Polymer Free Volume and Its Connection to the Glass Transition

In this Perspective we summarize the most widely used definitions of free volume and illustrate the differences between them, including the important distinction between total free volume and excess free volume. We discuss the implications when alternative estimates for free volume are inserted into relationships that connect experimentally measured properties (e.g., the viscosity) to free volume, such as those proposed by Doolittle, Fox and Flory, Simha and Boyer, Cohen and Turnbull, and Williams, Landel, and Ferry. Turning to the results of our own locally correlated lattice (LCL) model, we demonstrate, by analyzing data for a set of over 50 polymers, that our calculations for total percent free volume not only lead to a predictive relationship with experimental glass transition temperatures but also allow us to place the different definitions of free volume within a physical picture of what the proposed contributions represent. We find that melts go glassy upon reaching a "boundary" of minimum (total) percent free volume that depends roughly linearly on temperature. We interpret this boundary as being close to the T-dependent free volume associated with solid-like segmental vibrational motions. Since the LCL model is a first-principles thermodynamic theory, we are also able to link our free volume predictions to similar patterns that we find in the predicted entropy per theoretical segment. Our results are consistent with a picture wherein the difference in entropy between the melt (liquid) state and corresponding solid state vanishes as the glass transition is approached. This leads us to a new connection with the work of Adams and Gibbs, whose model reflects a similar vanishing of the configurational entropy. We conclude by discussing why the approach to the glassy state is best viewed as being controlled via the linked contributions of free volume and temperature.