THE ELECTRIC DOUBLE-LAYER INSIDE A SPHERICAL AQUEOUS CAVITY - A COMPARISON BETWEEN EXACT NUMERICAL AND APPROXIMATE ANALYTICAL SOLUTIONS

An approximate analytical solution of the Poisson-Boltzmann equation for a spherical aqueous cavity is obtained. In this solution the first nonlinear correction to the linear solution is taken into account. The first nonlinear correction removes more than 70% of the discrepancy between the exact and the linear solution of the Poisson-Boltzmann equation, at least under conditions typical for phospholipid vesicles (surface charge densities up to 1. 5 e/nm**2 and monovalent electrolyte concentrations from 1 to 145 mM). The approximate analytical solution is accurate within 10% for surface potentials up to 3 kT/e, and within 25% for surface potentials up to 5 kT/e. In order to illustrate its application the approximate solution was used to calculate the electrostatic disjoining pressure inside a phospholipid vesicle.