Simple and General Approach for Reversible Condensation Polymerization with Cyclization

We develop a simple recursive approach to treat reversible condensation polymerization with cyclization. Based upon minimum set of balance equations, the law mass action, Gaussian chain statistics, and assumption independent reactions, we derive exact analytical solutions for systems without cyclization, containing only smallest loops, or that exclusively form loops. Exact numerical are computed general case homopolymerization flexible precursor polymers. All were tested Monte-Carlo simulations. A generalization good solvent is discussed it shown this agrees previous work in limit low high polymer volume fractions. The new aspect our its flexibility allows rather more complex situations. These include different kinds linear polymerization, nonlinear first shell substitution effect, semiflexibility, low-molecular-weight cutoff