Simulation of Structural Transition in an Isotropic Melt of Nematic and
Smectic Polymers
V. B. ROGOZHIN, S. G. POLUSHIN, A. A. LEZOVA, G. E. POLUSHINA, A. S. POLUSHIN
Department of Physics,
St. Petersburg University,
7-9 Universitetskaya Embankment, 199034, St Petersburg,
RUSSIA
Abstract: - The isotropic phases of four fractions of a mesogenic comb-shaped polymer were studied using the
electric birefringence method. The fractions have either nematic – isotropic melt, or smectic-A – isotropic melt
phase transition, depending on the degree of polymerization. All samples showed a structural transition in
isotropic phase. Mathematical modeling of the electro-optical properties was performed based on the modified
Landau-De Gennes theory using three- order parameters. The reason for the transition in the isotropic phase is
the mutual rearrangement of the polar side groups of the polymer as a result of dipole-dipole interaction.
Key-Words: - comb-shaped polymer, short order, Kerr effect, iso - iso transition, mathematical modeling,
dipole - dipole interaction.
Received: June 16, 2023. Revised: November 27, 2023. Accepted: January 2, 2024. Published: February 12, 2024.
1 Introduction
Structural transitions in the isotropic phase (iso-iso)
are an interesting but insufficiently studied
phenomenon. They are found in simple substances,
[1], [2], [3], [4], in low molecular weight liquid
crystals, [5], [6] and in flexible chain polymers, [7],
[8], [9], [10]. Such transitions have also been found
in liquid crystalline polymers. Liquid crystal
polymer materials are widely used nowadays. It is
important to understand the physical properties of
their isotropic melts to use them, since the isotropic
state is used in production process technologies.
Furthermore, structural transitions in the isotropic
phase can affect the properties of the liquid
crystalline phase of a polymer material. This has
been shown in works, [11], [12], [13]. The P8*NN
comb-shaped chiral LC polymer was found to have
bistable phase behavior. It forms either a smectic-A
phase or a TGB phase upon cooling. This depends
on the cooling rate of the isotropic melt. A follow-
up study of P8*NN using the electro-optic (the Kerr
effect) and X-ray scattering methods has shown that
there is a structural transition in the isotropic phase.
The transition is apparently associated with chirality
of the polymer, since the same effects were found in
the isotropic phase of chiral low molecular weight
liquid crystals. The presence of such a transition in
P8*NN made it possible to explain the reason for
the existence of two alternative liquid crystalline
phases, [13]. In [14], two comb-shaped copolymers
were studied by electro-optic methods. They
contained both mesogenic side groups and
isophthalic acid groups in their structure. The
isotropic phase was conventional for a sample with
a fraction of acid groups of 18 mol %. The iso-iso
transition appeared after increasing the proportion of
acid groups to 37 mol %. In this case, the transition
is caused by microphase separation due to a
significant difference in the physicochemical
properties of the monomer units of the copolymer,
[15]. It should be noted that iso-iso transitions also
exist in conventional flexible chain polymers that do
not have a mesophase, such as polystyrene, [7], [8],
[9], [16]. They are caused by a change in the
cooperativity of the segmental thermal motion of
macromolecules in a narrow temperature range near
the temperature of the structural transition. As
temperature rises, kinetic flexibility or “chain
melting” increases. This is a common phenomenon
for polymer melts. Thus, we can conclude that iso-
iso transitions in various polymers are not
uncommon. Their appearance is due to the structural
features of macromolecules. And the nature of the
transition can be associated with a number of
reasons, such as temperature changes in dynamics of
the main chain, chirality of the molecular system,
heterogeneity of its chemical composition, and so
on.
This work is a continuation of studies of iso-iso
transitions in polymers. In this regard, we have
selected a series of liquid crystalline comb-shaped
polymers of the same structure, differing from each
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DOI: 10.37394/23202.2024.23.12
V. B. Rogozhin, S. G. Polushin,
A. A. Lezova, G. E. Polushina, A. S. Polushin
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other in the length of the main chain and the type of
liquid crystalline phase.
