, one can expect a
decreasing number of mobile charge carriers because some of them will be incorporated
in the crystals and will be blocked. But at the very early stages, it is hard to imagine that
charge carriers are blocked by the assumed pre-ordered structures or some nuclei. It
seems to be more reasonable to assume a reduction of mobility of the charge carriers.
May be this reduction of mobility is due to some trapping of charge carriers at the
interfaces of the pre-ordered structures. Because the decrease in ε′ and ε′′ starts
significantly earlier than the decrease of the non-crystalline fraction, other structures than
crystals formed in the bulk must be considered to explain the observed behavior.
Electrode polarization is related to charge carriers traveling between the electrodes. To
affect mobility on such length scales, it needs structures influencing the whole sample
volume and not only small spots like nuclei.
(iii) The contribution of electrode polarization to permittivity can be reduced by
much thicker samples or higher frequencies. As can be seen in figure (4.14), where
electrode polarization is reduced by using larger sample thickness we see some
peculiarity starting at the same time as the reduction of electrode polarization discussed
in (ii). Also for the thin sample at medium frequencies, we observe a maximum in ε′ and
a decrease in ε′′ starting at the same times as the decrease of electrode polarization.
Because electrode polarization can be neglected under these particular conditions,
electrode polarization and processes related to the interaction between electrode and
sample can not be the origin of the increasing ε′ seen in figures (4.12) and (4.15).
Discussion . 72
The observed maximum in ε′ can also not be explained by changing dipole mobility
during crystallization because this always results in a decrease of ε′, as discussed in
section (i). Electrode polarization alone can not explain the observed maximum because
it appears also under experimental conditions where electrode polarization is avoided due
to larger sample thickness, as shown in figure (4.15), or higher frequencies, see
figure (4.12) at frequencies between 2.5 Hz and 250 Hz. The reason for the increase and
the resulting maximum in ε′ between 30,000 s and 40,000 s in the frequency range under
consideration must be another one. The increase of ε′ can only be explained under the
assumption of at least one additional process. This process, which is not present in the
supercooled, equilibrated melt, appears during annealing at the crystallization
temperature. The increasing permittivity can only be explained by an additional dipole
moment, as e.g. discussed for a cross linking system [104], or by the formation of
additional internal surfaces, which results in a Maxwell/Wagner/Sillars (MWS) process,
different from electrode polarization. These additional dipole moments or interfaces must
be created before crystallinity can be detected by DSC. The result is an increasing
permittivity during the induction period of isothermal crystallization. For
Polyoxymethylene, the increase in ε′ at frequencies below 0.9 Hz at crystallization may
be also interpreted as additional internal surfaces as discussed for PCL. Such behavior is
clear in figure 4.24B. This increase takes place earlier, before the non-crystalline fraction
start to decrease (crystallization starts), see figure 4.24D. As a result, this effect may also
give us some hints about formation of some ordered structure before the main
crystallization process.
The formation of really crystalline structures on the other hand reduces dipole and
charge carrier mobility and consequently, the permittivity decreases with ongoing time
yielding in the superposition of the maximum in ε′. The right hand side of ε′ peak is seen
just when crystal formation starts and some dipole and charge carrier processes are
freezing. The corresponding times for the different temperatures are marked in figure
(4.20) by arrows. With increasing crystallinity more and more, dipole and charge carrier
polarizations are hindered and finally ε′ decreases. This is in analogy to the behavior at
high frequencies; see figures (4.16) and (4.17).
Discussion . 73
The formation of new molecular dipoles before crystallization seems unrealistic.
Therefore, the formation of internal surfaces and the resulting MWS process seems
responsible for the increase in ε′. This must happen before crystal formation. But how
one can understand the appearance of additional surfaces in the melt before crystal
formation? One possibility would be the known surface induced crystallization at the
electrodes. The result would be a thin crystalline layer, which covers the electrodes. The
dielectric contrast between the remaining amorphous sample and the crystalline layers
would result in an additional MWS process and consequently, an increasing permittivity.
For electrode polarization the mean relaxation time EPτ is given as [52]
D
sEP L
D20
0
σεετ ≈ (5.1)
Where ε0 is the vacuum permittivity, εs is the static permittivity, σ0 is the dc-
conductivity, D is the sample thickness and LD is the effective thickness of the double
layer at the electrodes. If a transcrystalline layer affects LD, one would expect a shift
towards higher frequency with increasing transcrystalline layer thickness. This is not
observed in our measurements. The position of the peak observed in ε′ is frequency
independent.
