SOME REMARKS ON METHODS FOR DETERMINING THE GLASS TRANSITION TEMPERATURES OF POLYMERS

R. M. KESSENIKH, A. V. PETROV

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

The basic thermal properties of polymers used in electrical and radio structures are just as important as their dielectric properties. The study of thermal characteristics is associated with a number of specific features. One of these features is the relaxation character of the response of amorphous polymers to external influences, and therefore many properties of polymers depend on time. When a polymer passes through the glass-transition region, its properties change continuously; moreover, the glass transition temperature \((T_c)\) may turn out to be either overestimated (high rates) or underestimated (low rates).

The time required for the establishment of an equilibrium structure increases with decreasing temperature according to the exponential law

\[ \tau = \tau_0 e^{\frac{U}{RT}} \tag{1} \]

Therefore, in an experimental study of glass transition temperatures it is necessary to choose reasonable cooling (heating) rates. As is readily seen from (1), the exponential dependence of the relaxation time \((\tau)\) on temperature causes a shift of \(T_c\) by only a few degrees when the cooling rate is changed severalfold. However, if the study is carried out at high rates, curves of a different form, with maxima of the property—temperature \([1]\)—may be obtained. Usually heating or cooling rates up to \(1\ \text{deg/min}\) are chosen. Heat treatment of the samples under investigation is also essential; without it, it is practically impossible to obtain reliable experimental material. Heat treatment is carried out at temperatures approximately \(10\text{–}20^\circ\text{C}\) above \(T_c\) for a long time (up to 10 hours) and is intended to relieve mechanical stresses in the sample.

Various methods are used to determine glass transition temperatures \([2, 3, 4]\). However, different methods are sensitive to different types of motion of macromolecules, and it is natural to expect that \(T_c\), determined by different methods, need not coincide at all. In the literature there are contradictory statements on this point. In some works the noncoincidence of \(T_c\) determined by different methods is clearly indicated \([2, 3]\); in others, either no statements are made on this point, or it is asserted that all methods register one and the same fact—segmental thermal motion—and therefore the tempera-

glass-transition temperatures must coincide [4]. But such a point of view may lead to a very undesirable consequence when choosing polymers for engineering purposes. Indeed, if we have a polymer with sufficiently flexible chains, it is quite possible that the difference in \(T_c\) determined by different methods will lie within a narrow temperature interval; but if we have a polymer containing bulky elements, then the difference in \(T_c\) determined by different methods may reach \(20\)—\(30^\circ\text{C}\) or more [5]. Failure to take this effect into account is highly undesirable.

Table 1 gives a list of some methods used for determining glass-transition temperatures and attempts to show why, in principle, all methods cannot be regarded as equivalent. When the dielectric and mechanical (dynamic) properties of polymers are compared in the temperature–frequency course, an analogy suggests itself. Common to them are relaxation processes, i.e., a certain limitation of the mobility of molecular chains and, consequently, the presence either of a phase-shift angle between polarization and stress (dielectric relaxation), or between deformation and the applied mechanical stress (mechanical damping). As a result, regions of relaxation with maxima appear on the curves \(\operatorname{tg}\delta = \varphi(t^\circ\text{C})\). Moreover, the maximum of dielectric losses \((\operatorname{tg}\delta)\) is located at higher temperatures than the maximum of the damping coefficient \((\alpha)\).

Table 1

List of some methods for determining the glass-transition temperatures of polymers

To illustrate what has been said, Fig. 1 shows the temperature dependence of \(\operatorname{tg}\delta\) and \(\alpha\) for polyvinyl acetate at a frequency equal to \(2 \cdot 10^6\ \text{Hz}\) [6]. The presence of losses indicates absorption of energy by the polymer, with the maximum absorption being observed in the region of elevated temperatures in Fig. 1. However, there is also a deeper difference between these two processes, namely: in a mechanical field, during propagation of a sound wave, attenuation occurs—the damping of ultrasonic vibrations. The viscosity of the medium, thermal conductivity, and scattering of ultrasonic energy at inhomogeneities of the polymer structure determine the absorption of the energy of ultrasonic

oscillations. In the softening interval the polymer passes into a highly elastic state, and rotational motion of segments around the bonds joining them into a single chain is observed. The damping in the softening interval is large [7].