2 Problem Formulation
The choice of research objects is due to the fact that
we have discovered signs of a structural transition in
an isotropic melt of one of these polymers
previously, [17]. The selected polymers do not have
chirality; the side groups have the same chemical
nature. It follows that in this case a new version of
the iso-iso structural transition is observed.
Presumably, it is associated with the dipole-dipole
interaction of polymer molecules. This work is
devoted to the experimental and theoretical study of
a new short-range order effect.
We use a conceptually new approach to study
the electro-optical effect in the isotropic melt.
Previously, the properties of the isotropic phase of
low- and high-molecular mesogens have been
studied in the range from the temperature of the
isotropic melt-LC phase transition, , to
temperatures that are no more than 20-30 degrees
higher. Both the value of the Kerr constant and its
relative change are maximum under these
conditions. In addition, the physical effects in this
temperature range are well described by the Landau-
De Gennes theory of phase transitions. We have
expanded the research area. The properties of the
isotropic phase were studied over the entire
temperature range available for measurements.
Mathematical modeling was performed for the same
temperatures.
Polymer fractions with an acrylic main chain
and mesogenic side groups were studied. The
molecular weights of the fractions are in the region
of transition from oligomers to polymers. For this
reason, phase properties vary significantly with
changes in molecular weight. We have set the
following tasks:
1. The study of polymer fractions where
different types of transition are realized:
nematic-isotropic melt and smectic-A-
isotropic melt.
2. The measurement of the Kerr effect in the
isotropic melt over a wide temperature range
and with an accuracy sufficient to detect
possible structural transitions.
3. The modeling of electro-optical properties of
the isotropic phase of liquid crystalline
polymers based on the obtained experimental
data.
3 Problem Solution
3.1 Material and Method
The four fractions studied are designated as P-15, P-
86, P-200, and P-572, where the numbers
correspond to the degree of the sample
polymerization. The structure of the monomer unit
is shown in Figure 1. The polymer synthesis and the
phase behavior of the fractions were described in
[18]. The samples have either a nematic and
smectic-A phase (P-15, P-86 samples), or only a
smectic-A phase (P-200 and P-572 samples),
depending on the degree of polymerization. Thus, P-
15 and P-86 polymers undergo a nematic – isotropic
phase transition, while P-200 and P-572 polymers
undergo a smectic-A – isotropic phase transition.
CNO
(CH2)5
OC
O
[ CH2 CH ]
Fig. 1: Structure of a monomer unit
The isotropic melt was studied by the Kerr
effect method. The magnitude of birefringence ΔnE
induced by an electric field is related to the Kerr
constant K and the electric field strength E by the
relation ΔnЕ=КЕ2. The value of K is calculated from
this. The measurements were carried out using a
pulsed rectangular field with a strength E of up to
1.5×103 V/cm. The duration of each pulse did not
exceed 100 ms, the interval between pulses reached
several seconds. A highly sensitive compensation
method for measuring birefringence was used with
the application of an elliptical light polarization
modulator, [19]. This made it possible to measure
induced birefringence of less than 10-9.
Measurements of the Kerr constant K were made
both when the temperature increases and when it
decreases. Thermostatting was performed at each
temperature point with an accuracy of 0.1 degrees
for 15-20 minutes, followed by measurements. The
temperature dependence of K was completely
reproducible, that is, temperature hysteresis of K or
polymer destruction was not observed.
3.2 Experimental Results
The results of measurements in the isotropic phase
over a wide temperature range are presented in
Figure 2. An important feature is the division of the
general dependence 1/K=f (T) into two straight
segments with different slopes. Apparently, this is
due to changes in molecular packing and short-
range order. On this basis, we can talk about the
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V. B. Rogozhin, S. G. Polushin,
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presence of two isotropic phases and the transition
between them.
a)
b)
c)
d)
Fig. 2: Temperature dependences of the inverse Kerr
constant for samples P-15 (a), P-86 (b), P-200 (c),
and P-572 (d). Experimentally obtained inverse
values of the Kerr constant are indicated by points,
theoretically calculated values are shown by solid
lines.
