  We study the low-frequency dielectric response of highly charged spheres
arranged in a cubic lattice and immersed in an electrolyte solution. We focus
on the influence of the out-of-phase current in the regime where the ionic
charge is neutral. We consider the case where the charged spheres have no
surface conductance and no frequency-dependent surface capacitance. Hence, the
frequency dispersion of the dielectric constant is dominated by the effect of
neutral currents outside the electric double layer. In the thin double-layer
limit, we use Fixman's boundary condition at the outer surface of the double
layer to capture interaction between the electric field and the flow of the
ions. For periodic conditions, we combine the methods developed by Lord
Rayleigh for understanding the electric conduction across rectangularly
arranged obstacles and by Korringa, Kohn and Rostoker for the electronic band
structure computation. When the charged spheres occupy a very small volume
fraction, smaller than one percent, our solution becomes consistent with the
Maxwell Garnett mixing formula together with the single-particle polarization
response, as expected, because inter-particle interactions become less
prominent in the dilute limit. By contrast, the inter-particle interaction
greatly alters the dielectric response even when charged spheres occupy only
two percent of the volume. We found that the characteristic frequency shifts to
a higher value compared to that derived from the single-particle polarization
response. At the same time, the low-frequency dielectric enhancement, a
signature of charged spheres immersed in an electrolyte, becomes less prominent
for the periodic array of charged spheres. Our results imply that the signature
of the dielectric response of a system consisting of densely packed charged
spheres immersed in an electrolyte can differ drastically from a dilute
suspension.
