EQUILIBRIUM POLYMERIZATION AND GELATION .1. INTEGRAL-EQUATION THEORY

This is the first of a series of papers on the application of Wertheim 's multidensity formalism to study the connectivity and related proper ties of equilibrium polymerizable particles. We first consider in deta il the case in which each monomer has two sites available for covalent bonding. We modify Wertheim's treatment to apply it to the case where the two sites on a monomer are indistinguishable, i.e., to homofuncti onal units. A study is presented of the connectedness behavior in thes e systems, including expressions for the weight-average molecular weig ht and cluster size. The application of these results to specific mode ls is reported in subsequent parts of this series.