Nonlinear dielectric susceptibilities in supercooled liquids: a toy model

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.

13 pages, 5 figures