Linear Response Theory for Hard and Soft Glassy Materials

TL;DR

This paper develops a shear-transformation-zone (STZ) theory extended with a distribution of thermal-activation barriers to explain the universal linear rheological behavior observed in both hard and soft glassy materials, aligning well with experimental data.

Contribution

It introduces a broad distribution of internal barriers into STZ theory and links it to nonequilibrium thermodynamics to explain universal rheological properties.

Findings

Theoretical loss modulus $G''()$ peaks at the b relaxation rate.

Power-law decay of $G''()$ with frequency, $^{- ext{z}}$, matches experiments.

Universal rheological behavior explained by barrier distribution and effective-temperature thermodynamics.

Abstract

Despite qualitative differences in their underlying physics, both hard and soft glassy materials exhibit almost identical linear rheological behaviors. We show that these nearly universal properties emerge naturally in a shear-transformation-zone (STZ) theory of amorphous plasticity, extended to include a broad distribution of internal thermal-activation barriers. The principal features of this barrier distribution are predicted by nonequilibrium, effective-temperature thermodynamics. Our theoretical loss modulus $G"(\omega)$ has a peak at the $\alpha$ relaxation rate, and a power law decay of the form $\omega^{-\zeta}$ for higher frequencies, in quantitative agreement with experimental data.