  Using Brownian dynamics simulations, we investigate the effects of
confinement, adsorption on surfaces and ion-ion interactions on the response of
confined electrolyte solutions to oscillating electric fields in the direction
perpendicular to the confining walls. Nonequilibrium simulations allow to
characterize the transitions between linear and nonlinear regimes when varying
the magnitude and frequency of the applied field but the linear response,
characterized by the frequency-dependent conductivity, is more efficiently
predicted from the equilibrium current fluctuations. To that end, we (rederive
and) use the Green-Kubo relation appropriate for overdamped dynamics, which
differs from the standard one for Newtonian or underdamped Langevin dynamics.
This expression highlights the contributions of the underlying Brownian
fluctuations and of the interactions of the particles between them and with
external potentials. While already known in the literature, this relation has
rarely been used to date, beyond the static limit to determine the effective
diffusion coefficient or the DC conductivity. The frequency-dependent
conductivity always decays from a bulk-like behavior at high frequency to a
vanishing conductivity at low frequency due to the confinement of the charge
carriers by the walls. We discuss the characteristic features of the crossover
between the two regimes, most importantly how the crossover frequency depends
on the confining distance and the salt concentration, and the fact that
adsorption on the walls may lead to significant changes both at high- and
low-frequencies. Conversely, our results illustrate the possibility to obtain
information on diffusion between walls, charge relaxation and adsorption by
analyzing the frequency-dependent conductivity.
