Micellization and relaxation kinetics of diblock copolymers in dilute solution based on A–W theory: I. Description of a model for core–corona type micelles

On the basis of the Aniansson–Wall (A–W) theory, a calculation method for the time evolution of association-number distribution during micelle formation of diblock copolymer in solution is presented. The rate constant for the elemental process of a chain expulsion from a micelle is evaluated as a function of the association number by application of Halperin's treatment based on the Kramers rate theory. Numerical calculations are carried out for both cases of micellization from unimer state and micellar relaxation under a temperature jump from one micellar state to another. In the micelle relaxation, the micelle size changes stepwise with two steps, clearly showing the characteristic feature of the A–W mechanism, where there exist two processes, the fast process undergoing by consuming/releasing free unimers and the slow process accompanied with almost no change of unimer concentration. On the contrary, in the micellization from unimer state, the very fast process is observed, where the free chains get together quickly to form temporal micelles, and is followed by an ordinary micellar relaxation.