Theory of heterogeneous viscoelasticity

TL;DR

This paper presents a new theoretical framework for understanding the viscoelastic behavior of glass-forming liquids near the glass transition, incorporating spatial heterogeneity in viscosity and elasticity, and explains various relaxation phenomena.

Contribution

It introduces a CPA-based model that accounts for spatial fluctuations in viscosity and elastic moduli, predicting temperature dependence and relaxation features in glasses.

Findings

Predicts Arrhenius temperature dependence of viscosity at low frequencies.

Describes the alpha relaxation peak in glasses using Gaussian barrier distributions.

Explains boson-peak vibrational anomalies through heterogeneous elasticity theory.

Abstract

We review a new theory of viscoelasticity of a glass-forming viscous liquid near and below the glass transition. In our model we assume that each point in the material has a specific viscosity, which varies randomly in space according to a fluctuating activation free energy. We include a Maxwellian elastic term and assume that the corresponding shear modulus fluctuates as well with the same distribution as that of the activation barriers. The model is solved in coherent-potential approximation (CPA), for which a derivation is given. The theory predicts an Arrhenius-type temperature dependence of the viscosity in the vanishing-frequency limit, independent of the distribution of the activation barriers. The theory implies that this activation energy is generally different from that of a diffusing particle with the same barrier-height distribution. If the distribution of activation barriers is assumed to have Gaussian form, the finite-frequency version of the theory describes well the typical low-temperature alpha relaxation peak of glasses. Beta relaxation can be included by adding another Gaussian with center at much lower energies than that responsible for the alpha relaxation. At high frequencies our theory reduces to the description of an elastic medium with spatially fluctuating elastic moduli (heterogeneous elasticity theory), which explains the occurrence of the boson-peak-related vibrational anomalies of glasses.