Equation of State of Polymer Liquids and Glasses at Elevated Pressures

Abstract

By a combination of experimental isotherms and making use of theoretical results, we establish the validity of the theorem of corresponding states for chain liquids and derive an explicit expression for the reduced pressure—volume—temperature surface encompassing oligomer and high‐polymer liquids. For this purpose empirical Tait isotherms are employed with one adjustable parameter only, by showing that they describe experimental data for high‐polymer liquids also. One observes furthermore that the Tait relation remains valid below the glass transitiontemperature with only one of the parameters changing its functional dependence on temperature in the transition. We are able to conclude that a reduced equation of state describes the isotherms of polymer glasses with the same reducing parameters which characterize the liquid. This permits appropriate predictions at elevated pressure from volume—temperature studies of the glass at atmospheric pressure, combined with equation of state results of the liquid polymer. Our results thus support for both chain liquids and glasses the postulates formulated by others as a basis for a principle of corresponding states. A correction must be made, however, in computing enthalpies or cohesive energy densities for polymers with highly asymmetric units from equation of state properties by means of this principle. Deviations between the reduced experimental and theoretical equations of state at low temperatures are entirely determined by the characteristic failure of cell theory in respect to the internal pressure. At elevated temperatures, the theoretical thermal expansions are also in error. The principle of corresponding states and the general equation of state derived from it are, of course, unaffected and serve as a guide for further theoretical developments. Finally, it turns out that the Tait equation describes the isotherms of partially crystalline branched polyethylene whereas it predicts larger compressibilities than are observed for linear crystalline polymethylene. Above the melting region we interpret the departures from the Tait relation for both polyethylene and polymethylene as due to crystallization effects and compute the variation of crystallinity with pressure.