Strong Interaction of Colloidal Particles: An Extension of Langmuir's Method

Abstract

According to Langmuir's suggestion, that is, sinh y ≈ ey/2 in the nonlinear Poisson−Boltzmann equation for high surface potentials of the particles, we derive simple approximate expressions for the repulsive energy and force between two dissimilar plates with constant high surface potentials. By use of Derjaguin's method and the improved Derjaguin method, the expressions of the repulsive energy between two dissimilar spheres with constant high surface potentials have been derived. These formulas are applicable in the regime of a repulsive system and can only be used at κh < 2π, and the accurate location is at ∼κh < 4. These formulas are considerably in agreement with the exact numerical values of the interaction of dissimilar plates given by Devereux and de Bruyn for high surface potentials.