Free-Volume Model of the Amorphous Phase: Glass Transition

TLDR

Free volume is the portion of excess volume that can be redistributed without energy change, and its introduction and random distribution in the amorphous phase contribute to the glass transition and entropy. Using a Lennard‑Jones potential, the model shows that at small excess volume energy is required to redistribute it, but beyond a threshold δv̄g most added volume can be freely redistributed. The model predicts that all liquids would vitrify at sufficiently low temperatures unless crystallization intervenes, and that glass formation is governed by crystallization kinetics, cooling rate, and the ratio of cohesive energy to crystallization entropy.

Abstract

Free volume vf is defined as that part of the thermal expansion, or excess volume Δv̄ which can be redistributed without energy change. Assuming a Lennard-Jones potential function for a molecule within its cage in the condensed phase, it can be shown that at small Δv̄ considerable energy is required to redistribute the excess volume; however, at Δv̄ considerably greater than some value δv̄g (corresponding to potentials within the linear region), most of the volume added can be redistributed freely. The transition from glass to liquid may be associated with the introduction of appreciable free volume into the system. Free volume will be distributed at random within the amorphous phase and there is a contribution to the entropy from this randomness which is not present in the entropy of the crystalline phase. According to our model all liquids would become glasses at sufficiently low temperature if crystallization did not intervene. Therefore whether or not a glass forms is determined by the crystallization kinetic constants and the cooling rate of the liquid. The experience on the glass formation is consistent with the generalization: at a given level of cohesive energy the glass-forming tendency of a substance in a particular class is greater the less is the ratio of the energy to the entropy of crystallization.