Structure and thermodynamics of micellar solutions in isotropic and cell models

This paper presents a combined Monte Carlo and integral equation study of micellar solutions. In the first part of the paper, new simulation results for an isotropic model of micellar solutions containing macroions and counterions are compared with the results of the much simpler cell model. The conclusion is that the spherical cell model, in conjunction with the Poisson-Boltzmann equation, yields reliable results for the osmotic pressure over the whole concentration range studied here. The conclusion is valid for solutions with monovalent counterions up to moderate concentrations, which have not been studied before. However, for model solutions containing divalent counterions, the cell model is not an adequate approximation. In the second part of the paper, the results for a three-component model of micellar solutions, containing macroions, counterions, and a free amphiphile, are presented. Again the Poisson-Boltzmann cell model results are tested against the results of the isotropic model. The thermodynamics and structure of the isotropic model are obtained via two integral equation theories: (i) the hypernetted chain (HNC) integral equation and (ii) the so-called associative HNC (two-density theory) approximation, developed recently. Overall, the agreement between the isotropic and cell model calculations (note that the latter are based on the Poisson-Boltzmann approximation) for the osmotic pressure is good.