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.

We present new correlations revealed by our study of polymer mixture miscibility. Applying our simple lattice-based equation of state, we search for patterns in a large sample of experimental blends and uncover some intriguing relationships. One such correlation connects the value of the difference in pure component energetic parameters with that of the mixed segment interactions, suggesting new possibilities for predictive modeling that would require only pure component data. Our work reveals different patterns for UCST-type and LCST-type blends which we connect with physical underpinnings reflected in the microscopic parameters. Throughout we emphasize the importance of modeling protocol, most notably, the importance of carefully and consistently applying a fitting procedure to the same temperature range for the two pure components. The reasons for this are demonstrated and discussed in terms of a careful analysis of the model behavior which includes a look at the sensitivity to pure component fitting. We provide details (applicable to other equations of state as well) on the methodology needed in order to obtain the most robust and consistent results.

Polymeric mixtures are important materials, but the control and understanding of mixing behaviour poses problems. The original Flory–Huggins theoretical approach, using a lattice model to compute the statistical thermodynamics, provides the basic understanding of the thermodynamic processes involved but is deficient in describing most real systems, and has little or no predictive capability. We have developed an approach using a lattice integral equation theory, and in this paper we demonstrate that this not only describes well the literature data on polymer mixtures but allows new insights into the behaviour of polymers and their mixtures. The characteristic parameters obtained by fitting the data have been successfully shown to be transferable from one dataset to another, to be able to correctly predict behaviour outside the experimental range of the original data and to allow meaningful comparisons to be made between different polymer mixtures.

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