Ising models of charge storage in multifile metallic nanopores

Ising type models of charging of conductive nanopores with ions have already been proposed and investigated for single file cylindrical or single layer slit nanopores. In such pores, the state of ions, the coulombic interactions of which are exponentially screened by their images in pore walls, was named superionic. In the present work we extend the analysis of the superionic state to nanopores that can accommodate multiple rows of ions. By grouping multiple charges in the same row into 'supercharges', we map the arrangement of ions in polarised electrodes on a multi-row Ising model in an external field. We investigate one-, two- and three-row cases, which we solve exactly, using a purpose-built semi-numerical transfer matrix method. For pores of different radii, which can accommodate the corresponding number of ion rows, we calculate the dependence of the electrical capacitance and stored energy density on electrode potential. As in charging the single file pores, we find that in narrower pores higher energy densities can be achieved at low applied potentials, while wider pores perform better as the voltage is increased.