On the Colloidal Stability of Spherical Copolymeric Micelles

Using self-consistent field (SCF) calculations, we systematically quantify the pair interactions between spherical diblock copolymer micelles following a bottom-up approach. From the equilibrium properties of self-assembling micelles at different separation distances, a simple yet insightful pair interaction can be extracted. The SCF results match with an analytical model based upon closed expressions for the free energy change per diblock copolymer in the micelle. To gain insights into the colloidal stability of dilute micelle suspensions, the second virial coefficient normalized by the undistorted micelle volume (B ₂ ^*) is evaluated. For stable micelles (B ₂ ^* ≳ -6), we find a weak dependence of B ₂ ^* on solvophilic block length for varying core-forming block properties (core solvation and block length). The micelle suspension gets unstable (B ₂ ^* ≲ -6) when the corona-forming block crosses Θ-solvent conditions toward poor solvency. In contrast with what is expected from models where the soft nature of the micelle is not taken into account, increasing the effective grafting density of solvophilic tails from the core then leads to colloidal destabilization of the micelle suspension.