Dynamical heterogeneity in a model for permanent gels: Different behavior of dynamical susceptibilities

TL;DR

This study investigates dynamical heterogeneity in a permanent gel model, revealing how fluctuations relate to cluster size and percolation, with different behaviors observed in various heterogeneity measures.

Contribution

It provides a systematic analysis of dynamical heterogeneity near gelation, highlighting the contrasting behaviors of different fluctuation measures and their relation to cluster size.

Findings

Fluctuations of the self intermediate scattering function increase and plateau at the mean cluster size.

Fluctuations of the self-overlap show a peak and decay, scaling with the mean cluster size.

Non-Gaussian parameter reaches a finite plateau, increasing with volume fraction and remaining finite at percolation.

Abstract

We present a systematic study of dynamical heterogeneity in a model for permanent gels, upon approaching the gelation threshold. We find that the fluctuations of the self intermediate scattering function are increasing functions of time, reaching a plateau whose value, at large length scales, coincides with the mean cluster size and diverges at the percolation threshold. Another measure of dynamical heterogeneities, i.e. the fluctuations of the self-overlap, displays instead a peak and decays to zero at long times. The peak, however, also scales as the mean cluster size. Arguments are given for this difference in the long time behavior. We also find that non-Gaussian parameter reaches a plateau in the long time limit. The value of the plateau of the non-Gaussian parameter, which is connected to the fluctuations of diffusivity of clusters, increases with the volume fraction and remains finite at percolation threshold.