Cluster survival and polydispersity in aggregation

E. K. O. Hellén; P. E. Salmi; M. J. Alava

doi:10.1209/epl/i2002-00225-3

All issues

Volume 59 / No 2 (July 2002)

Europhys. Lett., 59 2 (2002) 186-192

Abstract

Issue		Europhys. Lett. Volume 59, Number 2, July 2002


Page(s)		186 - 192
Section		General
DOI		https://doi.org/10.1209/epl/i2002-00225-3
Published online		01 July 2002

Europhys. Lett., 59 (2), pp. 186-192 (2002)

Cluster survival and polydispersity in aggregation

E. K. O. Hellén, P. E. Salmi and M. J. Alava

Laboratory of Physics, Helsinki University of Technology P.O. Box 1100, FIN-02150 HUT, Finland

Received: 7 November 2001
Accepted: 17 April 2002

Abstract

We study the probability, $P_\ab{S}(t)$ , of a cluster to remain intact in one-dimensional cluster-cluster aggregation when the cluster diffusion coefficient scales with size as $D(s) \sim s^\gamma$ . $P_\ab{S}(t)$ exhibits a stretched exponential decay for $\gamma < 0$ and the power laws $t^{-3/2}$ for $\gamma=0$ , and $t^{-2/(2-\gamma)}$ for $0<\gamma<2$ . A random walk picture explains the discontinuous and non-monotonic behavior of the exponent. The decay of $P_\ab{S}(t)$ determines the polydispersity exponent, τ, which describes the size distribution for small clusters. Surprisingly, $\tau(\gamma)$ is a constant $\tau = 0$ for $0<\gamma<2$ .

PACS: 05.40.-a – Fluctuation phenomena, random processes, noise, and Brownian motion / 05.70.Ln – Nonequilibrium and irreversible thermodynamics / 05.50.+q – Lattice theory and statistics (Ising, Potts, etc.)

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