Field theoretical modeling of the coexistence of micelles and vesicles in binary copolymer mixtures

Abstract

Using the self-consistent field (SCF) theory for inhomogeneous polymer systems, we elaborate a molecular model on a united atom level and discuss the possibility of coexistence of spherical micelles and small unilamellar vesicles in binary copolymer mixtures in a selective solvent. Our analysis is in line with recent neutron scattering and cryo-TEM results for the mixture of two members of the poly(butylene oxide)-b-poly(ethylene oxide) (referred to as PB_nPE_m) family, namely the (n, m) = (10, 10) and (10, 18) species in water that clearly pointed towards such coexistence. The -PE₁₈ is a micelle forming and the -PE₁₀ a lamellae forming copolymer. Upon increasing concentration of -PE₁₈ the micelle concentration that coexists with the vesicles increases dramatically. In this situation the micelles determine the chemical potentials of the copolymers and with increasing fraction PE₁₈/PE₁₀ the vesicle size becomes dramatically smaller. The selection of vesicle size indicates its thermodynamic stability. The strategy to arrive at thermodynamically stable vesicles with sizes much smaller than 100 nm is of interest for a wide range of applications.