Kinetics and dynamics of gelation reactions

Gelation, which can occur when molecules react or colloids aggregate, is defined as the divergence of second and higher moments of molecular-weight and cluster-size distributions. Distribution kinetics and dynamics, described by population balance equations for aggregation and fragmentation, provide a framework for investigating quantitatively when and how gelation occurs and the conditions for existence of a nongelling steady state. We solve these integrodifferential equations for the size distribution by a numerical method and confirm the results by comparison with moment solutions. The results show how pregelation behavior is influenced by parameters in the aggregation and breakage kernels.