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Center for Nonlinear Studies |
We study shear relaxation and density fluctuations within simple dynamic models of randomly crosslinked macromolecular networks. The sol phase is characterized by a stretched exponential decay of shear relaxation, which can be traced to the random connectivity of molecular clusters such that weakly connected regions dominate the relaxation of shear. Anomalous time decays are also observed for density fluctuations. These can be related to a broad distribution of relaxation times, reflecting the corresponding cluster size distribution. The transition from the sol to the gel is - like the glass transition - characterized by a diverging static shear viscosity, if the transition point is approached from the fluid side, respectively by a vanishing shear modulus, if the approach is from the amorphous solid side. The critical behaviour can be calculated exactly within the Rouse model, including the coefficients of normal stresses. Hydrodynamic interactions can be taken into account approximately within the Zimm model, for which we have analysed the scaling of the diffusion constant and the shear viscosity with cluster size.
Host: Eli Ben-Naim, T-13