ON THE QUESTION OF THE ENERGY PARAMETERS OF ACTIVATION OF SEGMENTAL DIELECTRIC RELAXATION IN RIGID-CHAIN POLYMERS

R. M. Kessenikh, A. V. Petrov, L. A. Korshunova,
L. G. Svetlakova

(Presented by the scientific seminar of the Department of Electrical Insulation and Cable Engineering)

One of the principal quantities characterizing dielectric relaxation is the activation energy. In [1] it is shown that, in the case of segmental dielectric relaxation, the use of the various existing methods for calculating the activation energy gives overestimated values, comparable with the magnitude of the energy of rupture of chemical bonds. The large values of the activation energy of segmental dielectric relaxation are often explained by the cooperativity of segmental motion [2]. In the literature on chemical kinetics, the limited applicability of the Arrhenius and Eyring equations to cooperative processes in condensed systems is pointed out. However, in treating experimental material on dielectric relaxation, a very widespread method is used for calculating the activation energy by means of the indicated equations. Therefore the values of the activation energy thus often obtained have a conditional character. Nevertheless, in a number of cases it is possible to obtain information on the character of the change in the activation energy of kinetic relaxation processes and to establish the relation of this energy to changes in intermolecular interaction. Thus, for example, useful information may be provided by analysis of the values of the energy parameters of activation in studying the influence of modification on polymer systems, and also in the case of studying various homologous series of polymers.

When using the Eyring equation, it may be assumed that the rate of establishment of relaxation polarization is determined by the rate at which the activated complex passes over the top of the barrier. The residence time of the relaxator in the activated state is determined by the expression [3]

\[ \tau = \frac{h}{\kappa \cdot T}\cdot e^{\Delta F/RT}, \tag{1} \]

where \(h\) is Planck’s constant;
\(R\) is the universal gas constant;
\(\kappa\) is Boltzmann’s constant;
\(\Delta F\) is the free energy of activation in the formation of the activated complex, referred to one mole of substance;
\(\tau\) is the most probable relaxation time, determined from

\[ \tau = \frac{1}{2\cdot \pi \cdot f_{\max}}. \]

Plotting the dependence of \(\lg f_{\max}\) on reciprocal temperature, we find \(\Delta H\) as the tangent of the angle of inclination of the corresponding straight line. The free energy of activation \(\Delta F\) depends on the heat of activation \(\Delta H\) and the entropy of activation \(\Delta S\). As is known, these three energy parameters are related by the thermodynamic equation [4]

\[ \Delta F=\Delta H-T\cdot \Delta S. \tag{2} \]

Thus, having calculated the free energy \(\Delta F\) from expression (1) and determined \(\Delta H\), one can find the entropy of activation \((\Delta S)\). In this case the entropy of activation represents the difference between the entropy of the activated state and that of the initial state. It is known that the entropy of activation is a function of the thermodynamic probability of the system and is related to the mutual arrangement of its structural elements. Therefore, if the structure of the system is acted upon by various external factors (thermal field, electrical, mechanical, etc.), one can record either a positive value of the entropy of activation or its negative value. The first case means disordering of the structure, and the second—its ordering [4].

To illustrate the above, Table 1 gives the results of calculating the energy parameters according to equation (2) for temperatures equal to the glass-transition temperatures of the modified epoxy polymers under study.

Table 1

Results of calculating the energy parameters
for modified epoxy polymers

* — dibutyl phthalate
** — polyester
*** — aliphatic epoxy resin

The modifiers used were DBP, MGF-9, and DEG-1. Hot-cured epoxy polymers were prepared on the basis of ED-6 resin and methyltetrahydrophthalic anhydride. As follows from the table given, the free energy of activation decreases monotonically with increasing weight content of DBP, MGF-9, and DEG-1 in the epoxy polymer. Moreover, the absolute values of \(\Delta F\) lie within the range 14.6–16.7 kcal/mol. The heat of activation \(\Delta H\) also decreases with an increase in the parts by weight of plasticizers, which can be interpreted as a decrease in intermolecular interactions. Noteworthy is the fact that for the composition with chemical modification (DEG-1—30 parts by weight and 50 parts by weight) the heat of activation increases.