With increasing sample thickness, one would expect a shift towards lower
frequencies and the influence of electrode polarization would become smaller. This is
observed in figure (4.14), compared to figure (4.11). But the measurements in figure
(4.15) show also for a 5 mm thick sample, a peak in ε′, which is comparable to the thin
sample. Therefore, the formation of thin crystalline layers directly at the electrodes can
not be the origin of the additional internal surfaces with dielectric contrast. It has to be a
bulk property.
In figure (4.12), in the frequency range between 16 Hz and 100 Hz, ε′ stays
constant at the end of the crystallization process, but at a higher value compared to the
supercooled melt. The same is observed for the thicker sample at frequencies below
100 Hz, see figure (4.15). In the just described picture, this is only possible if the newly
formed surfaces survive main crystallization together with the corresponding MWS
process, what seems to be reasonable.
Discussion . 74
Let us assume pre-ordered structures in a polymer melt before crystal formation as
discussed by Strobl [43]. During pre-ordering, a quasi parallel alignment of chain
segments lead to the formation of a mesomorphic phase with additional internal surfaces
between the mesomorphic structures and the surrounding entangled polymer melt. Our
results are in agreement with such a picture.
5.1.2 Discussion of pre-ordered structure by simultaneous SAXS/ DRS
experiments
To evaluate the structural change during crystallization of PCL, the non-crystalline
fraction (1-invariant) from SAXS and the real part of the dielectric permittivity ε′ from
DRS as a function of crystallization time were discussed.
In Figure (4.21), the decrease in real part of the dielectric permittivity ε′ at
frequencies higher than 320 Hz starts after approximately 80 min. At these frequencies, ε′
behaves exactly as expected from the decreasing amount of the non-crystalline structure
(1-invarainat), as observed from DSC experiments (for details see Figs. 4.16 and 4.17).
This again proves that we were following at high frequencies the crystallization directly.
Based on above, our findings obtained from DRS, DSC and SAXS shed some new light
on the ongoing discussions on polymer crystallization. Upon cooling PCL, some
preordering has already observed before crystallization starts [106, 107]. This is also
proof that crystallization is a multi-step process [43].
5.2 Discussion of dielectric relaxation experiments for isotactic
polypropylene, poly (ethylene terephthalate), polyethylene and
isotactic polystyrene For iPP, PE, PET and iPS changes in the real part of the dielectric permittivity ε′ started
simultaneously with the first change detected in heat flow from DSC experiment or ε′ at
high frequencies. This means nothing can be seen prior crystal formation for such
polymers under the assumed conditions. The possible reasons for this behavior may be
attributed to the external conditions applied to these polymers. For example, the
crystallization and melting behavior of iPP are closely related not only to the external
Discussion . 75
conditions such as undercooling and cooling rate, but also to the molecular weight,
molecular weight distribution and chain structure characteristics such as tacticity
distribution [105]. Also, one of the possible reasons may be attributed to the small
differences between the assumed pre-ordered structure and the surrounding melt in
morphologies of these polymers do not influence the dynamics of charge carriers
polarization processes (MWS or electrode polarization).
Conclusion . 76
6. Conclusion
Our findings may be summarized as follows.
During the crystallization of poly (ε-caprolactone) (PCL), pronounced effects in ε′ are
observed before changes in crystallinity can be detected. Especially for isothermal
crystallization two observations strongly support the idea of pre-order in the polymer
melt before the formation of crystals [106].
(i) Electrode polarization is reduced significantly before crystallinity changes can
be detected. Indicating that the structure formation at early stages reduces charge carrier
mobility on length scales comparable with sample thickness, which is of the order 1 mm.
(ii) In cases where electrode polarization is not dominating permittivity an
increase in ε′ due to the formation of internal surfaces and finally a maximum is
observed. The increase in ε′ starts again much earlier than changes in crystallinity can be
detected. The start time of the increase in ε′ corresponds to the start time of the reduction
of electrode polarization.
The structures formed at the early stages of polymer crystallization reduce charge
carrier mobility on large length scales which are related to electrode polarization. The
same structures yield additional Maxwell/Wagner/Sillars relaxation processes, which
result in an increase of ε′ at intermediate frequencies. The reduction of the large scale
charge carrier movements (reduction of electrode polarization) supports the idea of large
scale structures formed at the early stages of polymer crystallization rather than the
formation of a large number of small structures (nuclei).
