Polymer coupling and theory of on‐random crosslinking: an analytical solution

Abstract Gel formation is an important feature in free‐radical polymer coupling. Due to the different possible combination reactivities of each polymer backbone radical, polymer chains are crosslinked in a non‐random manner. Equations of the moments have been derived to predict the pregel molecular weight development and the crosslink density at gel point. This work provides an analytical solution for the differential equations. The model agrees with the Flory‐Stockmayer gelation theory under the condition of random crosslinking. The magnitude of deviations from the classical theory for non‐random crosslinking depends on the product of the radical termination reactivity ratios ( r 1 r 2 ), the ratio of the rate constants of backbone radical generation ( k ), the ratio of the weight‐average chain lengths of primary polymers ( y ), and the polymer weight fractions ( w 2 ).