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: $D(m,p)\sim m^{-0.69}$, 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.