Electrostatic interaction between two charged spherical molecules

An explicit analytic expression is obtained for the electrostatic energy of the interaction between two ion-impenetrable space-charged hard spheres as a model for spherical molecules in an electrolyte solution on the basis of the linearized Poisson-Boltzmann equation. An explicit expression for the potential distribution in a 3D-space is also found. The polarization effects due to the mutual influence between the spheres are taken into account. The analysis is done by assuming different dielectric permittivities of the respective spheres and of the solution as well. It is shown that the correction terms in the expression for the total energy of interaction arising from the polarization effects always correspond to forces of attraction between the spheres. The contribution of these terms to the total energy of interaction depends on the distance between the two spheres and the dielectric permittivities of the spheres and the solution as well as on the electrolyte concentration in the solution. A numerical simulation of the potential field topography is carried out at several values of the Debye-Hückel parameter. It is shown that the polarization effect can produce significant changes in the potential distribution in the case of strong interacting spheres.