Low-temperature equation of state for amorphous polymer glasses

Abstract

A configurational partition function is developed from cell theory in the harmonic approximation to the cell potential, and given in the quantum formulation. The frequency is an explicit function of volume, and the intermolecular Grüneisen parameter of the Einstein system has an approximate value of three which varies but slightly with volume. Formal expressions for the corresponding Debye system are also presented. The theory is applied to our dilatometric measurements at liquid-helium temperatures and atmospheric pressure on three classes of amorphous polymers, namely, polystyrene and a methyl derivative, a series of methacrylates with varying side chains, and three engineering plastics. It turns out that the reduced quantum temperature assumes a universal value and thus a low-temperature principle of corresponding states obtains. The theoretical thermal expansivities are in good accord with experiment up to a reduced temperature of 4×10−3, corresponding to actual temperatures between 53 and 71 K for the above polymers. Thereafter, and well within the expected applicability of the harmonic approximation, systematic departures from the low-temperature principle of corresponding states as well as the theory appear. These are discussed in terms of available information on location and intensity of low-frequency mechanical relaxation processes.