Analytical expressions for calculating the depletion interaction produced by charged spheres and spheroids

Analytical expressions for predicting the depletion interaction in charged systems where long-range electrostatic effects are important are presented. The approach used was to model the nonadsorbing materials as hard particles but with an effective size representing the hard-core size and the effective size of the charged double layer. This effective size was then substituted into analytical expressions for predicting the depletion interaction between two hard spherical particles in solutions of nonadsorbing hard spheres or spheroids. We also found the effective thickness of the charged double layer providing the most accurate approximation to be the surface-to-surface separation distance between the particle and nonadsorbing species at which the electrostatic repulsion equals 0.5 kT.