Dielectric response of a polar fluid trapped in a spherical nanocavity

We present extensive Molecular Dynamics simulation results for the structure, static and dynamical response 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 $\epsilon' \geq 1$. The polarisation 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 generalised 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 behaviour 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 primitivity.