Mechanisms of the exchange of diblock copolymers between micelles at dynamic equilibrium

The exchange dynamics of chains between micelles of diblock copolymers in dilute solution in a selective solvent has been studied by a semianalytical approach. A close inspection of dynamic Monte Carlo simulation trajectories showed that there are mainly two types of exchange mechanisms, chain insertion/expulsion and micellar merger/splitting. The relative contributions of the two mechanisms to the overall exchange dynamics are examined as a function of the following variables: the concentration of the diblock copolymers, the energy of interaction between the insoluble block and the surroundings, and the size of the insoluble block. A kinetic scheme, which incorporates the possible states of association and the mechanisms by which the exchange takes place, is constructed. The corresponding transition rates matrix, with the rate constants extracted from simulations, is used in a Master equation formalism to demonstrate that the two mechanisms involved in the exchange dynamics operate on time scales differing by at least 1 order of magnitude, in conformity with recent experimental observations. Application of a filtering technique to the transition rate matrix showed that the high-frequency modes of the relaxation are from the chain insertion/explusion mechanism and the relatively slower modes, which dominate the tail parts of the time decay of correlation functions, are from the micellar merger/splitting type of transitions. The analysis thus provides an explanation for the two processes observed in the recent characterization of the exchange dynamics of chains between micelles by the efficiency of nonradiative singlet energy transfer. The chain insertion/expulsion mechanism is shown to be predominantly important at low concentrations and at high interaction energies between the insoluble block and the surroundings, while the micellar merger/splitting is activated at higher concentrations.