Transport properties of incipient gels

TL;DR

This study examines how shear viscosity and diffusion coefficients behave near the gelation transition in a model, revealing divergence of viscosity, mass-dependent diffusion, and breakdown of the Stokes-Einstein relation.

Contribution

It provides detailed analysis of transport properties across the gel transition, highlighting the divergence and mass dependence of diffusion and viscosity.

Findings

Shear viscosity diverges as (p_c - p)^{-0.65} at the gel point.

Diffusion coefficient scales with mass as m^{-0.69}.

Stokes-Einstein relation breaks down away from the gel point.

Abstract

We investigate the behavior of the shear viscosity $\eta(p)$ and the mass-dependent diffusion coefficient $D(m,p)$ in the context of a simple model that, as the crosslink density $p$ is increased, undergoes a continuous transition from a fluid to a gel. The shear viscosity diverges at the gel point according to $\eta(p)\sim (p_c-p)^{-s}$ with $s\approx 0.65$. The diffusion constant shows a remarkable dependence on the mass of the clusters: $D(m,p)\sim m^{-0.69}$, not only at $p_c$ but well into the liquid phase. We also find that the Stokes-Einstein relation $D\eta\propto k_BT$ breaks down already quite far from the gel point.