Static transverse dielectric function of model molecular fluids

It is customary in the physicochemical literature to define the static transverse dielectric function of a polar fluid according to the relation ε_T(k) = 1 + 4πβS_T(k), where β=(k _BT)^-1 and S_T(k) is a measure of the static fluctuations of the Fourier components of the transverse part of the electric polarization field in the fluid. In this work we evaluate ε_T(k) for models of two classes. (1) In a DS model each molecule is a hard sphere with a point dipole at its center. It is the simplest representative of models in which the long range intermolecular interactions are generated by a set of point multipoles located at a single point in the molecule. In this case S _T(k) is S_M,T(k), the static correlation function of the transverse part of the dipole polarization density M̂(k). (2) In a ζDS model fluid, comprising nonideal dipolar hard spheres, the long range interactions are accounted for by two opposite partial charges on either side of the sphere's center and separated by a distance ℓ. The ζDS model is the simplest interaction site model (ISM) of a polar fluid. For an ISM the relevant structure factor S_T(k) is S_Pμ,T(k), the static correlation of the transverse part of the full electric polarization density vector P̂_μ(k). Here we compare ε_T(k) for DS and ζDS models with the help of the mean spherical approximation for the required structure functions. The ζDS-DS difference in ε _T(k) at large k is found to parallel the behavior of the static longitudinal dielectric function ε_L(k). However, ε_T(k), unlike ε_L(k), is a damped oscillatory function of k with no poles on the real k axis.