Concentration-Driven Slowdown of Chain-Exchange Kinetics in Block Copolymer Micelle Solutions

We investigate the dependence of chain-exchange kinetics on polymer concentration for spherical micelles prepared from a polystyrene-b-poly(ethylene-alt-propylene) (SEP) diblock copolymer (M_n = 75 kDa, Đ = 1.05, and f_PS = 0.18) in the PEP-selective solvent squalane. Solutions with concentrations of 15 vol % or more adopt a body-centered-cubic (BCC) packing of micelles, or a dense liquid-like packing (LLP), as confirmed by small-angle X-ray scattering. Concurrently, the mean aggregation number of the micelles grows steadily from about 60 in dilute solution to nearly 200 by 50 vol %. Time-resolved small-angle neutron scattering (TR-SANS) analysis reveals a monotonic and substantial (i.e., more than 4 orders of magnitude) decrease in the rate of chain exchange as the polymer concentration increases from 1 to 50 vol %. The TR-SANS relaxation functions are analyzed, taking into account both changes in contrast (due to chain exchange) and evolution in the structure factor (due to refinement of micelle packing). The activation energy for chain pullout is extracted using an established model and can be expressed as a linear function of polymer concentration, indicating that, in addition to the enthalpic barrier for extracting the core block, the evolution of micelle characteristics with increasing concentration imposes further constraints on chain exchange. Consistent with a theory of Halperin, these results suggest that the dominant factor reflects steric penalties during core block pullout arising from a reduced interfacial area per chain and associated increased corona crowding, due to the increase in aggregation number. The rate of exchange is independent of whether the micelles adopt a BCC or LLP arrangement, confirming that the rate-limiting step is extraction of the core block.