Coagulation and self-duplication processes of a chain-shaped polymer system

We propose an irreversible coagulation model with monomer duplications or/and self-duplications, in which two aggregates of the same species can themselves coagulate and an aggregate of any size can yield a new monomer or double itself through self-duplications. By employing the mean-field rate equation approach we analytically investigate the evolution behavior of the system. For the system only with monomer duplications, the aggregate size distribution can follow a power law in size in the long-time limit. For the system only with self-duplications, the aggregate size distribution approaches a generalized scaling form. For the system with both monomer duplications and self-duplications, the aggregate size distribution takes the power-law form in some cases and has a more complicated form in other cases, which depends crucially on the details of the monomer duplication probability.