Static and dynamic heterogeneities in a model for irreversible gelation

TL;DR

This paper investigates the structure and dynamics of irreversible gelation using molecular dynamics simulations, revealing critical heterogeneities and scaling behaviors near the gelation transition.

Contribution

It introduces a novel analysis of dynamical heterogeneities and critical exponents in irreversible gelation through simulation data.

Findings

Dynamical susceptibility peaks near the percolation threshold.

At gelation, the susceptibility scales with wave vector as $k^{ ext{"eta"}-2}$.

The divergence of susceptibility at low wave vector follows the mean cluster size exponent.

Abstract

We study the structure and the dynamics in the formation of irreversible gels by means of molecular dynamics simulation of a model system where the gelation transition is due to the random percolation of permanent bonds between neighboring particles. We analyze the heterogeneities of the dynamics in terms of the fluctuations of the intermediate scattering functions: In the sol phase close to the percolation threshold, we find that this dynamical susceptibility increases with the time until it reaches a plateau. At the gelation threshold this plateau scales as a function of the wave vector $k$ as $k^{\eta -2}$, with $\eta$ being related to the decay of the percolation pair connectedness function. At the lowest wave vector, approaching the gelation threshold it diverges with the same exponent $\gamma$ as the mean cluster size. These findings suggest an alternative way of measuring critical exponents in a system undergoing chemical gelation.