Micellization of Diblock Copolymers in Polymeric Solvents

We study micellization for A-B diblock copolymers of length N-1 with the volume fraction of the insoluble block f(B) in A polymeric solvents of length N by dilute solution thermodynamics. For short-chain solvents, the micelle is "wet", and the critical micelle condition is given by (chi N)(c.m). - 1/2 similar to (f(B)N(1))N--1/2(1/2) with the optimal aggregation number at the transition m(c.m.)* similar to N(1/2)p(3/2)(p=b(2)/v(0)(2/3) is the stiffness parameter), in agreement with the extended Lifshitz theory. However, the micellization point for the "dry" micelle is (chi N)(c.m). - 1/2 similar to (f(B)N(1))N-1 with m(c.m.)* similar to (f(B)N(1))(1/2)p(3/2) in the long-chain solvents. A theoretical analysis shows that the micellization point is a universal function of the apparent scaling variable x(m) equivalent to N/f(B)N(1). Interestingly, on combining the scaling behavior of m(c.m.)*, (chi N)(c.m.) shows a universal scaling behavior with an intrinsic scaling variable x equivalent to (pN)(3/2)/m*f(B)N(1), which has a clear physical meaning as the ratio between the pervaded volume of the polymeric solvent and the physical volume of the micellar core. In addition, after proper nondimensionalizing, the micelle density profile and the interfacial thickness at the micellization point also show universal behaviors with both x(m) and x. Importantly, micelles with several to thousands of chains show great potential for application in drug and gene delivery diagnostics, nanoreactors, and microcapsules.