We can assume the following mechanism of
structural transition in these polymers. The side
groups have a dipole moment. Its magnitude is
approximately 5 D, and the dipole is directed along
the axis of the group. The architecture of the comb-
shaped macromolecule forces neighboring side
groups, and hence their dipoles, to be oriented
parallel to each other. The energy of the dipole-
dipole interaction is high, therefore, such an
arrangement is energetically unfavorable for them.
They strive to take an antiparallel position whenever
possible. The temperature rise increases the
flexibility of the polymer chain by rotating the units
around single bonds. As a result, when the critical
temperature is reached, some of the side groups are
rearranged into a more stable antiparallel
orientation, [20]. Consequently, the molecular
effective dipole moment decreases, which manifests
itself in a change in the temperature dependence of
the Kerr constant.
The strong dipole interaction of alkoxy-
cyanbiphenyl molecules, which are used as side
groups in the polymer, is confirmed by experiments
and calculations. In [21], it was found that most of
the neighboring 8CB molecules are oriented
antiparallel using the molecular dynamics method.
This pattern is performed in all phases, including
isotropic. Neutron and X-ray scattering methods
showed that the layered structure is formed in alkyl-
and alkoxy-cyanbiphenyls by a double molecular
layer with partial overlapping of the layers, [22].
This also means a predominantly antiparallel
orientation of the polar mesogenic groups.
3.3 Modeling
The Landau-De Gennes theory, which was
originally developed for nematics, is successfully
used to describe the electro-optical properties of the
isotropic phase in the region of transition to the
liquid crystalline phase, [23], [24]. Later, versions
of this theory were extended to the case of isotropic
phase – smectic-A phase transitions, in the
description of which it is necessary to use both
orientational and translational order in calculations,
[17], [23], [24], [25], [26]. Further complications of
the theory were associated with the fact that
structural transitions were discovered in polymer
melts, at which a sharp change in the temperature
dependence of the electro-optical constant K was
observed. The reason for this behavior of the melt
was different, including microphase separation of
molecular fragments with different chemical natures
and chirality of the molecules, [14]. In these works,
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another, third order parameter was introduced in
addition to the orientational and translational order
parameters. It was used in work [14], where
microphase separation in a copolymer that had
chemically dissimilar side groups was discussed.
The parameter was called “microphase”, and we
will use the term in this work, but its meaning is
much broader. It is responsible for rearrangements
at the molecular level. Electro-optical
measurements, which were carried out in our work,
also demonstrate a complex dependence of the Kerr
constant on temperature (Figure 2). This is due to
the dipole-dipole interaction of the polar side groups
of the polymers. The change in the mutual
orientation of such groups should be especially
considered in the calculations, since they, unlike the
units of the main chain, form short-range order in
the melt. Therefore, to describe the experimental
results, we use the theoretical model of the electro-
optical effect that we have developed, which also
includes the third order parameter.
The electro-optical properties of liquid
crystalline polymers in the vicinity of the isotropic
liquid – liquid crystal phase transition temperature
can be described using the Landau-De Gennes
phenomenological approach. According to this
approach, the Helmholtz energy of the polymer melt
(F) is expanded into a series of powers of the
orientational (S) and translational () order
parameters. The presence of fragments with
different chemical natures in the composition of
macromolecules can lead to the appearance of a
large number of disordered microdomains in the
melt. Such a microstructured phase can exist even in
the absence of orientational ( ) and layer (
) ordering, [27] and is characterized by the
microphase separation parameter . The measured
quantity in experiments to determine the electro-
optical properties of copolymer melts is the Kerr
constant , where is the birefringence.
