Particle Survival and Polydispersity in Aggregation

Details Particle Survival and Polydispersity in Aggregation Particle Survival and Polydispersity in Aggregation

2001-11-28

arxiv.org/abs/cond-mat/0111522v1

Europhys. Lett. 59, 186 (2002).

Physics

Condensed Matter

Statistical Mechanics

submitted to Europhysics Letters

Scientific paper

10.1209/epl/i2002-00225-3

We study the probability, $P_S(t)$, of a cluster to remain intact in one-dimensional cluster-cluster aggregation when the cluster diffusion coefficient scales with size as $D(s) \sim s^\gamma$. $P_S(t)$ 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 $P_S(t)$ determines the polydispersity exponent, $\tau$, which describes the size distribution for small clusters. Surprisingly, $\tau(\gamma)$ is a constant $\tau = 0$ for $0<\gamma<2$.

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