Molecular Weight Distribution of Linear Chains in Step-Growth Polymerization Under the Influence of Cyclization Reactions

Two different equations are presented describing the frequency distribution (fl) of linear chains in step-growth (SG) polymerizations. Two related equations for the weight distribution (wl) are formulated as well. All equations contain either an exponent a that represents the reaction rates (or probabilities) of chain growth versus cyclization reactions or they contain a cyclization factor beta. Plots of fl and wl versus conversion or degree of polymerization are presented and discussed. Distribution curves of individual oligomers versus conversion and versus beta are described. Furthermore, the consequences for hyperbranched polymers resulting from polycondensations of abn monomers are discussed. Analogous to Flory's theory all equations concern kinetically controlled SG polymerizations.