SOLUBILIZATION IN SPHERICAL BLOCK COPOLYMER MICELLES - SCALING ANALYSIS BASED ON STAR MODEL

We develop a theory of solubilization of low molecular weight species in block copolymer micelles, employing the scaling approach and buildi ng on the analogy between micelles and star polymers. Specifically, we consider spherical micelles of AB-diblock copolymers formed in select ive solvents, in which the core and the shell regions are assumed to h ave radial concentration variations similar to those occurring in the solution state of a star polymer. Invoking the results for the conform ation of a star polymer derived by Daoud and Cotton, expressions are d eveloped for the free energy per molecule of the micelle DELTAG, the c ore radius R, the shell thickness D, and the overall volume fraction o f the polymer within the core phi(A) as functions of the micellar aggr egation number g. From the minimization of the free energy of an isola ted micelle, the equilibrium values for all the micellar structural pa rameters and for the extent of solubilization are obtained. The result s expressed as scaling relations for g, R, D, and phi(A) are derived f or various situations of interest including those of the solvent S bei ng 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.