Model simulation of cationic polymerization by an iterative technique

Using a simple, instructive model of living polymerizations, we develop an economic technique for solving a complete set of kinetic equations for active polymers P_n^* with chain length n. The method consists of two steps: (i) solution of the global kinetic equations for the global species P^* which comprises all individual polymers P_n^* together with monomer M and other non-polymeric species, followed by (ii) iterative solution of the original kinetic equations, successively for the individual polymers P₁^*, P₂^*, P₃^*, …, P_n^*. The method is applied successfully to a rather complex, realistic model of cationic polymerizations. In general, our iterative scheme serves to reduce numerical storage requirements, in comparison with traditional direct integrations for all individual kinetic equations. Therefore it may allow simulations of very demanding polymerizations, including very high degrees of polymerization, which cannot be evaluated by traditional techniques.