A MODEL OF MICELLIZATION FOR BLOCK-COPOLYMERS IN SOLUTIONS

Block copolymers are generally polydisperse, and the molecular weight distribution of a block copolymer has a profound effect on its micellization behavior in solution. When the block copolymer concentration is lower than the mixed critical micelle concentration [cmc(mix)], the insoluble block is assumed to adopt a spherical collapsed conformation. This leads to the proposal that the association energy of the collapsed spheres can be described by the Hamaker equation, i.e., that the interaction energy is proportional to the radius of the spheres. From this model, a relationship between the cmc of each component and the length of the insoluble block can be obtained. This relationship is used in combination with a treatment of mixed micellization to account for the dependence of the cmc(mix) on the insoluble chain length and on its polydispersity, and satisfactory results are obtained for the poly(styrene-b-isoprene)/n-hexadecane and poly(styrene-b-sodium acrylate)/water systems. From this model, the single chain fraction of the block copolymer can be calculated as a function of the total block copolymer concentration. The molecular weight distributions of the single chain and the micellar fractions can also be obtained. The cmc(mix) was found to decrease as the polydispersity index increases. The single chain fraction and molecular weight distributions of the single chain and the micellar fractions are found to be influenced by the dependence of the cmc of each component on the insoluble chain length.