Superionic state in double-layer capacitors with nanoporous electrodes

In the recent experiments [Chmiola et al, Science 313, 1760 (2006); Largeot et al, J. Am. Chem. Soc. 130, 2730 (2008)] an anomalous increase of the capacitance with a decrease of the pore size of a carbon-based porous electric double-layer capacitor has been observed. We explain this effect by the image forces which exponentially screen out the electrostatic interactions of ions in the interior of a pore. Packing of ions of the same sign becomes easier and is mainly limited by steric interactions. We call this state `superionic' and suggest a simple model to describe it. The model reveals a possibility of a voltage-induced first-order transition between a cation(anion)-deficient phase and a cation(anion)-rich phase which manifests itself in a jump of capacitance as a function of voltage.