To calculate the value of K, it is necessary to add the
summand to the expression for calculating the
Helmholtz energy, considering the influence of the
electric field, [24], where
, is
the dielectric anisotropy of the melt at S = 1. Due to
the smallness of the orientational ordering induced
by a weak electric field, the expansion of the
Helmholtz energy can be limited to summands of no
higher than the second degree in S, [24].
In this case, the energy of the melt F can be
expanded into a series in powers of S, , and
parameters as follows:
(1)
where А, е, and α coefficients depend on the melt
temperature Т: , ,
, while , , , , , and
have a positive value. The remaining expansion
coefficients are assumed to be independent of
temperature.
The choice of degrees of expansion parameters
in relation (1) is determined by the necessity to
comply with experimental data. It allows one to
describe the behavior of the melt in the vicinity of
first kind phase transitions into nematic and smectic
states with discontinuous changes in S and
parameters. The summands proportional to the first
powers of the expansion parameters are absent in
expression (1), since they exclude the possibility of
the existence of an isotropic phase, where S, , and
are equal to zero. We can leave only summands
with even degrees to describe layer ordering in
equation (1), since [24], [25]. The
summands containing , , and
products are introduced to consider the mutual
influence of these parameters.
Minimization of the Helmholtz energy (1)
according to , , and
expansion parameters allows us to
determine the conditions for the equilibrium
existence of the smectic, microstructured and
nematic phases, respectively (2-4):
(2)
(3)
(4)
Thus, the parameter values of in (2)
correspond to the presence of layer ordering and,
accordingly, the presence of the smectic phase.
Wherein:
(5)
The parameter corresponding to this state in
this case is expressed as:
) (6)
where:
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The simultaneous solution of the system of
equations (4-6) by numerical methods makes it
possible to determine the equilibrium values of the
order parameters at a given temperature in the
smectic phase.
The trivial solution (2) corresponds to the
absence of layer ordering and, accordingly, the
smectic phase. For this case, we obtain expression
(7) from condition (3) for ѱ>0. Expression (4),
which meets the condition of equilibrium existence
of the nematic phase at , is transformed into
(8), from which the value of the orientational order
S can be calculated considering (7):
(7)
(8)
The parameter ѱ cannot take negative values; its
smallest value is
0
. In this case, expansion (1)
takes the form (9), and expression (4) transforms to
the form (10):
(9)
(10)
Thus, in the temperature region where
microstructuring is absent ( ), expression (9)
fully corresponds to the expansion of the Helmholtz
energy in the Landau-De Gennes form for nematics,
[23], [24].
Finally, let us consider two possible states of the
melt, where the orientational ordering parameter is
S=0 in the absence of an electric field (W=0). The
state in which , , ѱ > 0 can be
considered as a separate microstructured phase,
consisting of microdomains randomly distributed
throughout the entire volume of the melt.
Expression (7) in this case takes the form (11):
(11)
Coefficient е depends on temperature as
. Respectively, (11) is chosen as a
solution when , and when , the second
case is realized from the non-negativity condition of
, when corresponds to the solution to
equation (3). This case corresponds to an isotropic
state. That is why value can be considered
as the temperature of transition from the isotropic
phase to the microstructured one. There is no jump
in the microphase ordering parameter at
P
TT
,
and such a transition can be considered a second
kind phase transition.
Turning to a discussion of the electro-optical
properties of isotropic copolymer melts, it should be
emphasized that the appearance of even a very weak
electric field (W>0) inevitably induces long-range
orientational ordering SЕ>0 in the temperature
range, where there is no long-range orientational
ordering in the absence of a field. This is due to the
partial orientation of mesogenic fragments of
macromolecules by the electric field. Such ordering
is extremely small due to the smallness of the
electric field in comparison with the orientational
ordering in the nematic or smectic phases. The value
of SЕ directly depends on the field and is determined
by the shift of the minimum Helmholtz energy from
the position S=0 at W=0 to the region of positive
values SЕ>0 at W>0. The position of this minimum
is determined directly by formulas (1), (7)-(11).