A simultaneous SAXS/DRS experiment verified that at high frequencies dielectric
permittivity depends on changes in crystallinity (non-crystalline fraction) only. For this
experiment the pronounced effects observed in ε′ at low frequencies [106] were observed
long before crystallinity can be detected too [107].
Summary . 77
7. Summary A great deal of effort has been devoted in literature in studying the early stages of
crystallization by scattering techniques such as SAXS, WAXS, and differential scanning
calorimetry. These techniques depend on the probably small electron density contrast
between the assumed pre-ordered structure and the surrounding super cooled melt. Most
of these studies have been therefore limited to the observation of crystal growth processes
and little information exists about the early stages of polymer crystallization. Therefore,
there are still a lot of unanswered questions concerning crystallization. In contrast,
dielectric spectroscopy related to the dynamics of dipoles and charge carriers is known to
be one of the most sensitive techniques to detect the relaxation behavior associated to
even weak changes in polymeric structure. Dipole polarization is seen in common
relaxations processes like α, β and γ. Charge carrier polarization on the other hand, results
from the separation of charges (Maxwell/Wagner/Sillars or electrode polarization). So,
the present study was considered as one of the most important attempts which done to
give good information about the early stages of polymer crystallization by means of
dielectric relaxation experiments. At these early stages, some ordered structure were
formed during cooling the polymeric material from the melt.
For pre-ordered structures one expects changes in mobility due to changes in
chain conformation during pre-ordering. But without additional morphological
information, the interpretation of relaxation experiments is often speculative. Therefore, a
combination between differential scanning calorimetry, SAXS and dielectric relaxation
experiments close to the melting temperature (melt crystallization) were performed. The
differential scanning calorimetry (DSC) was used for different samples to investigate the
time dependence of crystallinity. We performed isothermal crystallization experiments
for thin and thick PCL samples. Pronounced effects in ε′ at low frequencies (between
0.01 and 250 Hz) were observed long before changes in crystallinity can be detected. For
high frequencies, where dipole relaxations instead of charge carrier processes and
conductivity influence the dielectric signal, ε′ shows the expected decrease
simultaneously with the increase in crystallinity. Also, it was found from Arrhenius
diagram at temperature between 40 and 60 °C that the maximum position of common
Summary . 78
relaxation processes is above 1 MHz and therefore the effects observed in ε′ at low
frequencies are not due to one of these relaxation processes. These effects were
considered as one of the most important results relating to some ordered-structure formed
before crystallization [106]. This pre-ordered structure strongly affects the charge carrier
processes only (Maxwell/Wagner/Sillars polarization) and was considered to be related to
an additional internal surface formed at the very beginning of crystallization. Therefore,
interpretation and explanation of the early stages of crystallization on the basis of dipole
polarization was excluded.
Because of DSC experiments give only an indirect link to morphology, we used
X-ray scattering experiments which give access to morphology directly. Accordingly, a
combination between small angle X-ray scattering (SAXS) and dielectric experiments
were carried out to get simultaneous information during changes in morphologies and
dynamics for PCL at isothermal crystallization (at 53 °C). In order to avoid the problems
arising from separate experiments, a special sample cell was designed [107]. SAXS
experiments were carried out at the European Synchrotron Radiation Facility (ESRF) in
Grenoble, France [77]. At high frequencies ε′ follows, as expected, the decreasing
amount of the amorphous material, as revealed from DSC experiments [90]. This proves
again that we were following at high frequencies the decreasing number of mobile
dipoles only and obtain a direct measure of crystallinity. For low frequencies, similar
pronounced effects in ε′ were observed again long before a decrease of the non-
crystalline fraction (1-invariant) from SAXS experiments can be detected. Accordingly,
all observations obtained from dielectric relaxation experiments in addition to
calorimetric and X-ray scattering experiments support the idea of pre-ordered structures
formed before crystallization.
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Appendix
App. [1] Dielectric Measuring program
• Connect the sample cell to BDS device.
• Connect the computer controlling the system to BDS device.
• Have a look at the whole system before starting measurement, and make sure that
everything is set up in the right way.
• Switch on BDS Device by using four buttons (Mains, Vacuum, Mains and Load) which
they are located on the front panel, and then turn on the computer.
• Use the six white buttons located below the display of the QUATRO. These buttons
used to set PID of liquid nitrogen or Dry gas N2 mode, since each of them has its own
mode. The first button on the right hand used to set and to check all other parameters.
In the case of using liquid nitrogen we have to set the Iec address = 6.
