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 cross link 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) approximately (p(c)-p)(-s) with s approximately 0.65. The diffusion constant shows a remarkable dependence on the mass of the clusters: D(m,p) approximately m(-0.69), not only at p(c) but well into the liquid phase. We also find that the Stokes-Einstein relation Deta proportional, variant k(B)T breaks down already quite far from the gel point.