Cluster diffusion at the gelation point

TL;DR

This paper uses molecular dynamics simulations to investigate the dynamics of cluster diffusion at the gelation point, revealing a power-law relationship between diffusion constant and cluster size with a non-trivial exponent.

Contribution

It demonstrates the dynamic behavior of clusters at gelation, specifically identifying a power-law decay of diffusion constants with cluster size, and confirms 3D percolation as the static universality class.

Findings

Diffusion constant D(s) scales as s^{-0.69} at gelation.

Cluster dynamics follow a power-law behavior.

Static universality class is 3D percolation.

Abstract

We use molecular dynamics simulations to study a model of the gelation transition with a dynamic bond forming procedure. After establishing evidence for 3D percolation as the static universality class, we turn our attention to the dynamics of clusters at the gelation point, focusing in particular on the behavior of the diffusion constant D(s) as a function of cluster size s. We find a very clear power law behavior D(s)\sim s^{-k} with a non-trivial exponent k\approx 0.69.