One of the main measured quantities in electro-
optical experiments is the Kerr constant
, where is the birefringence in a fully
oriented phase (S=1), is the orientational order
parameter in the presence of an external electric
field with strength Е, [19], [23], [24].
The expansion of the Helmholtz energy F can
be limited to summands of no higher than the
second degree according to [23], [24], due to the
smallness of the orientational ordering induced by a
weak electric field.
In the isotropic phase, where there is no
microphase separation, the expression for
coincides with that obtained in the Landau-De
Gennes theory for isotropic nematic melts, [23],
[24]:
(12)
In the microstructured phase, the parameter
E
S
is determined by the relation:
(13)
The inverse value of the Kerr constant of the
melt for an isotropic phase, considering (12), is
determined by relation (14), and for a
microstructured phase, considering (13), by relation
(15):
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(14)
(15)
The temperature dependence of the inverse
value of the Kerr constant is thus linear (14) in the
isotropic phase at temperatures
P
TТ
, while in
the microstructured phase at
P
TТ
this
dependence is nonlinear (15).
To analyze the obtained relationships, numerical
calculations of the temperature dependences of the
inverse value of the Kerr constant were carried
out in the MatLab package under conditions when a
microstructured state appears in the melt. The
temperature of the phase transition from
microstructured to nematic (samples P-15 and P-86)
or smectic state (sample P-200 and P-572) was
determined based on the condition of coincidence of
the Helmholtz energy minima for states with S=0
(microstructured state) and S>0 (nematic or smectic
state).
Table 1 and Table 2 show the values of
coefficients calculated for the indicated samples, as
well as the
calculated phase transition temperature TC. The
values of some coefficients remained constant:
kJ/mol, kJ/mol, kJ/mol,
kJ/mol, kJ/mol, kJ/(K×mol),
kJ/(K×mol).
Table 1. Values of coefficients that were used in
modeling
Fraction
,
kJ/mol
,
kJ/mol
,
kJ/mol
,
J/mol
P-15
60
4.90
2.00
0.43
P-86
60
3.45
2.25
0.43
P-200
90
2.35
2.71
0.43
P-572
90
2.35
2.71
0.43
Table 2. Values of coefficients defining the
temperature dependence during modelling
Fraction
,
kJ/(K×mol)
Tf ,
0C
TP ,
0C
TS ,
0C
TC ,
0C
P-15
0.40
95.0
160
119.0
106.0
P-86
0.42
110.0
172
129.6
120.9
P-200
0.56
124.7
165
131.9
126.5
P-572
0.60
123.0
155
128.0
126.5
3.4 Discussion
Low-temperature segments of the versus
curves occupy intervals of the order of 25 – 40 0С,
depending on the fraction, Figure 2. High-
temperature segments are more extended, since on
the side of maximum temperatures they are limited
only by the temperature of polymer destruction.
Thereby, it was possible to observe the properties of
the isotropic phase from 106 to 200 0С in the P-15
oligomer. The wide temperature range distinguishes
the present work from earlier works, [19], [28], [29]
and from our previous results, [13].
The nature of the dependence of on for
fractions P-15, P-86, P-200, and P-572 is
independent of the type of phase transition to the LC
phase. Therefore, the electro-optical properties were
described using a general theoretical approach.
The macromolecules of acrylic homopolymer
are polar. The electro-optical effect in a melt is
determined by optically and electrically anisotropic
side cyanobiphenyl groups. In addition, the electro-
optical effect depends on the short-range order in
the arrangement of these groups. They can change
their mutual orientation relatively freely due to long
aliphatic spacers connecting them to the main
polymer chain of the molecule.
