The cooperative free volume rate model for segmental dynamics: Application to glass-forming liquids and connections with the density scaling approach^⋆

Abstract.

In this paper, we apply the cooperative free volume (CFV) rate model for pressure-dependent dynamics of glass-forming liquids and polymer melts. We analyze segmental relaxation times, $\tau$ , as a function of temperature (T and free volume ( $V_{\rm free}$ , and make substantive comparisons with the density scaling approach. $V_{\rm free}$ , the difference between the total volume (V and the volume at close-packing, is predicted independently of the dynamics for any temperature and pressure using the locally correlated lattice (LCL) equation-of-state (EOS) analysis of characteristic thermodynamic data. We discuss the underlying physical motivation in the CFV and density scaling models, and show that their key, respective, material parameters are connected, where the CFV b parameter and the density scaling $\gamma$ parameter each characterize the relative sensitivity of dynamics to changes in T , vs. changes in V . We find $\gamma\approx 1/[b(V_{{{\rm free}}}/V)_{@T_{\rm g}}]$ , where $(V_{{{\rm free}}}/V)_{@T_{\rm g}}$ is the value predicted by the LCL EOS at the ambient $T_{\rm g}$ . In comparing the predictive power of the two models we highlight the CFV advantage in yielding a universal linear collapse of relaxation data using a minimal set of parameters, compared to the same parameter space yielding a changing functional form in the density scaling approach. Further, we demonstrate that in the low data limit, where there is not enough data to characterize the density scaling model, the CFV model may still be successfully applied, and we even use it to predict the correct $\gamma$ parameter.

Graphical abstract