Nonlinear dielectric susceptibilities in supercooled liquids: a toy model

TL;DR

This paper presents a toy model using asymmetric double wells to describe the nonlinear dielectric susceptibilities in supercooled liquids, revealing how higher-order susceptibilities relate to dynamical heterogeneities and matching experimental data.

Contribution

It introduces a simplified model linking nonlinear susceptibilities to dynamical heterogeneities, providing analytical results consistent with experimental observations.

Findings

Higher-order susceptibilities depend on moments of $N_{corr}$

Linear susceptibility $ ext{chi}_1$ is independent of $N_{corr}$

Model reproduces experimental behavior of $ ext{chi}_3$ in glycerol

Abstract

The dielectric response of supercooled liquids is phenomenologically modeled by a set of Asymmetric Double Wells (ADW), where each ADW contains a dynamical heterogeneity of $N_{corr}$ molecules. We find that the linear macroscopic susceptibility $\chi_1$ does not depend on $N_{corr}$ contrary to all higher order susceptibilities $\chi_{2k+1}$. We show that $\chi_{2k+1}$ is proportional to the $k^{th}$ moment of $N_{corr}$, which could pave the way for new experiments on glass transition. In particular, as predicted by Bouchaud and Biroli on general grounds [Phys. Rev. B, {\bf 72}, 064204 (2005)], we find that $\chi_3$ is proportional to the average value of $N_{corr}$. We fully calculate $\chi_3$ and, with plausible values of few parameters our model accounts for the salient features of the experimental behavior of $\chi_3$ of supercooled glycerol.