A universal equation of state for polymer liquids

Abstract

Recently it has been shown that the compression response of polymer liquids, glasses and solutions satisfies a strong temperature—pressure superposition principle. Using a phenomenological argument, a new isothermal equation of state was developed to describe this new principle quantitatively. In this paper we extend the range of applicability of this new equation of sate, enabling it to describe quantitatively polymer liquids at any temperature. This is achieved by taking advantage of the empirical observation that for polymers both the density and the logarithm of the bulk modulus are linear functions of temperature. This allows the development of a corresponding states equation of state where each polymer is distinguished by a characteristic temperature T ∗ , pressure P ∗ and mass density ϱ ∗ . These parameters have been tabulated for 61 polymer liquids. The accuracy of the new equation of state approaches the accuracy of experimental PVT data. The equation of state parameters ( T ∗, P ∗, ϱ ∗ ) also have simple physical interpretations. One in particular is significant: the reduced temperature, T T ∗ , is shown to be equal to the free volume fraction at temperature T. This may prove to be useful for the interpretation of gas permeability through polymers. It is also shown that 1/ϱ ∗ is related to the calculated van der Waals' volume and that P ∗ is a measure of the cohesive energy density. The new equation of state will be useful for extrapolating equation of state properties and estimating bounds for negative pressures.