• Put the sample which should be measured between the two electrodes of the sample
cell.
• Apply the measurement you using WinDETA software program supplied from
Novocontrol.
• Go to Temperature Controller, then select Initiation from WinDETA, and then go to
Activation to set the temperature at around 23 °C.
• Go to File, then select Set file name to write the name of the experiment.
• Measurement
Select the Sample specification to write thickness and diameter of the sample.
Go to start conditions, then set the starting temperature and frequency.
Go to End conditions, then set the end Temperature and frequency.
Select List order to define the order of the temperature and frequency loops.
Select value list, from which the temperature and frequency points can be chosen.
Select Averaging to enter the Averaging option which determines the number of points
between 0.01 and 107 Hz. Then Start the Experiment.
Selbstständigkeitserklärung
Ich versichere hiermit an Eides statt, dass ich die vorliegende Arbeit selbstständig angefertigt und ohne fremde Hilfe verfasst habe, keine außer den von mir angegebenen Hilfsmitteln und Quellen dazu verwendet habe und die den benutzten Werken inhaltlich und wörtlich entnommenen Stellen als solche kenntlich gemacht habe. Rostock, 07.11.2005
Lebenslauf Persönliche Daten
Name: Ragab M. Soliman
Geburtsdatum: 24.12.1966
Geburtsort: Kairo Stadt
Familienstand: verheiratet
Schulausbildung
1972 - 1978 Grundschule: Kairo, Ägypten
1978 - 1985 Gymnasium: Kairo, Ägypten
Hochschulausbildung
1986- 1991 Bachelor Studium der Physik an der Universität Helwan, Kairo,
Ägypten
1992-1993 PreMaster Studium an der Universität Helwan, Kairo, Ägypten
1993-2000 Forschungsassistent am Nationalen Zentrum für Forschung, Kairo,
Ägypten
1999 MSC der Physik
Ab 1999 Lecturer assistant am Nationalen Zentrum für Forschung, Kairo,
Ägypten
2000-2002 Doktorand am Nationalen Zentrum für Forschung, Kairo, Ägypten
ab 01.07. 2001 Promotionsarbeit an der Universität Rostock
List of publications 1. A.M. Ghoneim and R.M. Mahani. “Electrical and mechanical properties of some
composites with polymeric matrix”. Inter. J. Polymeric Matter 2001, 50, 141.
2. Wurm A, Soliman R, Schick C. “Early stages of polymer crystallization – a dielectric
study”. Polymer 2003, 44, 7467.
3. Wurm A, Soliman R, Schick C. “Evidence of pre-crystalline-order in super-cooled
polymer melts revealed from simultaneous dielectric spectroscopy and SAXS”. J.
Non-Cryst. Solids 2005, 351, 2773.
Acknowledgements
This work was carried out at the University of Rostock, Germany, Institute of Physics,
Polymer Physics group under the supervision of Prof. Dr. Christoph Schick. The Project
was financially supported by the German Science Foundation (DFG) Grant Schi 9-1 and
the Government of Egypt.
First of all, I would like to express my profound gratitude to Prof. Dr. Christoph
Schick for suggesting the subject of research and for his generous support throughout the
duration of this work.
I would like to express my warm thanks to Dr. Andreas Wurm, Institute of
Physics, Rostock University for his continuous help and advice during my work. Thank
you very much for your generous help.
I give my profound thanks to all the staff of Polymer Physics Group, Rostock
University, because they really let me feel as if I am at my home institute.
I acknowledge valuable discussions with A. Schönhals, Berlin, I. Alig, Darmstadt,
and F. Kremer, Leipzig.
I sincerely thank Dr. Wim Brass, European Synchrotron Radiation Facilities
(ESRF), Grenoble, France for his generous help and facilities of small angle X-ray
scattering technique. I sincerely thank Dr. Han Goossens working in Eindhoven
University of Technology, Chemical Engineering and Chemistry, The Netherlands for his
great efforts to arrange small angle X-ray scattering experiment.
I would like deeply thank Prof. Dr. Ahmed Ghoneim (National Research Center,
Microwave Physics Department, Egypt, Cairo) for his great efforts to get me this good
chance to work with Prof. Dr. Christoph Schick group. Thank you very much; really you
deserve a lot because you always give me the helping hand.
Finally, I would like to express my gratitude and thanks to my beloved wife, Amal
A. Gomaa, for her love, understanding, encouragement and support throughout the
duration of my Ph. D. work.