The simplest model of charge storage in single file metallic nanopores

The problem of voltage controlled accumulation of ions in a narrow nanopore, which can accommodate just one row of ions of an ionic liquid and is filled with ions when the electrode is unpolarised, is mapped on an exactly solvable one-dimensional two state Ising model. Analytical solution of this, presumably simplest, statistical mechanical model reveals the dependence of the electrical capacitance on voltage, pore radius, and temperature. The voltage dependence of capacitance has the character of a smeared resonance, whose position and height is affected by a tiny change of the pore radius. Consequently, even the slightest dispersion of pore radii in the whole electrode, unavoidable in any real system, softens the voltage dependence.