Extension of simple polycondensation gelation theories to simple radical and mixed polycondensation/radical gelation

Abstract

The existing theories of polycondensation concentrate on the determination, by different mathematical approaches and different physicochemical approximations, of the degree of conversion and, hence, of the advancement of polymerization at the point of gel, and on the calculation of basic polymer parameters derived from the determination of the gel point. Among these, in the field of polycondensation, must be remembered (1) the gel theory of Carothers in which the critical degree of conversion at the gel point ( pgel) is defined as pgel 5 2/f, with f being the average functionality of the monomers in the system; (2) the probabilistic gel theory of Flory–Stockmayer in which pgel is defined through the coefficient of branching a 5 1/( f 2 1), f being the functionality of the monomer of greater functionality, through the expression a 5 rpr/[1 2 rp 2) 2 r)]—where p is both the degree of conversion and the probability that a certain reactive group has in fact reacted, r is the proportion of such a reactive group belonging to branching units, and r is the ratio of the types of reactive groups of the two monomers participating in the polycondensation; (3) the cascade process theory of Gordon based on more complex functions than the two preceding ones, but also offering some further advantages on them; (4) the Miller–Macosko recursive method; and (5) the stochastic graph theory of Bruneau, more complete but very complex and very complicated to use, as well as even more complex theories that can be found in the review literature. Although the more complex theories define to a much greater extent the reality of gelation, the simpler ones are much more used to solve applied, everyday problems. Thus, among these theories, the first two are of such a simplicity as to be constantly used in applied practice, whereas the third and fourth theories are also sometimes used in more complex research applications. Recently, in the quest of simple systems to solve everyday applied networking problems, an equation, and simpler regressions also, correlating the relative deflections obtained by thermomechanical analysis with the sum of the interfacial energy of interaction of a synthetic polymer with wood plus the internal cohesive strength of the hardened synthetic polymer has been obtained, namely