Nonuniformities of Distributions of Molecular Weights of Grafted Polymers

The nonuniformities of graft (co)­polymers have been analyzed using the probability generating functions and their moments. The nonuniformity is described by ratios of averages of molecular weights of the graft (co)­polymers. The general feature of the nonuniformity of graft (co)­polymers is that, with increasing degree of grafting and degree of polymerization of the backbone, the nonuniformity of a graft (co)­polymer passes through a maximum and approaches more or less closely the nonuniformity of the backbone (co)­polymer. The nonuniformities of graft (co)­polymer are a function of the number- and weight-average degrees of polymerization of the backbone and grafts and are independent of the type of the degree-of-polymerization distribution. The nonuniformity depends markedly on the disparity in the molecular weights of monomer units of the backbone copolymer and the grafts if the graft copolymer has a small number of grafts per backbone, but the disparity effect gets smaller with increasing degree of polymerization of the backbone and fraction of graftable units.