Molecular theory of solvation and dielectric response in polar fluids

The response of a polar fluid to an electric field of arbitrary spatial and temporal characteristics is considered. Microscopic expressions are derived for the transverse and longitudinal dielectric functions εT (k,ω) and εL (k,ω). The notions of ‘‘transverse relaxation time’’ and ‘‘longitudinal relaxation time’’ are discussed and clarified. We propose an algorithm, by which data from macroscopic dielectric relaxation measurements, which probe the dielectric response at long wavelengths, may be used to predict the dielectric response of a polar fluid on molecular length scales. We construct a partially resummed density expansion of the polarization response of a model system composed of interacting dipoles which undergo rotational Brownian motion. Numerical calculations are given of the temporal and spatial behavior of the polarization induced in this system by the sudden introduction of a point charge.