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

Mean‐square radius of gyration Rg 2 and the maximum span length L MS 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 Rg 2 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 L MS /(degree of polymerization) and k shows the analogous behavior with that for g ‐ratio and k . The magnitude of Rg 2 is proportional to L MS , with Rg 2 = 0.18 L MS , irrespective of the breadth of the primary polymer chain length distribution.