Micellization of Diblock Copolymers in Polymeric Solvents

Abstract

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 false( χ N false) normalc . normalm . − 1 / 2 ∼ ( f B N 1 ) − 1 / 2 N 1 / 2 with the optimal aggregation number at the transition m c.m. * ∼ 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 false( χ N false) normalc . normalm . − 1 / 2 ∼ ( f B N 1 ) − 1 N with m normalc . normalm . * ∼ ( 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 ≡ N/f B N 1. Interestingly, on combining the scaling behavior of m c.m. *, (χN)c.m. shows a universal scaling behavior with an intrinsic scaling variable x ≡ (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.

Two-Step Coil-to-Globule Transition in Mixed Mono-/Polymeric Solvents

“…In addition, the C–G transition also shows interesting chain length dependence in the presence of the polymeric solvent. For the short-chain solvents, the transition point is (χ N ) tr – 1/2 ∼ ( pN ) 3/4 N 1 –1/2 , which can be well explained by an extended Lifshitz theory. , However, the test chain is well segregated with the solvent chain, leading to a different transition point as χ tr ∼ N 1 –2/3 in the long-chain solvents. ,,− …”