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Dynamics of gelling liquids

Wednesday 11th January 2006 - 11:10 to 12:00
INI Seminar Room 1

The dynamics of randomly crosslinked liquids is addressed via a Rouse- and Zimm-type model with crosslink statistics taken either from bond percolation or Erdoes-Renyi random graphs. While the Rouse type model isolates the effects of the random connectivity on the dynamics of molecular clusters, the Zimm-type model also accounts for hydrodynamic interactions on a preaveraged level. The incoherent intermediate scattering function is computed in thermal equilibrium. It is shown that the cluster size distribution gives rise to an anomalous time decay (stretched exponential) in all of the sol phase. The critical behaviour near the sol-gel transition is analysed and related to the scaling of cluster diffusion constants at the critical point. Second, non-equilibrium dynamics is studied by looking at stress relaxation in simple shear flow. Anomalous stress relaxation and critical rheological properties are derived. Some of the exact results contradict long-standing scaling arguments.

University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons