Derivation of interaction energy and force between identical spheres in linear superposition approximation

We define an effective surface potential of spherical particle, which can I ,e decomposed as phi(kappah)=Y(h) + DeltaY(h). First part of the effective surface potential is the unperturbed surface potential which is expressed b y equation(6) in the text and other part is a perturbed surface potential o f the particle due to the presence of the other particle. Furthermore, a de tailed derivation of interaction energy and force between identical spheres in linear superposition approximation is presented. Thus very simple analy tic formulas are presented between two identical spherical particles for in teraction energy at moderate potential. The agreement with exact numerical results is considerably improved for free energy, but not force. The reason is that the relation of the energy and the force is the relation of integr ation and differentiation but integration can smooth an integrand and deffe rentiation exposes singularity of a function. Terefore, the agreement with exact numerical results is better for free energy, but not force.