A Simple New Way To Account For Free Volume In Glassy Dynamics: Model-Free Estimation Of The Close-Packed Volume From Pvt Data

In this article we focus on the important role of well-defined free volume (V-free) in dictating the structural relaxation times, tau, of glass-forming liquids and polymer melts. Our definition of V-free = V - V-hc, where V is the total system volume, means the use of V-free depends on determination of V-hc, the system's volume in the limiting closely packed state. Rejecting the historically compromised use of V-free as a dynamics-dependent fitting function, we have successfully applied a clear thermodynamics-based route to V-hc using the locally correlated lattice (LCL) model equation of state (EOS). However, in this work we go further and show that V-hc can be defined without the use of an equation of state by direct linear extrapolation of a V(T) high-pressure isobar down to zero temperature (T). The results from this route, tested on a dozen experimental systems, yield ln tau vs 1/V-free isotherms that are linear with T-dependent slopes, consistent with the general ln tau similar to f(T) x (1/V-free) form of behavior we have previously described. This functional form also results by implementing a simple mechanistic explanation via the cooperative free volume (CFV) rate model, which assumes that dynamic relaxation is both thermally activated and that it requires molecular segmental cooperativity. With the degree of the latter, and thus the activation energy, being determined by the availability of free volume, the new route we demonstrate here for determination of V-free expands the potential for understanding and predicting local dynamic relaxation in glass-forming materials.