Structure of Dielectric Fluids. II. The Free Energy and the Kerr Effect in Polar Fluids

Abstract

The Helmholtz free energy of a molecular fluid of rigid dipoles in the absence of any external field is studied. An explicit formal expression for the excess free energy due to the dipolar interaction is found. It is shown that the free energy per particle is independent of the shape of the sample, although shape‐dependent long‐range correlations are present in the fluid. For the special case of the Onsager model of polar fluids an explicit expression is obtained for the contribution to the free energy due to the dipolar interactions. Next, we study the long‐range part of the three‐particle correlation function for an arbitrarily shaped sample of the molecular fluid in the absence of an external field. This long‐range part is dependent on the shape of the sample. The three‐particle correlation function arises in the expression for the Kerr constant, which measures the birefringence of the fluid when a strong electric field is applied. We show explicitly that, in the lowest nonvanishing order in the field, the birefringence is proportional to the square of the resulting local macroscopic electric field with a proportionality constant (the Kerr constant) which is independent of the shape of the sample. A formal expression is given for the Kerr constant in terms of the local properties of the fluid.