LONG-RANGE CORRELATION BETWEEN POLAR-MOLECULES ADSORBED ONTO A DIELECTRIC SOLID

We consider a polar liquid in contact with a perfect dielectric solid and we investigate the total correlation function h(1,2) in the interfacial region. An exact expression is derived when the distance between molecules 1 and 2 becomes very large. We show that h(1,2) looks like the result expected from a dielectric continuum approach provided the molecular dipole moment μ(i) is replaced by an effective dipole moment M(i) which depends on the distance to the solid. In bulk phase, we recover the classical expression giving the asymptotic behavior of h(1,2). In presence of a solid, we generalize some results obtained in the theory of the dielectric constant which are exact except in the boundary region near the wall which is precisely the region of interest when we focus on adsorption phenomena. We introduce a quantity g(i) which is short ranged and generalized the g-Kirkwood factor to inhomogeneous situations. An exact integral equation is derived which relates M(i), g(i) and the profile p(i) via some functions which are known and of purely geometrical content. In general cases, the vectors μ(i) and M(i) are no more collinear and the relation between M(i) and g(i) is non-local. The result remains formally the same if molecules 1 and 2 are different from the other particles of the liquid. We discuss M(i) by considering a particular model. From this example we analyze the concept of effective dielectric constant in adsorbed layer. We point out the limitations in the use of this local dielectric constant. The main results obtained in this paper are exact provided the interaction between molecules may be represented by a pairwise additive intermolecular potential. © 1990.