A theoretical interpretation of free volume at glass transition

• Published in: Chinese journal of polymer science Vol. 35; no. 11; pp. 1415 - 1427
• Main Authors: Ren, Yi-kun, Li, Yun-tao, Li, Liang-bin
• Format: Journal Article
• Language: English
• Published: Beijing Chinese Chemical Society and Institute of Chemistry, CAS 01.11.2017; Springer Nature B.V
• Subjects: Chain branching; Characterization and Evaluation of Materials; Chemistry; Chemistry and Materials Science; Condensed Matter Physics; Crosslinking; Entropy; External pressure; Glass; Industrial Chemistry/Chemical Engineering; Phase transitions; Polymer Sciences; Temperature; Glass transition; Relaxed lattice model; Predicted phase diagram; Iso-free volume
• ISSN: 0256-7679; 1439-6203
• DOI: 10.1007/s10118-017-1968-8

We device a relaxed lattice model (RLM) to study the mechanism of glass transition, which unifies the cageeffects 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.