Ion filling of a one-dimensional nanofluidic channel in the interaction confinement regime

Ion transport measurements are widely used as an indirect probe for various properties of confined electrolytes. It is generally assumed that the ion concentration in a nanoscale channel is equal to the ion concentration in the macroscopic reservoirs it connects to, with deviations arising only in the presence of surface charges on the channel walls. Here, we show that this assumption may break down even in a neutral channel due to electrostatic correlations between the ions arising in the regime of interaction confinement, where Coulomb interactions are reinforced due to the presence of the channel walls. We focus on a one-dimensional channel geometry, where an exact evaluation of the electrolyte's partition function is possible with a transfer operator approach. Our exact solution reveals that in nanometer-scale channels, the ion concentration is generally lower than in reservoirs and depends continuously on the bulk salt concentration, in contrast to the conventional mean-field theory that predicts an abrupt filling transition. We develop a modified mean-field theory taking into account the presence of ion pairs that agrees quantitatively with the exact solution and provides predictions for experimentally relevant observables, such as the ionic conductivity. Our results will guide the interpretation of nanoscale ion transport measurements.