Mass distribution in n-polymer stochastic aggregation and large-mass behaviour

Abstract

The exact solutions of the rate equations of the n-polymer stochastic aggregation involving two types of clusters, active and passive for the kernel ∏nk = 1sik(sik = ik) and ∑nk = 1sik(sik = ik), are obtained. The large-mass behaviours of the final mass distribution of the active and passive clusters have scaling-like forms, although the models exhibit different properties. Respectively, they have different decay exponents γ = (2n + 1)/(2(n-1)) and γ = q + (2n + 1)/(2(n-1)) for ∏nk = 1sik(sik = ik) and γ = 3/(2(n-1)) and γ = q + 3/(2(n-1)) for ∑nk = 1sik(sik = ik), which include exponents of two-polymer stochastic aggregation. We also find that gelation is suppressed for kernel ∏nk = 1sik(sik = ik) which is different from the deterministic aggregation.