Homopolymer solubilization and nanoparticle encapsulation in diblock copolymer micelles

We use self-consistent mean-field theory to investigate a system of A homopolymer, AB copolymer, and C homopolymer, where there are attractive interactions between the B and C components. We calculate volume fraction profiles and chemical potentials of formation for unswollen micelles, swollen micelles, and flat interfaces using a theory that is generalized for multiple components and a general copolymer composition distribution. We find that swollen spherical AB copolymer micelles form in the A matrix with a preferred radius that controls the amount of C homopolymer solubilized in the center of the micelle and that they form at chemical potentials lower than the chemical potential of micelle formation in the absence of C homopolymer. The swollen spherical micelles are also preferred over a flat interface geometry because the copolymer changes the preferred interfacial radius of curvature. The calculations also show that nanoparticles can be encapsulated in the center of swollen micelles by introducing an attraction between the surface of the particle and the C homopolymer. These results indicate that a nanocomposite could be formed by utilizing attractive B-C interactions to encapsulate C homopolymer and nanoparticles in AB diblock copolymer micelles.