A General Theory of Gel Formation with Multifunctional Interunit Junctions

Abstract

Abstract A theory is presented for a general treatment of the molecular size distribution, the gel point, and the post-gelation phenomena with respect to polymerization with formations of various kinds of interunit junctions, assuming (1) that all functional groups are equally reactive, and (2) that no kind of intramolecular interunit junction occurs. These interunit junctions appear concurrently in a system composed of a mixture of monomeric molecules and with a distributions of functionalities. Two cases are treated: (1) when the interunit junction is characterized only by the number of functional groups involved in its formation, and (2) when the interunit junction is characterized not only by the number of groups, but also by the magnitude of the free energy of its formation. The former is illustrated by the poly condensation with bi- or terfunctional interunit junctions or with both. The latter is illustrated by the polycondensation between A and B groups in a mixture of A-monomers with equireactive A groups and B-monomers with equireactive B groups, where a B-monomer is regarded as a kind of interunit junction.