Dimensions of Crosslinked Polymers without Rings

Abstract

AbstractMean‐square radius of gyration Rg2 and the maximum span length LMS of each polymer molecule formed in the crosslinking of polymer chains that follow the Schulz–Zimm distribution are determined by using the Monte Carlo simulation method for the generation of various crosslinked polymer architecture. For the random crosslinking, it is found that the expected g‐ratio of Rg2 of the crosslinked polymer to that of a linear polymer for a given number of crosslinks k does not change with the crosslinking density up to the gel point. The g‐ratio for a given k is larger for broader primary chain length distribution, and a convenient formula for the relationship between g and k is proposed. The linear relationship, Rg2 = 0.178 LMS applies, at least approximately, regardless of the primary chain length distribution and the crosslinking density. The relationship is essentially the same as for the branched polymers. The effect of nonrandom crosslinking is investigated through the theoretical simulation for the free‐radical vinyl/divinyl copolymerization conducted in a steady‐state continuous stirred tank reactor (CSTR). It is found that the nonrandomness induced by this reaction system does not change either of the universal relationships, g–k and Rg2–LMS.