The electro-optical constant is used
to quantify the electro-optical effect. Here is the
temperature of the imaginary second order
transition. In this work, the dependence of on
is not linear. Thus, the values of this constant for
different segments of the experimental dependence
in Figure 2 can be found as , where is the
slope of the experimental curve. A change in the
slope in the region of the structural transition
indicates a change in the electro-optical constant.
For example, for the P-572 fraction the ratio is
, where indices 1 and 2
correspond to the low- and high-temperature
segments of the curve. This is a big change. The
effective dipole moment is greatly decreased as a
result of the reorientation of side groups from
parallel to antiparallel orientation while the
temperature is increased.
4 Conclusion
The temperature dependence of the inverse Kerr
constant in the region of the phase transition from
the isotropic to the liquid crystalline phase should be
linear according to the theory of electro-optical
properties of mesogens. The experimentally
discovered nonlinearity of the temperature
dependence does not fit into these theoretical
concepts. The nonlinearity arises from the dipole-
dipole interaction of the side cyanobiphenyl groups.
The groups are partially reoriented when the
temperature changes, and a structural transition
occurs with a change in short-range order.
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Therefore, the Landau - De Gennes
phenomenological approach was modified. The
contribution of an additional parameter responsible
for the dipole rearrangement is considered in the
expansion of the Helmholtz free energy. It is shown
that varying the expansion parameters makes it
possible to obtain temperature dependences for the
inverse Kerr constant that correspond to the
experimental ones.
The measurements performed made it possible
to observe the iso-iso transition in four fractions
using the electro-optic method. Other methods are
also necessary to characterize the transition
properties, changes in structure, and physical
properties of polymer melts. The list of possible
methods includes X-ray diffraction analysis,
precision calorimetry, dielectric spectroscopy, and
so on.
The study of short-range order effects in the
isotropic phase of polymers is a general trend of our
research. The orientational short-range order in
comb-shaped polymers is formed by anisometric
side groups. They are connected to the main chain
through flexible spacers and are capable of self-
organization. A short-range order depends on the
degree of freedom of mesogenic groups, the nature
of intermolecular interactions, and temperature. The
combination of these factors, as well as their
changes, determine the properties of the isotropic
phase, including, among others, the appearance of
iso-iso transitions. Interesting objects for future
research may be comb-shaped polymers, in which
side mesogenic groups are connected to the main
chain through short spacers. Such spacers limit the
freedom of orientation of side groups [30], [31]. A
polymer may lose its ability to form the LC phase.
Under these conditions, the short-range order among
mesogenic groups can be quite perfect, but at the
same time the polymer chain will have a strong
effect on it. The competition of various factors can
lead to the appearance of previously unknown
nanostructural effects. Thus, new opportunities are
opening up for the creation of promising polymer
materials.
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DOI: 10.37394/23202.2024.23.12
V. B. Rogozhin, S. G. Polushin,
A. A. Lezova, G. E. Polushina, A. S. Polushin
E-ISSN: 2224-2678
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Contribution of Individual Authors to the
Creation of a Scientific Article (Ghostwriting
Policy)
- V. B. Rogozhin: investigation, theory, modeling,
writing original draft.
- S. G. Polushin: conceptualizing, data curation,
writing original draft.
- A. A. Lezova: modeling, writing - review and
editing.
- G. E. Polushina: writing - review and editing.
- A. S. Polushin: data curation.
Sources of Funding for Research Presented in a
Scientific Article or Scientific Article Itself
No funding was received for conducting this
research.
Conflict of Interest
The authors have no conflicts of interest to declare.
Creative Commons Attribution License 4.0
(Attribution 4.0 International, CC BY 4.0)
This article is published under the terms of the
Creative Commons Attribution License 4.0
https://creativecommons.org/licenses/by/4.0/deed.en
_US
WSEAS TRANSACTIONS on SYSTEMS
DOI: 10.37394/23202.2024.23.12
V. B. Rogozhin, S. G. Polushin,
A. A. Lezova, G. E. Polushina, A. S. Polushin
E-ISSN: 2224-2678
112
Volume 23, 2024
