On the asymptotic structure of far-field electrostatic interactions between charged molecules and charged surfaces

A general asymptotic theory is presented for approximating the electrostatic free energy of interaction between a charged spherical solute of radius a and an arbitrarily shaped charged wall at distance / in the limit a ≪/ The Debye screening length is assumed to be of order / or larger. Thus, the analysis specifically addresses the most interesting case where strong interactions arise from the overlap of solute and wall double layers. Surface charges are represented in terms of constant-potential boundary conditions. The asymptotic theory is shown to agree well with detailed numerical calculations for the illustrative case of sphere-plane interaction even when the solute surface is only one radius away from the wall.