NUMERICAL-CALCULATION OF DIFFUSE DOUBLE-LAYER PROPERTIES FOR SPHERICAL COLLOIDAL PARTICLES BY MEANS OF A MODIFIED NONLINEARIZED POISSON-BOLTZMANN EQUATION

A numerical solution of a modified nonlinearized Poisson-Boltzmann equation (PBE) is presented. The method is designed for the case of a charged surface or polyelectrolyte in solution. The approach allows for the effects of finite ion sizes (i) and the dependence of the dielectric constant on the electric field strength (ii). Spherical geometry is considered (iii) and allowance is made for competition between an arbitrary number of differently charged ions (iv) to a charged surface. For the description of electrolyte solutions in the presence of charged surfaces a general model is proposed. Calculations are made which enable the counterion concentrations in the vicinity of spherically shaped charged surfaces (colloidal particles, micelles) to be obtained. Our treatment is compared to the approach using the unmodified nonlinearized PBE neglecting (i) and (ii) (Gouy-Chapman approximation) for a model polyelectrolyte system which is suitable for a micellar solution (charged spheres of radius 15 Å with univalent counterions and an additional 2-2 electrolyte). It is shown that the different approximations of the PBE yield similar results only for small surface potentials and small additional electrolyte concentrations. © 1979.