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volume 4, issue 5, 2025
415
HEAT CAPACITY AND THERMAL CONDUCTIVITY PROPERTIES OF
CRYSTALLINE AND AMORPHOUS POLYMERS
Khaydarov Tuymurod Zoyirovich
Associate Professor, Karshi State Technical University Karshi Uzbekistan
E-mail tuymurodkhaydarov228@gmail.com tel:+998908666680
Rakhmankulov Alikul Amirkulovich
Professor, Karshi State Technical University Karshi Uzbekistan;
E-mail: raxmankulovalicul@gmail.com
Ruziyev Rufat Toshboyevich
Associate Professor, Karshi State Technical University Karshi Uzbekistan
E
-
mail: ruziyev.2022@bk.ru
Abstract:
The article analyzes theoretically and experimentally the thermodynamic properties of
crystalline and amorphous polymers, such as heat capacity, thermal conductivity and thermal
expansion. The application of the Debye and Tarasov models to the heat capacity of polymers,
especially their behavior at low temperatures, is considered. The influence of the degree of
crystallization on thermal conductivity is also illustrated by the example of polymers such as
polyethylene. The influence of low-frequency optical vibrations arising in amorphous polymers
on heat capacity is emphasized. The article also provides theoretical formulas for determining the
expansion coefficients of polymers and explains their physical meaning.
Key words:
polymers, crystalline and amorphous structure, heat capacity, thermal conductivity,
thermal expansion, Debye model, Tarasov model, low temperature physics, thermodynamic
properties, degree of crystallization, polyethylene, optical vibrations.
Introduction
The thermal conductivity of polymers is much lower than that of other solids.
λ → 0,2 −
0,3
�
��∙�
This is why polymers are considered thermal insulators. Due to the relative mobility of
bonds and the change in conformation in polymers, they have a high coefficient of linear
expansion.
10
−4
− 10
−5
∙ �
−1
have. Therefore, it can be assumed that they differ from
materials with a smaller coefficient of linear expansion, such as metals and semiconductors.
However, the high elasticity and relatively low operating temperatures of polymers allow them to
be used as films on the surface of any material [1].
Very few experimental results on the heat capacity of polymers agree with those obtained by
theoretical interpretation. The heat capacity of polymers in the solid state is expressed as:
C = C
1
+ C
2
+ C
3
in this:
C
1
– heat capacity of vibrating grates;
C
2
– characteristic oscillations,
i.e., the heat capacity of individual links moving independently;
�
3
– heat capacity of an existing
defect in the polymer [1].
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volume 4, issue 5, 2025
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At present, it is advisable to compare the experimental results of the heat capacity with the
results of simpler theoretical models. As these models, the Debye and Tarasov models can be
considered. For this purpose, one of the main issues is the issue of determining the limit of
application of the Debye theory for polymers. During the propagation of long Debye waves in
polymer chains, the chains interact based on the result of intermolecular forces. This, in turn,
creates three-dimensional vibrations in polymers. As is known, three-dimensional vibrations can
be explained by the Debye theory. During the propagation of short Debye waves, the main role
in the spectra is played by vibrations directed along the polymer chain. As is known. In this case,
the one-dimensional nature of polymer molecules is manifested. We know that this corresponds
to the Tarasov model. The disadvantage of these models, namely, that they cannot calculate the
heat capacity with high accuracy, is that they do not take into account the dispersion of Debye
waves. It is known from the Debye theory that,
С ≈ Т
3
Contact
Т < θ
D
/12
, however, as a result
of dispersion, this bond remains in the region of very low temperatures. The study of the
dependence of heat capacity on temperature provides very important information about the
nature of polymers and is a factor in creating a mechanism for theoretical assessment of the
thermal properties of polymers [2]. Polyethylene is a partially crystalline polymer and forms an
orthorhombic cell during crystallization. The repeating unit in PE consists of a methylene (H2)
group, therefore its molar heat capacity
� = 14,03 �
belongs to the mass. Density of fully
crystallized polyethylene
�
�
= 0,999 ��/�
3
, density of completely amorphous polyethylene
�
�
= 0,8525 ��/�
3
will be [2].
