2003/03/31 by Matthias Küntzel, M. Küntzel, Henning Löwe +3 · 1 citation
Materials Science · Mathematics · Physics and Astronomy · #Material Dynamics and Properties #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat.soft #cond-mat.stat-mech
paper · pdf · doi:10.1140/epje/i2003-10066-x
published as Eur. Phys. J. E 12, 325--331 (2003) · 7 pages, 4 figures; slightly expanded version, typos corrected; to appear in Eur. Phys. J. E
openalex publication_date 2003/10/01 · arxiv created 2003/10/09 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Starting from a Zimm model we study selfdiffusion 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 nontrivial scaling of the Kirkwood diffusion constant averaged over all clusters of fixed size n, Dn∼ n^- b with b=1/ds-1/2 given in terms of the spectral dimension ds 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 D\rm eff∼ εa of the cluster-averaged effective diffusion constant at the gel point with exponent a = (3/2 -τ+1/ds)/σ.