Emulsion stabilization by diblock copolymers: Droplet curvature effect

The Cantor-Leibler theory of macroscopic emulsion stabilization by adding d iblock copolymer is reexamined with regard for the curvature of the equilib rium droplets. The treatment is based on the assumption that the equilibriu m state of the system corresponds to adsorption of most diblock copolymer m olecules at the interface which leads to a one-to-one correspondence betwee n the average droplet size, R, and the interfacial area per copolymer molec ule, Sigma. First we find R in the approximation of zero interfacial curvat ure and then investigate the equilibrium emulsion characteristics using the interfacial free energy expansion over the interfacial curvature (up to th e second-order terms). The curvature effect is shown to lead to small corre ctions for R as calculated for the flat interface model. As a result, R doe s not depend strongly (inversely proportional) on the relative difference i n copolymer block lengths unlike the results of the previous considerations of the emulsion stabilization. For the cases of a semidilute copolymer lay er at the interface and the unpenetrable copolymer layer ("dry brush") the corrections due to the curvature effect are calculated explicitly. The cond itions of a complete diblock copolymer adsorption at the interface are disc ussed.