Equilibrium chain exchange kinetics in block copolymer micelle solutions by dissipative particle dynamics simulations

Abstract

The kinetics of chain exchange between diblock copolymer micelles in solution at equilibrium were studied by dissipative particle dynamics simulation. We performed hybridization simulations for A₂B₃ or A₄B_x (x = 4, 6, 8) micelle solutions in which approximately half of all micelles and free chains were initially colored and chain exchange between micelles was monitored by analyzing the time-dependent fraction of colored chains in aggregates. We found that in all cases the chain exchange is dominated by chain (or small aggregate) expulsion and follows a first-order kinetic process with the characteristic time, τ, increasing exponentially with core block length, N_A and interaction parameter between blocks, χ_AB as τ ≈ exp (0.67χ_ABN_A). We determined that chain exchange between micelles does not depend on concentration but occurs via several kinetic mechanisms: unimer expulsion/insertion, small aggregate fragmentation/merging and unequal size micelle fission/fusion, which all exhibit very similar relaxation times. Chain exchange between micelles in A₄B_x micelle solutions is found to occur more rapidly for diblock copolymers with a longer corona-block length, as the area per chain and critical micelle concentration are larger (while micelle size and critical micelle temperature are lower) in this case, implying a lower potential barrier for chain (or small aggregate) expulsion from micelles.