Theoretical Explanation Of The Equal Free Volume In The Glass Transition Under Quasi-static Conditions

Glass Transition is an old but challenging physical question.Almost all the materials have glass transition behavior,but no theory has been proved to be successful for any kind of material.Glass transition has vital influence on intensities of materials,such as light scattering ability,intensity,modulus,relaxation time and so on.The glass transition temperature is sensitive to thermodynamic history.Especially,different from crystallization temperature,glass transition temperature will change with the change of cooling rate.Experiments about glass transition has been intensive studied.The experimental factors were chemical parameters(such as:molecular weight,structure of main chain,branched chain structure,degree of branching and so on)and physical parameters(such as:cooling rate or pressure).Experiments methods changed from old methods like DSC to new methods like PAT.But experiments results could only be accurately expressed by a half-empirical function(WLF function),which makes the trial of finding the theoretical explanation of WLF equation important.Old and new theories of glass transition have been proposed over 100 years.No theories could match the glass transition experiments like WLF did.However,WLF is build on Flory's iso-free volume.In another words,the demonstration of Flory's iso-free volume is equal to demonstration of the basis of WLF.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 demonstrates that the free volume at glass transition is rigorously deduced out to be 2.6%for a perfect one-dimensional linked particle system like linear polymer under normal pressure,which provides a theoretical basis for the iso-free volume of 2.5%given by 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 change free volume at glass transition.