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=1 sik(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 dexay exponents γ=2n+1/2(n-1) and γ=q+2n+1/2(n-1) for ∏nk=1 sik(sik=ik) and γ=3/2(n-1) and γ=q+3/2(n-1) for ∑n k=1 sik(sik=ik),which include exponents of two-polymer stochastic aggregation.We also find that gelation is suppressed for kernel ∏n k=1 sik(sik=ik) which is different from the deterministic aggregation.