Transport properties of incipient gels

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: $D(m,p)\sim m^{-0.69}$,notonlyat$p_c$ but well into the liquid phase. We also find that the Stokes-Einstein relation $D\eta \propto k_{B}T$ breaks down already quite far from the gel point.