Theory of Nonrandom Cross-Linking: Free-Radical Polymer Grafting

Free-radical polymer−polymer grafting may lead to gel formation. Due to the different possible combination and termination reactivities of each polymer backbone radical, polymer chains are cross-linked in a nonrandom manner. A general model has been developed using the method of moments to predict the development of molecular weights in the pregel period and the gel point. It is found that the gelation behavior is governed by the product of the radical termination reactivity ratios (r 1 r 2) irrespective of their individual values. Analytical solutions of the differential equations of the moments have been derived for the limiting cases of r 1 r 2 = 0, 1, and ∞. The model reduces to the Flory−Stockmayer classical gelation theory under the condition of random cross-linking. It deviates from the classical theory when the cross-linking process becomes nonrandom. The magnitude of the discrepancies depends on the kinetic parameters and reaction conditions.