A systematic interpretation of differential capacitance data

Keith Promislow† Department of Mathematics, Michigan State University, East Lansing, MI Abstract Differential capacitance (DC) data has been widely used to characterize the structure of electrolyte solutions near charged interfaces and as experimental validation of models for electrolyte structure. Fixing a large class of models of electrolyte free energy that incorporate finite volume effects, a reduction is identified which permits the identification of all free energies within that class that return identical DC data. The result is an interpretation of DC data through the equivalence classes of non-ideality terms, and associated boundary layer structures, that cannot be differentiated by DC data. Specifically, for binary salts, DC data, even if measured over a range of ionic concentrations, is unable to distinguish between models which exhibit charge asymmetry, charge reversal, and even ion crowding. The reduction applies to capacitors which are much wider than the associated Debye length and to finite-volume terms that are algebraic in charge density. However, within these restrictions the free energy is shown to be uniquely identified if the DC data is supplemented with measurements of the excess chemical potential of the system in the bulk state.