Modelling current-induced electrolyte sorption by floating ideally-polarizable nanoporous electrodes

Modelling of charging of nanoporous conductors in electrolyte solutions is complicated by simultaneous occurrence of ion diffusion and electromigration. This communication shows that very significant simplifications can be achieved in the limiting case of extremely small nanopores where the diffuse parts of Electric Double Layers are perfectly well overlapped because in this limiting case ion transport occurs only via diffusion. Concentration gradients arise due to Donnan-like electrostatic-potential “jumps” at the external surfaces of current-polarized nanoporous conductors. Especially simple results can be obtained for floating (bipolar) nanoporous electrodes due to the existence of non-trivial steady state and realistic galvanostatic charging mode. Stationary salt accumulation and voltage drop are described by elementary expressions. For cations and anions of equal diffusion coefficients, the dynamics of buildup of voltage and salt accumulation can also be modelled by simple analytical formulae or single quadratures. In stark contrast to the previous analytical results, these solutions have unlimited applicability in time and current magnitude. Numerical analysis of the case of different diffusion coefficients reveals that for observable quantities (salt accumulation, voltage drop) deviations from the “symmetrical” case are limited to a couple of percent even when the diffusion coefficients differ by as much as a factor of three. The results are also of interest for emerging bipolar configurations of capacitive deionization.