A KINETICS APPROACH TO NONLINEAR POLYMERIZATION

Three formal equations are presented that describe the time dependence of the size distribution of polymer species in the tree-like homopolymerization of f-functional monomer, the copolymerization of 3- and 2-functional monomers and the homopolymerization of 3-functional monomer with cyclization taken into account. The equations have the form of the Smoluchowski coagulation equation extended to take into account substitution effects that may alter the reactivities of functional groups. Average degrees of polymerization up to gel point can relatively easily be extracted from the proposed equations. The results, illustrating applications of the kinetics approach, confirm that statistical theories are inadequate to model kinetically-controlled polymerization reactions if substitution effects are present.