Regular Solution Theory for Nonlinear Composition Dependency of Enantioselectivity by Mixed Micelle

Mixtures of chiral and achiral building blocks of supramolecules exhibit interesting cooperative properties, as indicated by the nonlinear relationship between chiral properties and the mole fraction of chiral building blocks. However, the nonlinear composition dependence of the chiral recognition capability of spherical mixed micelles is poorly understood. This study hypothesized that the phenomenon could be described by the regular solution theory reported to be able to describe critical micelle concentration (CMC) and partition coefficients of the mixed micelle by interaction parameters β and B, respectively. CMC and mole fraction of chiral surfactant in the mixed micelle were simulated by using the theory of varying β and CMC of the two surfactants. Equations that describe the enantioselectivity are newly derived in this work, and the dependency of the enantioselectivity on B was studied in detail. The derived equations were applied to the earlier reported partition coefficient determined by mixed micellar electrokinetic chromatography (MEKC). It was found that the formula can describe the nonlinear composition dependency of the enantioselectivity of the mixed MEKC. The partition coefficient determined by MEKC was in agreement with the β vs. B relation, which was previously reported.