Heat capacities and volumetric changes in the glass transition range: a constitutive approach based on the standard linear solid

Abstract

A novel approach to represent the glass transition is proposed. It is based on a physically motivated extension of the linear viscoelastic Poynting–Thomson model. In addition to a temperature-dependent damping element and two linear springs, two thermal strain elements are introduced. In order to take the process dependence of the specific heat into account and to model its characteristic behaviour below and above the glass transition, the Helmholtz free energy contains an additional contribution which depends on the temperature history and on the current temperature. The model describes the process-dependent volumetric and caloric behaviour of glass-forming materials, and defines a functional relationship between pressure, volumetric strain, and temperature. If a model for the isochoric part of the material behaviour is already available, for example a model of finite viscoelasticity, the caloric and volumetric behaviour can be represented with the current approach. The proposed model allows computing the isobaric and isochoric heat capacities in closed form. The difference \(c_\mathrm{p} -c_\mathrm{v} \) is process-dependent and tends towards the classical expression in the glassy and equilibrium ranges. Simulations and theoretical studies demonstrate the physical significance of the model.