Consequently, segmental thermal motion begins to affect the process of sound-wave propagation immediately from the moment the polymer passes into the highly elastic state, whereas the electric field acts mainly on polar groups, orienting them. Therefore dipole groupings must overcome the forces of dipole–dipole interaction, and for a polarized state to be realized it is necessary that the structure of the polymer be more “loose.” This is why, at identical frequencies, the maximum of dielectric losses lies in the region of higher temperatures and the shape of the loss curve is broader than the analogous properties in the case of mechanical losses. It follows from the above that the dielectric method possesses a certain selectivity and therefore will not give the true value of the glass-transition temperature.

Fig. 1. Dependence of the damping coefficient \((\alpha)\) and \(\operatorname{tg}\delta\) on temperature for polyvinyl acetate [6]

It is natural to suppose that thermal methods will give the most reliable information about \(T_c\). Indeed, the temperature coefficient of linear expansion \((T_{k\alpha})\) of a glassy polymer is determined by anharmonic vibrations of atoms (intramolecular mean distances between atoms); when the polymer passes into the highly elastic state, \(T_{k\alpha}\) increases substantially, which probably can be explained by an increase in the heat capacity of the polymer. At the beginning of the transition there is a continuous increase in \(T_{k\alpha}\), and after the transition its constant value is established (Fig. 2). It is considered that the temperature interval of the transition lies in the range 15–20°C. The mean temperature of the transition region is taken as \(T_c\); sometimes it is proposed that the glass-transition temperature be determined as the onset of the transition temperature, i.e., at the moment when segmental motion begins.

Fig. 2. Qualitative dependence of the temperature coefficient of linear expansion \((T_{k\alpha})\) on temperature

The situation is analogous for heat capacity, which is related to the amount of heat necessary to increase the mean energy of thermal vibrations. The increase in the heat capacity of an amorphous polymer in the transition region is caused by its gradual softening.

Thus, in the glassy state of a polymer the heat capacity is always smaller than in the highly elastic state (Fig. 3). The mean temperature of the region of sharp change in heat capacity may be taken as the glass-transition temperature. It follows from the foregoing,

that thermal methods make it possible to record segmental motion in a polymer; in this case the specimen undergoes practically no deformation, and the heating rates may be in the range of \(1 \div 3\) deg/min, which is quite sufficient for establishing the equilibrium state of the polymer structure. The same applies to the DTA method.

Fig. 3. Qualitative dependence of \(C_p\) in the temperature course

The use of mechanical methods for determining \(T_c\) in the temperature course is associated, up to the inflection point, with elastic deformation; in the transition region, the time required for the development and relaxation of highly elastic deformation is of the same order as the measurement time. Therefore the characteristics determined by this method (elastic moduli) correspond to values obtained as the result of a deformation process that has not yet reached a steady state [1]. With this method of determining \(T_c\), overestimated values are often obtained (Table 2). The table is taken from [3].

When the material presented is compared, one may conclude that it is necessary to standardize the method for determining glass-transition temperatures and the thermal treatment of specimens, since for engineering applications of polymers it is difficult to make use of the variety of absolute values of \(T_c\) reported in the literature.

Table 2

Comparison of glass-transition temperatures determined by different methods

REFERENCES

1. P. P. Kobeko. Amorphous Substances. Publishing House of the Academy of Sciences of the USSR, 1952.
2. Structural Properties of Plastics, ed. by E. Baer, Khimiya Publishing House, 1967.
3. A. A. Tager. Physical Chemistry of Polymers. Goskhimizdat, 1963.
4. S. P. Kolesov, VMS, vol. VIII, No. 4, 1966.
5. R. M. Kessenikh, A. V. Petrov. VMS, vol. XI B, No. 7, 1969.
6. R. Kh. Khuvink, A. Staverman. Chemistry and Technology of Polymers, Khimiya Publishing House, p. 650, 1965.
7. I. G. Mikhailov et al. Fundamentals of Molecular Acoustics. Nauka Publishing House, p. 448, 1965.