Structure and thermodynamics of micellar solutions in the modified Poisson—Boltzmann theory

Abstract

The modified Poisson—Boltzmann theory, in conjunction with the spherical cell model of colloidal dispersions, is applied to a study of structural and thermodynamic properties of micellar solutions. The concentration profile of the small, simple ions with respect to the polyion, and the osmotic pressure are evaluated for different values of polyion surface charge, polyion radius, and cell radius. Comparisons are made with results from the classical Poisson—Boltzmann theory and Monte Carlo simulations. The osmotic pressures are also compared with those available from the anisotropic hypernetted chain theory. It is found that the modified Poisson—Boltzmann equation accurately represents the simulation results for monovalent simple ions, with the Poisson—Boltzmann equation only being adequate at low ionic concentrations. For divalent simple ions the thermodynamic properties of the modified Poisson—Boltzmann are superior to the other theories whereas its structural properties show improvement upon the Poisson—Boltzmann predictions only at large distances from the polyion.