Micellization Kinetics in Block Copolymer Solutions:  Scaling Model

The kinetics of micelle evolution of diblock copolymers from unimers toward the equilibrium state is studied analytically on the basis of consideration of the kinetic equations. The association/dissociation rate constants for unimer insertion/expulsion and micelle fusion/fission are calculated by applying Kramers' theory combined with a scaling approach. It is shown that the difference in the intermediate results and the rate of association for the "unimer exchange" mechanism and the joint "micelle fusion/fission + unimer exchange" mechanism is remarkable, with the latter being much more effective. According to this mechanism, at the beginning of the micellization, after coupling of free unimers is completed, fusion of micelles becomes dominant, whereas unimer exchange is effectively frozen by the high activation energy required for unimer release. The later stages of micelle evolution involve both unimer exchange and micelle fusion, which is considerably slowed with time as the average micelle size increases. Micelle fission is also a relatively slow process that however plays an important role in micelle reequilibration occurring with a decrease in the equilibrium aggregation number (as e.g., during T-jump experiments). Applications of the theory to experimental results are discussed in detail.