Role of Distance from Equilibrium in the Fragmentation Kinetics of Block Copolymer Micelles

The fragmentation kinetics of 1,2-polybutadiene-b-poly(ethylene oxide) (M_n = 17.2 kDa and f_PEO = 0.38) block copolymer micelles have been examined with an emphasis on elucidating the role of driving force for micellar fragmentation, represented by the aggregation number ratio Q/Q_eq. Large micelles with size Q > Q_eq were formed in an ionic liquid [C₂mim][TFSI] by the direct dissolution method. A broad range of Q/Q_eq was then obtained by altering the solvent quality after micelle formation by addition of a second solvent, selected from a series of imidazolium-based ionic liquids [C_xmim][TFSI] with x = 2, 4, 6, 8, 10, and 12. In order to quantify the change in solvent quality by dilution, the interfacial tension γ between the different ionic liquids and 1,2-polybutadiene homopolymer was determined using the pendant drop method. Micelles in a solution diluted with a second ionic liquid with x ≥ 2 were equilibrated by high-temperature annealing at 170 °C, during which in situ dynamic light-scattering measurements were made to follow the decay of average micelle size with time. Micelles were further characterized using small-angle X-ray scattering and cryogenic transmission electron microscopy to obtain micelle core size distributions. Q_eq and γ were found to exhibit a power-law correlation, Q_eq ∼ γ^6/5, in accordance with the scaling prediction for star-like micelles. The reduction in γ on dilution with a lower γ solvent (x > 2) results in a smaller equilibrium micelle size, enabling access to a higher Q/Q_eq, in the range from 1.1 to 5. The rate of fragmentation was found to increase significantly with an increase in Q/Q_eq, thus the greater thermodynamic driving force leads to a systematic acceleration of fragmentation kinetics. The detailed mechanism by which micelles with Q ≫ Q_eq achieve Q_eq remains to be elucidated; the data suggest that it is not a sequential process but concerted.