Mean field description of the structural heterogeneities in the region of cooperative diffusion

Abstract

A new mean-field description of the solid to liquid glass (SLG) transition, that incorporates the existence of cooperative rearranging regions (CRRs), is presented. Based on the concept that the cooperative diffusion is a bimodal process with one component being Arrhenius, a sigmoidal shape of the SLG cohesion energy is determined. Incorporation of the new mean-field idea into the Sanchez-Lacombe theory, allows for the first time the description of the free energy in the glassy region. In this way a definition of the size and the temperature dependence of CRRs is succeeded. The outcome is confirmed by a cluster analysis on simulated poly(ethylene) matrix. Moreover, an agreement with the experiment is verified by fitting of the SLG-Equation of State (EoS) with experimental PVT data. Our study, provides parameters for the mean-field description of various polymers, like: poly(styrene), poly(methyl methacrylate), poly(acrylic acid), poly(ethyl methacrylate), poly(methacrylic acid), atactic poly(propylene) and poly(carbonate).