THEORY OF SURFACTANT SELF-ASSEMBLY - A PREDICTIVE MOLECULAR THERMODYNAMIC APPROACH

A thermodynamic treatment of surfactant self-assembly in aqueous media is developed that allows an a priori quantitative prediction of the aggregation behavior of surfactants, starting from their molecular structures and the solution conditions. The treatment combines the general thermodynamic principles of self-assembly with detailed molecular models for various contributions to the free energy of aggregation. The treatment is employed to predict the aggregation behavior of surfactants that generate narrowly dispersed, small, spherical or globular aggregates; the transition from spherical to large, polydispersed, rodlike aggregates; the aggregation behavior of surfactants containing polymeric head groups such as the widely used poly(oxyethylene)-type nonionic surfactants; the solubilization of hydrophobic molecules in aggregates; the solubilization-induced transition from rodlike to spherical aggregates; the solubilization of binary mixtures of hydrocarbons; and the temperature dependence of micellization and solubilization. For illustrative purposes, calculated results concerning nonionic, zwitterionic, and ionic surfactants are presented and compared with experimental results generated by more than 20 different laboratories. The calculations show that, as a result of solubilization, microemulsion structures are formed with a single surfactant. However, the core of the solubilizate in these structures is rather small. In developing a molecular model for the free energy of aggregation, we consider contributions arising from (i) the transfer of the surfactant tail from water into the hydrophobic core of the aggregate assumed to behave like a liquid hydrocarbon, (ii) the conformational free energy of the tails inside the aggregates due to the constrained location of the head groups on the aggregate surface, (iii) the free energy of formation of the aggregate-water interface, and (iv) the interactions between the head groups of the surfactant at the aggregate surface. In the case of solubilization, the free energy of mixing of the solubilizates with the surfactants also makes a contribution. Expressions for each of the above free energy contributions are derived here. The transfer free energy is expressed as an explicit function of temperature. Analytical free energy expressions are derived for the dependence of the conformational free energy of the surfactant tails inside the aggregates as a function of the size and shape of aggregates. The interfacial tension characteristic of the aggregate-water interface is calculated using the Prigogine theory when more than two distinct molecular species are present as in the case of micellization involving poly(oxyethylene) surfactants and for the case of solubilization of one or more additives into the aggregates. The interactions among the poly(oxyethylene) head groups in nonionic surfactants are calculated on the basis of two limiting models which differ from one another in the description of the mixing and elastic deformation free energies of the poly(oxyethylene)-water region surrounding the aggregates. Also, the head group interactions between ionic surfactants are calculated using an approximate analytical solution for the Poisson-Boltzmann equation available in the literature. The thermodynamic treatment developed here is strictly predictive in the sense that it is free of information extracted from the aggregation behavior of surfactants. In addition, no arbitrary or empirical factors are involved. The only parameters that appear are molecular constants that can be reasonably determined on the basis of known molecular structures and properties.