Exact Solution of the Cluster Size Distribution for Multi-polymer Coagulation Process

We propose a simple irreversible multi-polymer coagulation model in which m polymers consist of multiple components bond spontaneously to form a larger cluster. We solve the generalized Smoluchowski rate equation with constant reaction rates to obtain the exact solution of the cluster size distribution. The results indicate that the evolution behaviour of the system depends crucially on the polymer number m of the coagulation reaction. The cluster concentrations decay as t^{-m/ (m-1)2}, and the typical size S(t) of the m-polymer coagulation system grows as t^1/(m-1). On the other hand, the cluster size distribution may approach unusual scaling form in some cases.