Diffusion of gelation clusters in the Zimm model

Details Diffusion of gelation clusters in the Zimm model Diffusion of gelation clusters in the Zimm model

2003-03-27

arxiv.org/abs/cond-mat/0303578v2

Eur. Phys. J. E 12, 325--331 (2003)

Physics

Condensed Matter

Statistical Mechanics

7 pages, 4 figures; slightly expanded version, typos corrected; to appear in Eur. Phys. J. E

Scientific paper

10.1140/epje/i2003-10066-x

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 $n$, ${\hat D}_n\sim n^{-{\hat b}}$ 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 $D_{\rm eff}\sim \epsilon^a$ of the cluster-averaged effective diffusion constant at the gel point with exponent $a = (3/2 -\tau +1/d_{s})/\sigma$.

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