Analytic results for finite systems of ringed flory polymers

Abstract

We examine Flory's RAf model of polymerization for a finite closed system of N monomers. Monomers have f functional groups of type A. Random stepwise reaction between A's, regardless of ring formation, bonds the monomers together.We give exact statistics for the resulting polymer distribution and verify the results of the Falk and Thomas computer simulation. As N → ∞, Flory's modification of the Stockmayer distribution gives the distribution of finite polymers, and cyclization is confined to the gel.Similar results hold for Flory's AgRBf−g model.