Molecular-Thermodynamic Theory of Micellization of pH-Sensitive Surfactants

Abstract

A predictive, molecular-thermodynamic theory is developed to model the micellization of pH-sensitive surfactants. The theory combines a molecular-thermodynamic description of micellization in binary surfactant mixtures with the protonation equilibrium of the surfactant monomers. The thermodynamic component of the theory models the pH-mediated equilibrium between micelles, surfactant monomers, and counterions. These counterions may originate from the surfactant or from added salt, acid, or base. The molecular component of the theory models the various contributions to the free energy of micellization, which corresponds to the free-energy change associated with forming a mixed micelle from the protonated and deprotonated forms of the surfactant and from the bound counterions. The free energy of micellization includes hydrophobic, interfacial, packing, steric, electrostatic, and entropic contributions, which are all calculated molecularly. The theory also requires knowledge of the surfactant molecular structure and the solution conditions, including the temperature and the amount of any added salt, acid, or base. To account for the pH sensitivity of the surfactant, the theory requires knowledge of the surfactant monomer equilibrium deprotonation constant (pK1), which may be obtained from experimental titration data obtained below the critical micelle concentration (cmc). The theory can be utilized to predict the equilibrium micelle and solution properties, including the cmc, the micelle composition, the micelle shape and aggregation number, the solution pH, and the micelle deprotonation equilibrium constant (pKm). Theoretical predictions of the cmc, the micelle aggregation number, and the pKm compare favorably with the available experimental data for alkyldimethylamine oxide surfactants. This class of pH-sensitive surfactants exhibits a form of self-synergy, which has previously been attributed to hydrogen-bond formation at the micelle interface. Instead, we show that much of the observed synergy is related to the electrostatic contribution to the free energy of micellization. Although we do not explicitly include hydrogen bonding in the molecular model of micellization, we briefly discuss how it may be incorporated and its anticipated effect on the predicted micellization behavior.