Molecular Weight Distribution in Free-Radical Polymer Modification with Cross-Linking:  Effect of Chain-Length-Dependent Termination

A general equation of molecular weight distribution has been derived for free-radical polymer modification with cross-linking. The equation takes into account chain-length-dependent diffusion-controlled radical termination. It reduces to Saito's equation when the termination becomes chain-length independent. A simple three-parameter chain-length-dependence function is employed. Calculations of molecular weight development, gel point, and gel/sol fraction for both polymer and radical populations have been made numerically with a uniform initial distribution. It has been shown that the chain-length-dependent termination has a strong effect on the molecular weight development and gelation behavior. It causes significant deviation from the well-studied random process of cross-linking. It delays gel point but accelerates gel growth.