Theoretical studies on the thermodynamic product size distribution in nucleation-elongation polymerization under imbalanced stoichiometry

Three different models are developed to calculate the thermodynamic product size distribution in a nucleation-elongation polymerization between a pair of A-A and B-B typed comonomers. These monomers are designed to undergo a single step of nucleation prior to an isodesmic chain elongation, namely, a cooperative, step-growth polymerization with dimerization being an energetically less favored process. Particularly, emphasis is laid on analyzing product distribution under conditions of imbalanced functionality stoichiometry. Consistent results are obtained from independent approaches, mechanistic and statistical, demonstrating that when the mole ratio of the comonomers deviates from unity, at polymerization equilibrium such a nucleation-elongation polymerization generates products of substantially higher molecular weights than those from a corresponding isodesmic system having an identical energetics for chain propagation yet without the nucleation process. This higher molecular weight is shown achieved by retaining a large portion of the excess monomer unreacted at equilibrium and selectively compose product chains with comonomers at a roughly stoichiometric ratio. Essentially, such a polymer-monomer coexisting bimodal distribution is a result from destabilization of the oligomeric species due to the nucleation effect.