  The transport of fluids at the nanoscale is fundamental to manifold
biological and industrial processes, ranging from neurotransmission to
ultrafiltration. Yet, it is only recently that well-controlled channels with
cross-sections as small as a few molecular diameters became an experimental
reality. When aqueous electrolytes are confined within such channels, the
Coulomb interactions between the dissolved ions are reinforced due to
dielectric contrast at the channel walls: we dub this effect `interaction
confinement'. Yet, no systematic way of computing these confined interactions
has been proposed beyond the limiting cases of perfectly metallic or perfectly
insulating channel walls. Here, we introduce a new formalism, based on the
so-called surface response functions, that expresses the effective Coulomb
interactions within a two-dimensional channel in terms of the wall's electronic
structure, described to any desired level of precision. We use it to
demonstrate that in few-nanometer-wide channels, the ionic interactions can be
tuned by the wall material's screening length. We illustrate this approach by
implementing these interactions in brownian dynamics simulations of a strongly
confined electrolyte, and show that the resulting ionic conduction can be
adjusted between Ohm's law and a Wien effect behavior. Our results provide a
quantitative approach to tuning nanoscale ion transport through the electronic
properties of the channel wall material.
