Dielectric response of a polar fluid trapped in a spherical nanocavity.
We present extensive molecular dynamics simulation results for the structure and the static and dynamical responses of a droplet of 1000 soft spheres carrying extended dipoles and confined to spherical cavities of radii R=2.5, 3, and 4 nm embedded in a dielectric continuum of permittivity epsilon(')>or=1. The polarization of the external medium by the charge distribution inside the cavity is accounted for by appropriate image charges. We focus on the influence of the external permittivity epsilon(') on the static and dynamic properties of the confined fluid. The density profile and local orientational order parameter of the dipoles turn out to be remarkably insensitive to epsilon('). Permittivity profiles epsilon(r) inside the spherical cavity are calculated from a generalized Kirkwood formula. These profiles oscillate in phase with the density profiles and go to a "bulk" value epsilon(b) away from the confining surface; epsilon(b) is only weakly dependent on epsilon('), except for epsilon(')=1 (vacuum), and is strongly reduced compared to the permittivity of a uniform (bulk) fluid under comparable thermodynamic conditions. The dynamic relaxation of the total dipole moment of the sample is found to be strongly dependent on epsilon(') and to exhibit oscillatory behavior when epsilon(')=1; the relaxation is an order of magnitude faster than in the bulk. The complex frequency-dependent permittivity epsilon(omega) is sensitive to epsilon(') at low frequencies, and the zero-frequency limit epsilon(omega=0) is systematically lower than the bulk value epsilon(b) of the static permittivity.