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

ZL Li and EE Dormidontova, SOFT MATTER, 7, 4179-4188 (2011).

DOI: 10.1039/c0sm01443e

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 A(2)B(3) or A(4)B(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, tau, increasing exponentially with core block length, N-A and interaction parameter between blocks, chi(AB) as tau approximate to exp (0.67 chi N-AB(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 A(4)B(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.

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