Diffusion of gelation clusters in the Zimm model
Institut für Theoretische Physik, Georg-August-Universität Göttingen, 37073 , Göttingen, Germany
* e-mail: Peter.Mueller@physik.uni-goettingen.de
Starting from a Zimm model, we study self-diffusion in a solution of crosslinked monomers. We focus on the effects of the hydrodynamic interaction on the dynamics and the critical behaviour at the sol-gel point. Hydrodynamic interactions cause the clusters’ diffusion constant to depend not only on the cluster’s size but also on the cluster’s shape --in contrast to the Rouse model. This gives rise to a non-trivial scaling of the Kirkwood diffusion constant averaged over all clusters of fixed size n, with given in terms of the spectral dimension of critical percolation clusters. The long-time decay of the incoherent scattering function is determined by the diffusive motion of the largest clusters. This implies the critical vanishing of the cluster-averaged effective diffusion constant at the gel point with exponent .
© EDP Sciences, Società Italiana di Fisica, and Springer-Verlag, 2003