The solution of a modified Poisson—Boltzmann equation for colloidal particles in electrolyte solutions

Abstract

The solution of a modified Poisson-Boltzman (PB) equation for the region between two colloidal particles immersed in a 1-1 electrolyte is investigated for low potentials. The practice familiar in the theory of colloidal stability, of replacing the particles by two infinitely thick parallel plates, is employed. Differences between this study and a similar one by Bell and S. Levine include a more rigorous treatment of the “imaging effect,” an avoidance of the iterative assumption of calculating modifications to the PB equation with classical forms for the potential, electric field and volume densities of the ions and a “constant charge” assumption with respect to adsorbed ions and the charge in the plate. Numerical solution shows that contrary to the latter work, with these changes the modifications can significantly effect the magnitude of the force between two particles.