Statistical treatment of the grafting reaction

Statistical calculations were performed for the fundamental quantities in the grafting reaction starting from a substrate polymer with a uniform and a most probable molar mass distribution: e.g. , the number of branches in one graft copolymer, the number average degree of polymerization (P̄ n ) of the backbone of the graft copolymer, the fraction of the mother polymer grafted. It is shown that P̄ n of the graft copolymer prepared from a mother polymer with a most probable molar mass distribution decreases at first with increasing number of grafted branches, reaches a minimum and then increases, if the P̄ n of the grafted branch is lower than that of the mother polymer. This peculiar behavior is attributed to the fact that the mother polymer molecule with a higher molar mass has a higher probability to participate in the grafting. In addition, the calculation denotes that the synthesized, unfractionated graft copolymer is a polymolecular mixture of the copolymer having branches whose number distribution is remarkably broad.