Molecular Size Distribution in Random Polyfunctional Condensation with or without Ring Formation: Computer Simulation

Abstract

We have re-examined the polymer size distribution in a model system initially composed of N₀ monomeric units RA_ƒ, where each unit R carries ƒ identical functional groups A. Self-condensation is postulated to proceed at random by the formation of [Formula: see text] bonds until the fraction α of A groups have reacted. The controversy regarding the applicability of the Flory–Stockmayer (F.S.) and the Whiteway–Smith–Masson (W.S.M.) expressions to this model has been resolved. Two variants of this model are distinguished, depending on whether ring formation is allowed or forbidden. It is shown that in the limit of an infinite system the incidence of rings in the ringsallowed model tends to zero below the critical value of α, α_c = 1/(ƒ − 1 ). Consequently, the limiting polymer size distributions for the rings allowed and ringsforbidden models coincide over the range [Formula: see text], and are both described by the F.S. expression. For the ringsforbidden model, the F.S. equation fails above α_c, but for the rings allowed model it continues to apply over the entire accessible range [Formula: see text] The W.S.M. equation represents the limiting distribution for the polymerization process in which one functional group per monomer is singled out (A*) and bonding is restricted to [Formula: see text] pairs. In that process, and in the limit of an infinite system, rings are not formed over the entire attainable range of α, from 0 to 2/ƒ.