Simplifications of the Poisson-Boltzmann equation for the electrostatic interaction of close hydrophilic surfaces in water

Simple solutions of the Poisson-Boltzmann (PB) equation for the electrostatic double-layer interaction of close, planar hydrophilic surfaces in water are evaluated. Four routes, being the weak overlap approximation, the Debye-Huckel linearization based on low electrostatic potentials, the Ettelaie-Buscall linearization based on small variations in the potential, and a new approach based on the fact that concentrations are virtually constant in the gap between close surfaces, are discussed. The Ettelaie-Buscall and constant-concentration approach become increasingly accurate for closer surfaces and are exact for touching surfaces, while the weak overlap approximation is exact for an isolated surface. The Debye-Huckel linearization is valid as long as potentials remain low, independent of separation. In contrast to the Ettelaie-Buscall approach and the weak overlap approximation, the Debye-Huckel linearization and constant-concentration approach can also be used for systems containing multivalent ions. Simulations in which the four approaches are compared with the PB equation for the constant-charge model, the constant-potential model, as being used in the DLVO theory, and the charge-regulation model are presented. (C) 2001 Academic Press.