Block copolymers can self-assemble into various structures, such as micelles and vesicles. Previous studies have shown that single chain exchange is the main mechanism for block copolymer micelles to achieve equilibrium. In this study, a new lower critical micelle temperature (LCMT) system, poly(methyl methacrylate)-block-poly(n-butyl methacrylate) in two room temperature ionic liquids, 1-ethyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide and 1-butyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide was developed, and its chain exchange kinetics were investigated using time-resolved small-angle neutron scattering (TR-SANS). In order to probe the effect of the core block length, the corona block length and the solvent selectivity on the chain exchange rate, we synthesized two series of protonated and deuterated copolymers, one with identical core block length and one with identical corona block length, as well as systematically varied the Flory-Huggins interaction parameter chi by tuning the ratio of the two ionic liquids in the solvent. Notably, the results show that the solvent selectivity has a remarkable effect on the chain exchange rate, and therefore we proposed a more elaborate function of chi for the energy barrier of chain expulsion, which is rationalized by a calculation in the spirit of Flory--Huggins theory. Besides the kinetic study, complementary dynamic light scattering (DLS) and small-angle X-ray scattering (SAXS) experiments were also conducted to investigate the structure of micelles. Particular emphasis was placed on elucidating the scaling relationship between the micelle core radii and the degree of polymerization of the core block in the copolymers.