Solubilization in spherical block copolymer micelles: Scaling analysis based on star model

Abstract

We develop a theory of solubilization of low molecular weight species in block copolymer micelles, employing the scaling approach and building on the analogy between micelles and star polymers. Specifically, we consider spherical micelles of AB-diblock copolymers formed in selective solvents, in which the core and the shell regions are assumed to have radial concentration variations similar to those occurring in the solution state of a star polymer. Invoking the results for the conformation of a star polymer derived by Daoud and Cotton, expressions are developed for the free energy per molecule of the micelle ΔG, the core radius R, the shell thickness D, and the overall volume fraction of the polymer within the core φA as functions of the micellar aggregation number g. From the minimization of the free energy of an isolated micelle, the equilibrium values for all the micellar structural parameters and for the extent of solubilization are obtained. The results expressed as scaling relations for g, R, D, and φA are derived for various situations of interest including those of the solvent S being a good or theta solvent for the shell block B, and the solubilizate J being a good or theta solvent for the core block A.