Regensburg 2002 – wissenschaftliches Programm
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DY: Dynamik und Statistische Physik
DY 52: Weiche Materie
DY 52.5: Vortrag
Freitag, 15. März 2002, 12:15–12:30, H2
Effective diffusion constant in the Zimm model for polymeric liquids at the gelation transition — •Matthias Küntzel, Peter Müller, and Annette Zippelius — Institut für Theoretische Physik, Georg-August-Universität, D-37073 Göttingen
Effects of the hydrodynamic interaction on the critical dynamics of gelling polymeric liquids are analyzed by means of a generalized Zimm model with randomly distributed harmonic crosslinks which are drawn from a mean-field distribution. The main focus lies on the disorder-averaged effective diffusion constant Deff defined via the long-time decay of the incoherent scattering function. Thanks to the preaveraging approximation Deff−1 decomposes into contributions ⟨ D−1⟩n from averages over all polymer clusters of fixed size n. Given the asymptotic power-law growth ⟨ D−1⟩n∼ nβ with cluster size, it follows that Deff vanishes with exponent 2β−1 at the gelation transition provided that β ≥ 1/2. Otherwise Deff does not vanish. Exact analytical arguments yield the lower bound β≥ 1/4. Numerical data for β lie closely above this lower bound, but well below 1/2, the Zimm value for linear chains. Thus, the results show that the diffusion constant of a cluster of size n depends not only on n—as in the Rouse model—but also on the topology of the cluster. Consequently, common heuristic approaches to gelation in the Zimm model based on a combination of cluster statistics and properties of linear chains are bound to fail.