Viscoelasticity near the sol-gel transition

We reconsider the exponents s and mu that characterize the behaviors of the viscosity and the elastic modulus near the Sol-Gel transition. This is done by studying the dynamics of the elastic chain that connects neighboring nodes. We assume that the characteristic time for the latter is the same as for the whole cluster. Assuming that the elastic chain has a motion similar to that of a linear chain in a melt enables us to get a simple relation between both exponents, s and mu. This allows us to provide a unified approach to the calculation of both s and mu. We find that if one assumes that the elastic chain carries an energy of the same order as the thermal energy kT, s = upsilon - beta/2, where upsilon and beta are the exponents far the mesh size and the gel fraction, respectively. This relation was conjectured by Kertesz some years ago. On the other hand, if one assumes that the elastic chain is stretched, and has an energy larger than kT, one recovers the de Gennes result, s = 2 upsilon - beta.