Use of a theoretical equation of state to interpret time-dependent free volume in polymer glasses

Abstract

Many physical properties of polymer glasses change spontaneously during isothermal aging by a process commonly modeled as collapse of free volume. The model has not been verified rigorously because free volume cannot be unambiguously measured. In the present investigation we tentatively identify the free-volume fraction with the fraction of empty sites in the equation of state of Simha and Somcynsky. With this theory, volume recovery measurements can be analyzed to yield directly the time-dependent, free-volume fraction. Using this approach, recent volume measurements on poly(methyl methacrylate) are analyzed. The resulting free-volume fractions are then used in the Doolittle equation to predict the shift in stress relaxation curves at 23 °C. These predicted shift factors agree with the experimental measurements of Cizmecioglu et al. In addition, it is shown that previous assumptions concerning temperature dependence of free volume are inconsistent with the theory.