THEORETICAL AND EXPERIMENTAL INVESTIGATIONS OF MICELLAR PROPERTIES OF AQUEOUS-SOLUTIONS CONTAINING BINARY-MIXTURES OF NONIONIC SURFACTANTS

We present a detailed description of a molecular model of mixed micellization for aqueous solutions containing binary surfactant mixtures. The molecular model incorporates the effects of surfactant molecular structure, surfactant composition, and solution conditions on the salient physicochemical factors which control mixed micelle formation and growth. These factors include (i) hydrophobic interactions between surfactant hydrocarbon chains and water, (ii) curvature-dependent interfacial effects associated with the creation of the micellar core-water interface, (iii) conformational effects associated with hydrocarbon chain packing in the micellar core, (iv) repulsive steric interactions between the surfactant hydrophilic moieties, (v) electrostatic interactions between charged surfactant hydrophilic moieties, and (vi) entropic effects associated with mixing the two surfactant species in a mixed micelle. The free energy of mixed micellization g(mic) is computed for various micellar shapes sh, micellar core minor radii l(c), and micellar compositions-alpha. The optimum equilibrium values sh*, l(c)*, and alpha* are then obtained by a minimization procedure. The deduced optimum micellar shape sh* determines whether the mixed micelles exhibit two-dimensional, one-dimensional, or no growth. These results are then used in the context of a thermodynamic theory of mixed micellar solutions, and the resulting molecular-thermodynamic formulation is utilized to predict a broad spectrum of mixed micellar solution properties as a function of surfactant molecular structure, surfactant composition and concentration, and solution conditions such as temperature. The predicted properties include the critical micellar concentration (cmc), the average mixed micellar composition at the cmc, the weight-average mixed micelle aggregation number, and the liquid-liquid phase separation coexistence curve, including the compositions of the two coexisting micellar-rich and micellar-poor phases. Thc theoretical predictions are compared with experimentally measured micellar properties of aqueous solutions of three binary mixtures of nonionic surfactants belonging to the alkyl poly(ethylene oxide) (C(i)E(j)) family, including C-12E6-C-12E8, C-12E6-C-10E6, and C-12E6-C-10E4. The broad spectrum of theoretical predictions compares very favorably with the experimental data.