Electrostatic interaction between two spherical soft particles at small separations

An approximate analytic expression is given for the potential energy of the electrostatic interaction between two identical spherical soft particles (ion-penetrable porous spheres) in a symmetrical electrolyte solution with the help of Derjaguinʹs approximation. This method uses accurate analytic expressions for the corresponding interaction energy between two parallel similar soft plates (ion-penetrable membranes) obtained previously (J. Colloid Interface Sci., 350 (2010) 249). Agreement with numerical data (J. Colloid Interface Sci., 36 (1989) 523) is excellent for arbitrary potentials and small particle separations, where the Debye–Hückel linearization approximation and the linear superposition approximation are not allowed.