Nonlinear effects in polar fluids: A molecular theory of electrostriction

A molecular theory of electrostriction arising from the study of dipolar adsorption at a wall in the presence of an electric field is described. The quadratic hypernetted chain (QHNC) approximation for the wall–particle closure is the first of the hierarchy of approximations generated by the hypernetted chain equation (HNC) to predict electrostriction; the mean spherical and linearized hypernetted chain fail to do so. It is found that the simplest bridge diagrams which are ignored in the HNC (and QHNC) approximations must be included if quantitative agreement with the thermodynamic theory for electrostriction as described by Kirkwood and Oppenheim is to be obtained. These bridge diagrams have been evaluated analytically resolving the above discrepancy in the term of O(E2), where E is the local electric field. The statistical mechanical approach has also been extended to evaluate a few of the contributions of O(E4) in electrostriction. Conditions under which the linear constitutive relation between the polarization density P(∞,E) and the electric field E is recovered are discussed; its extension to include nonlinear terms in E is also considered.