Diffusion and gelation in polyadditions. IV. Statistical theory of ring formation and the absolute gel point

Abstract

AbstractIn the model nonlinear polyaddition system methyl methacrylate/ethylene dimethacrylate (MMA/EDMA), the plot of the critical conversion against the rate of polymerization is a straight line. This is in accord with the classical theory of gelation, whose vindication is completed in this paper. To account quantitatively for the slope of the line, internal cyclization within the primary polymerization chains must be extensive. Thus of the order of half the pendent vinyls on such a chain fall to the radical on the same chain, in agreement with theoretical prediction on the basis of molecular models. The intercept of the critical conversion plot at zero rate can also be explained in terms of the internal cyclization reaction, while chain transfer makes at most a small contribution. The dependence of the gel point on the proportion ρ of EDMA unsaturation, over a 250‐fold range, is satisfactorily accounted for by the classical gelation theory. A statistical theory of internal cyclization suggests that a steady state is approached in the growth of a given radical chain. Pendent vinyls are then lost by cyclization as fast as they are added by polymerization. The limiting number of pendent vinyls on a primary chain is about 1000 ρ. A statistical theory of multiple crosslinking (cyclization involving more than one primary chain) suggests that it is unimportant. The number of pendent vinyls on a giant molecule grows proportionately to the number of primary chains of which it is comprised. Thus multiple crosslinking has little effect on the classical network theory of gelation, but makes a contribution to the parameter introduced into the theory to correct for internal cyclization. The interplay of kinetic and gelation measurements is useful in mechanistic studies of nonlinear polymerization.