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29 March 2024
 
  » arxiv » cond-mat/0303578

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Diffusion of gelation clusters in the Zimm model
Matthias Küntzel ; Henning Löwe ; Peter Müller ; Annette Zippelius ;
Date 27 Mar 2003
Journal Eur. Phys. J. E 12, 325--331 (2003) DOI: 10.1140/epje/i2003-10066-x
Subject Statistical Mechanics; Soft Condensed Matter | cond-mat.stat-mech cond-mat.soft
AbstractStarting 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 $n$, ${hat D}_nsim n^{-{hat b}}$ with ${hat b}=1/d_s-1/2$ given in terms of the spectral dimension $d_s$ 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 $D_{ m eff}sim epsilon^a$ of the cluster-averaged effective diffusion constant at the gel point with exponent $a = (3/2 - au +1/d_{s})/sigma$.
Source arXiv, cond-mat/0303578
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