Diffusion of gelation clusters in the Zimm model |
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Authors: | M?Küntzel H?L?we Email author" target="_blank">P?MüllerEmail author A?Zippelius |
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Institution: | (1) Institut für Theoretische Physik, Georg-August-Universität Göttingen, 37073 Göttingen, Germany |
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Abstract: | 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
.Received: 24 July 2003, Published online: 21 November 2003PACS:
64.60.Ht Dynamic critical phenomena - 61.25.Hq Macromolecular and polymer solutions; polymer melts; swelling |
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Keywords: | |
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