Structure of a polar fluid near a wall. Exact asymptotic behavior of the profile, relation with the electrostriction phenomena and the Kerr effect

Abstract

We study the asymptotic behavior of the position-orientation profile ρ(1) for a dipolar hard sphere fluid in contact with a neutral hard wall. First, by a virial expansion we show that ρ(1) is not totally determined by the classical image potential, i.e., by a dielectric continuum model. The exact expression of ρ(1) far from the wall is derived by using a renormalized cluster expansion. As predicted by the dielectric continuum model, ρ(1) exhibits an orientational structure and a long tail which decreases as the inverse cubic power of the distance to the wall. We first examine the density profile ρ0(1) which corresponds to the isotropic part of ρ(1). We show that ρ0(1) contains a part reminiscent of the image potential but also some contributions which depends on the pair correlation function and the triplet direct correlation function in bulk phase. When this last function is neglected, ρ0(1) can be considered as the result of a force balance in the interface. In the general result, the triplet direct correlation allows us to obtain a very compact expression for ρ0(1). It is shown that the asymptotic behavior of ρ0(1) reveals the same microscopic properties as the classical electrostriction phenomena which is observed in bulk phase and in presence of an external electric field. Thus, ρ0(1) can be considered as the result of a natural electrostriction induced in the interfacial region by the image potential. The term of lowest symmetry in the orientational structure describes the alignment of a molecule relative to the normal to the wall. Far from the wall, the orientational profile is proportional to the dipolar contribution of the Kerr constant. Thus, the asymptotic behavior of the profile and the Kerr effect are determined by the same function characterizing the alignment of dipoles. This alignment is observed via an external field in the case of the usual Kerr effect and it is naturally induced by the image potential in the interfacial region. The triplet direct correlation function gives rise also to some additional orientational structures which are ignored in the dielectric continuum model. The exact results derived in this paper include some bridge diagrams and consequently they are beyond the wall–particle hypernetted chain approximation.