Charge storage in nanotubes: the case of a 2-1 electrolyte

We consider a 2-1 electrolyte in contact with a narrow nanotube, which only allows one-dimensional storage along the axis. The asymmetry does not allow an a priori definition of the potential of zero charge; instead, the natural reference is the electrode potential at which both ions have the same electrochemical potential; the value of the latter can serve as a measure of ionophilicity. Near this potential, ionophobic tubes are filled with a dilute gas, ionophilic tubes are filled with a one-dimensional solid containing about the same number of the divalent ions and the monovalent counterions, a structure that is stabilized by a strong screening of the Coulomb interaction by an induced counter charge on the walls of the tube. The filling of the tube by the application of an electrode potential exhibits a complicated pattern of interactions between the two kinds of ions.