Particle Survival and Polydispersity in Aggregation

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