A feature of amorphous polymers is that at low temperatures, their temperature-dependent
changes in heat capacity are inconsistent with Debay's theory. Derived from Debay's theory in
amorphous polymers at low temperatures C/T
3
=const Coupling fails, maximum hail occurs in
the heat capacity graph near 5K temperature. This effect is explained by the presence of low
frequency optical vibrations in the polymer. Jump to search For example, the thermal capacity of
amorphous polyethylene is explained based on Tarasov's theory using a combination of
frequency spectrum in the low temperature region [2].
Thus, the heat capacity of amorphous bodies moves away from the calculations of Debay's
theory. This conclusion is especially evident in experimental experiments. For example; defined
for polymethylmethacrylate and polystrone
� � = �/�
3
In addition to acoustic vibrations, the
effect of non-acoustic vibrations is also evident at temperatures close to liquid helium. At
temperatures below 1.5K S/T
3
The amount decreases and tends to a limiting value. This change
is clearly visible in ultrasonic measurements. For polymethylmethacrylate and polystyrene, the
non-acoustic effect on the heat capacity is clearly noticeable in the helium temperature range [3].
An excessively high Debye heat capacity at low temperatures (explained by Einstein's theory) is
one of the characteristic features of organic and inorganic amorphous substances. The vibrational
spectra of ordered aggregates are discrete, and at low temperatures the formation of low
frequencies occurs. This has a certain effect on the heat capacity and thermal conductivity of the
system. This point of view is consistent with the modern molecular structure of amorphous
polymers [4].
Research result
Thermal conductivity of crystalline and amorphous polymers.
It is known that the degree of
crystallization χ thermal conductivity of polymers (λ) is one of the characteristics that affect the
thermal conductivity of partially crystallized polymers. Usually, the thermal conductivity of
partially crystallized polymers is considered as a combination of the thermal conductivity of
fully amorphous and crystalline polymers. The thermal conductivity coefficient of partially
crystallized polymers is expressed as:
� = ��
�
+ 1 − � �
�
(1)
In this
�
�
va
�
�
Thermal conductivity coefficient of crystalline and amorphous polymers; χ –
degree of crystallization.
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volume 4, issue 5, 2025
417
Aerman expresses the effect of the degree of crystallization on thermal conductivity using the
following formula::
� =
2�
�
+�
�
+2� �
�
−�
�
2�
�
+�
�
−� �
�
−�
�
(2)
In polymers, the x
k
and x
a
change significantly with temperature. In such cases, the polymers are
amorphous.
a
and crystal
K
The density also changes. The degree of crystallization
�
at room
temperatures
k
and
a
can be calculated by. Formula (1.2) cannot be used as an exact analytical
formula for all polymers. For polymers with a high degree of crystallinity, this formula cannot be
considered appropriate. In this case, the use of formula (1.1) for the thermal conductivity of
polymers gives a more accurate result [4].
The values of thermal conductivity calculated by theoretical methods for polymers differ
significantly from the values calculated experimentally. Currently, there are more than 40
theoretical formulas for the thermal conductivity of polymers, but all of them are used as
approximate calculation formulas. The creation of a single theory for the thermal conductivity of
polymers requires many experimental studies [4].
Thermal expansion of crystalline polymers. The thermal coefficient of thermal expansion of
crystalline polymers depends not only on volume and temperature, but also on the degree of
crystallization of the polymer. If the polymer is neither completely crystalline nor completely
amorphous, its specific volume
V
can be considered as the specific volumes
V
1
and
V
2
of the
crystalline and amorphous polymers. If these volumes are at the same temperature and pressure,
the following expression can be written:
� = ��
1
+ (1 − �)�
2
(3)
In this: χ – degree of crystallization of the polymer by mass;
� = �
1
/�
2
(
m
1
– mass of the
polymer in the crystal sphere,
�
2
−
its total mass).
