A triple layer, planar coordinate model for describing counterion association to micelles

A planar triple-layer model describing ion association to micelles composed of the anionic surfactant dodecylsulfate (DS-) was developed and evaluated . The governing Poisson-Boltzmann equation was solved (i) analytically and (ii) with a numerical shooting method. The second solution was developed to confirm the accuracy of the first and because the analytical solution is o nly valid for symmetrical electrolytes. The latter solution is applicable a lso to multiple valence counterion systems. Because the absolute value of t he electrical potential at the micelle surface is so large, the classical D ebye-Huckle approximation is invalid and was not made. To evaluate the resu lting algorithms, they were incorporated into an overall speciation model t hat describes surfactant and metal ion equilibria in aqueous solutions and includes an equation that describes DS- micelle-monomer phase distribution: log [DS-](w) = K-1 - e psi(s)/(2.3 kT). The Stern layer thickness (lambda( s)) and the Y-intercept of the cmc-electrical potential relationship (K-1) were calculated by minimizing residuals between experimental and calculated cmc values over a range of experimental aqueous Na+ concentrations, For so dium dodecylsulfate in NaCl solutions, the analytical model and numerical m odel provided essentially the game result, the same optimum lambda(s) and K -1 values, and accurate cmc predictions. For this system, lambda(s) = 1 Ang strom, and K-1 = -4.51.