A Theoretical Interpretation of Free Volume at Glass Transition

We device a relaxed lattice model （RLM） to study the mechanism of glass transition, which unifies the cage- effects from particle-particle interaction and entropy. By analyzing entropy in RLM with considering the influence of interactions on equilibrium, we demonstrate that glass transition is a second-order phase transition. For a perfect one- dimensional linked particle system like linear polymer under normal pressure, the free volume at glass transition is rigorously deduced out to be 2.6%, which provides a theoretical basis for the iso-free volume of 2.5% given by Willian, Landel and Ferry （WLF） equation. Extending to system with dead particles linked with higher dimensions like branched or cross-linked chains under positive or negative pressure, free volume at glass transition is varied, based on which we construct a phase diagram of glass transition in the space of free volume-dead particle-pressure. This demonstrates that free volume is not the single parameter determining glass transition, while either dead particles like cross-linked points or external force fields like pressure can vary free volume at the glass transition.