Both parts of the above equation are equivalent to the specific gravity of a fully crystalline
polymer.
�
1
0
we divide by volume. Here T=0 K and R=0 let . We write the following equations
by introducing dimensionless parameters:
� =
�
�
1
0
; � =
�
1
�
1
0
; � =
�
2
�
1
0
;
(4)
These equations take the following form for specific volume::
� = ��
1
+ 1 − � �
2
(5)
In this case, the thermal coefficient of expansion takes the following form::
� =
1
�
��
�� �
=
1
�
��
�� �
(6)
We can change this formula to the following::
� = ��
1
�
1
+ 1 − � �
2
�
2
/�
(7)
The indices 1 and 2 in the formula refer to crystalline and amorphous polymers. Accordingly, the
thermal expansion coefficient for crystalline and amorphous polymers takes the following form:
�
1
=
1
�
1
��
1
�� �
;
�
2
=
1
�
2
��
2
�� �
;
(8)
�
considering it as constant, (1.6) thermal coefficient of expansion from the equation β can be
calculated. In this case
�
1
,
�
2
,
�
1
and
�
2
considering it permanent, (1.6) thermal coefficient of
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volume 4, issue 5, 2025
418
expansion from the equation β can be calculated.
In this case
� �, � = �
0
(�) + �(�)�
(9)
In this:
R
0
(X) – 0 K
pressure at temperature;
g(X)T
corresponding thermal effect at a given
volume and temperature (
R
T
).
The shape of both functions in this formula depends on the relationship between the crystalline
and amorphous domains of the polymer..
��/��
�
= ��
�
,
�
�
=− � ��/��
�
Considering the last formula, the following expression
follows:
� =
��
��
�
(10)
For crystalline polymers, formula (1.8) is often appropriate. Considering crystalline polymers as
three-dimensional, their thermodynamic properties can also be calculated using other theoretical
models. [5].
Conclusion
The study of the thermodynamic properties of polymers further expands their practical
applications. According to the results of the study, crystalline and amorphous polymers have
significant differences in heat capacity, thermal conductivity, and expansion coefficient. The
degree of crystallization directly affects these properties. The temperature-dependent heat
capacity and vibration spectra of polymers are explained by the use of the Debye and Tarasov
models. Non-acoustic vibrations that occur in amorphous polymers, especially at low
temperatures, demonstrate the uniqueness of thermal behavior. Also, the differences between
theoretical models and practical applications require the development of more accurate models to
improve the thermodynamic analysis of polymers
.
References:
1. Yuli K. Godovsky Thermophysical Properties of Polymers//Prof. Dr. Yuli K. Godovsky
Karpov Institute of Physical Chemistry Ul. Obukha 10 103064 Moscow, 1992. DOI
10.1007/978-3-642-51670-2
2.Debye P. Zur Theorie der specifik Wärmen // Ann. Physik, 39 (1912) 789-839.
3. A.A. Rakhmankulov. Vliyanie dispersnykh napolniteley na struktur i teploprovodnst
nemodifitsirovannogo i modifitsirovannogo polyvinylideneftorida. Dis. kand.fiz.-mat.nauk.-Kiev:
1987. — 205 p.
4. Yanfei Xu, Xiaoxue Wang, Jiawei Zhou, Bai Song, Zhang Jiang, Elizabeth M. Y Lee, Samuel
Huberman, Karen K.Gleason., and Gang Chen Molecular engineered conjugated polymer with
high thermal conductivity DOI:10.1126/sciadv.aar3031
5.A. I. Slutsker., V. I. Wettegren., V. L. Gilyarov., G. Dadobaev., V. B. Kulik., L. S. Titenkov
Teplovoe rasshirenie kristalla polyethylene i macromolekul v nem 2012. 1168-1174 p
