Potential of mean force between polar molecules adsorbed onto a wall: The exact long-range behavior

In studies of adsorption from solutions, the potential of mean force between solute particles is a key quantity from which we may derive the thermodynamics of adsorption via the osmotic partition function. We consider the case of a polar solute in a polar solvent. The long-range part of the potential of mean force is obtained via a statistical mechanical derivation. The result contains a direct and an image potential as it is expected from a dielectric continuum approach. We show rigorously that the contribution of the dipole–dipole interaction comes essentially from a region far beyond the interfacial region where all electrostatic properties can be described in terms of dielectric constant. The new result consists in showing that the dipole moment of the solute particle must be replaced by an effective dipole moment which depends on the position of the molecule relative to the wall. We give the exact relation between the effective dipole moment and the short-range part of the solute–solvent pair correlation function, thus generalizing a previous result established in the context of the theory of dielectric constant. By using a simple model for the interfacial structure we discuss the magnitude of the effective dipole moment for a particle located onto the wall. The possibility of interpreting the lateral interactions in terms of local dielectric constant is analyzed.