Emergence of complex behavior in gelling systems starting from simple behavior of single clusters

TL;DR

This paper presents a theoretical and numerical study of the sol-gel transition, reproducing complex behaviors observed experimentally through percolation theory and simple assumptions on cluster relaxation.

Contribution

It introduces a framework linking cluster-level relaxation to macroscopic gel behavior using percolation theory and validates predictions with numerical simulations of permanent gels.

Findings

Good agreement between numerical data and analytical predictions

Complex dynamical behaviors can be derived from simple cluster assumptions

Critical exponents of percolation relate to observed gel dynamics

Abstract

A theoretical and numerically study of dynamical properties in the sol-gel transition is presented. In particular, the complex phenomenology observed experimentally and numerically in gelling systems is reproduced in the framework of percolation theory, under simple assumptions on the relaxation of single clusters. By neglecting the correlation between particles belonging to different clusters, the quantities of interest (such as the self intermediate scattering function, the dynamical susceptibility, the Van-Hove function, and the non-Gaussian parameter) are written as superposition of those due to single clusters. Connection between these behaviors and the critical exponents of percolation are given. The theoretical predictions are checked in a model for permanent gels, where bonds between monomers are described by a finitely extendable nonlinear elastic potential. The data obtained in the numerical simulations are in good agreement with the analytical predictions.