Dynamics of gelling liquids: a short survey
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The dynamics of randomly crosslinked liquids is addressed via a Rouse- and a 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, its 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 a simple shear flow. Anomalous stress relaxation and critical rheological properties are derived. Some of the results contradict long-standing scaling arguments, which are shown to be flawed by inconsistencies.
21 pages, 3 figures; Dedicated to Lothar Schaefer on the occasion of his 60th birthday; Changes: added comments on the gel phase and some references
21 pages, 3 figures; Dedicated to Lothar Schaefer on the occasion of his 60th birthday; Changes: added comments on the gel phase and some references