Random Branching of Polymer Chains with Schulz–Zimm Distribution. 2. Radius of Gyration and Maximum Span Length

Abstract

AbstractMean‐square radius of gyration Rg2 and the maximum span length LMS of each polymer molecule are investigated for the random branching of primary chains that follow the Schulz–Zimm distribution, by using the Monte Carlo simulation method. It is found that the expected g‐ratio of Rg2 of the branched molecule to that of a linear molecule for a given number of branch points k does not change with the branching density. The expected g‐ratio becomes larger for the primary chains with broader distribution. An approximate formula for the relationship between g‐ratio and k that accounts for the distribution breadth is proposed. The relationship between the weight fraction of the maximum span chain LMS/(degree of polymerization) and k shows the analogous behavior with that for g‐ratio and k. The magnitude of Rg2 is proportional to LMS, with Rg2 = 0.18 LMS, irrespective of the breadth of the primary polymer chain length distribution.