Unlike DBP and the polyester, DEG-1 enters into a chemical bond with the hardener of the epoxy composition; consequently, new bonds appear in the structure. If one follows the change in the activation entropy \(\Delta S\), the following regularity is observed here: first of all, the activation entropy is positive for physically modified systems and decreases with increasing parts by weight of DBP and polyester in the bulk of the epoxy polymer; for the chemically modified epoxy polymer, an increase in the activation entropy is characteristic.

The effect we have found—the decrease in the positive activation entropy of dielectric relaxation with the concentration of modifiers for epoxy polymers with physical modification—indicates that, as the parts by weight of modifiers (DBP and MGF-9) in the bulk of the epoxy polymer increase, the degree of ordering of the supramolecular structures changes. Our assumption is confirmed by experimental studies of the structure of modified epoxy polymers. The supramolecular structures were studied with a UEMV-100 electron microscope. The introduction of DBP and MGF-9 into the bulk of the epoxy compound substantially changes its supramolecular structure. The sizes of the globules increase from 300–1000 Å to 5000–10000 Å, and the glass-transition temperatures decrease sharply [5]. Along with the decrease in the activation entropy, the heat of activation also decreases, which likewise indicates a reduction in intermolecular interactions.

As was already indicated earlier, for an epoxy polymer chemically modified with the aliphatic resin DEG-1, the heat and entropy of activation increase with increasing concentration of it. The increase in the heat of activation is apparently associated with the appearance of new chemical bonds caused by the chemical reaction between the DEG-1 modifier and methyltetrahydrophthalic anhydride. The increase in the activation entropy may presumably be related to the presence in the polymer structure of a considerable number of aliphatic groups, which impart appreciable elasticity to the epoxy polymer. As a result, a monotonic decrease in the glass-transition temperatures is observed with increasing weight content of the DEG-1 modifier, while the supramolecular structure changes only slightly [5]. Evidently, the aliphatic units introduce considerable disorder into the supramolecular structure.

Table 2 gives the results of calculating the energy parameters for a homologous series of carbazoles, from which there follows a simultaneous decrease in the heat and entropy of activation as the length of the alkyl radical increases. This circumstance, as in the case of physically modified epoxy polymers, indicates a decrease in intermolecular interaction and a loosening of the structure of the homologues. At the same time, the glass-transition temperatures decrease regularly. An exception to this series is poly-3-vinyl-9-isopropylcarbazole, for which the heat of activation and the activation entropy increase, and the glass-transition temperature has an elevated value in comparison with the adjacent homologues. This feature of the isomer of the homologous series of carbazoles is due to the presence of stronger intermolecular interactions.

It should be noted that, when calculating the activation entropy for polymer systems (Tables 1 and 2), its absolute values lie within the range 95–315 cal/mol·deg. Such large activation entropies cannot be explained within the framework of transition-state theory, since the activation entropy of the transition complex is estimated to be of the order of 10–20 cal/mol·deg [6, 7]. Probably, the complexity of the structure of the...

copolymeric organic amorphous compounds may cause such large values of the activation entropy; for polymeric crystalline structures the activation entropy of segmental relaxation may take values on the order of 64 cal/mol·deg [8].

It is also known that for a number of inorganic glasses the entropy of viscous flow may be 500 cal/mol·deg [9].

Table 2

Results of calculation of energy parameters
for the homologous series of carbazoles

From the foregoing it follows that the use of the method for calculating activation parameters makes it possible to obtain additional useful qualitative information about changes in structure and intermolecular interaction in rigid-chain modified polymers and homologous series at glass-transition temperatures.

REFERENCES

1. R. M. Kessenikh, A. V. Petrov. Izvestiya vuzov SSSR, “Fizika”, No. 9, 1969, p. 7.
2. G. P. Mikhailov, T. I. Borisova. UFN, 83, 1, 1964.
3. S. Glasstone, K. Laidler, T. Eyring. The Theory of Rate Processes. Moscow, IL, 1948.
4. Ya. I. Frenkel. Introduction to Molecular Physics and Thermodynamics. Moscow, IL, 1962.
5. L. A. Korshunova. Candidate’s dissertation. Tomsk, 1971.
6. N. M. Shishkin. ZhTF, 26, 1461, 1956.
7. V. G. Levin. Vestnik AN SSSR, No. 7, 18, 1968.
8. A. A. Aryev, A. V. Sotnikov. Mechanisms of Relaxation Phenomena in Solids. Moscow, “Nauka,” 1972.
9. S. V. Nemilov. ZhPKh, 37, 293, 1964.