Diffusion of gelation clusters in the Zimm model
| dc.creator | Küntzel, Matthias | |
| dc.creator | Löwe, Henning | |
| dc.creator | Müller, Peter | |
| dc.creator | Zippelius, Annette | |
| dc.date | 2003-03-27 | |
| dc.date | 2003-10-09 | |
| dc.date.accessioned | 2026-07-07T02:50:25Z | |
| dc.date.available | 2026-07-07T02:50:25Z | |
| dc.description | 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 $D_{\rm eff}\sim ε^a$ of the cluster-averaged effective diffusion constant at the gel point with exponent $a = (3/2 -τ+1/d_{s})/σ$. | |
| dc.description | 7 pages, 4 figures; slightly expanded version, typos corrected; to appear in Eur. Phys. J. E | |
| dc.identifier | https://arxiv.org/abs/cond-mat/0303578 | |
| dc.identifier | http://arxiv.org/abs/cond-mat/0303578 | |
| dc.identifier | Eur. Phys. J. E 12, 325--331 (2003) | |
| dc.identifier | doi:10.1140/epje/i2003-10066-x | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/21102 | |
| dc.subject | Statistical Mechanics | |
| dc.subject | Soft Condensed Matter | |
| dc.title | Diffusion of gelation clusters in the Zimm model | |
| dc.type | text |