The nanofluidic capacitor: Differential capacitance in the absence of reservoirs

Within the framework of the classical, mean-field Poisson-Boltzmann (PB) theory, we carry out direct numerical simulations to determine the differential capacitance of a closed nanochannel of a circular cross section, embedded in a polymeric host with charged walls and sealed at both ends by metal electrodes under an external potential bias. Our approach employs the modified PB equation, which accounts for the finite size of ions and the dependency of the electrolyte's relative permittivity on the local electric field. In view of the absence of reservoirs, the modified PB equation becomes subject to global algebraic constraints, without prior knowledge of a bulk electrolyte concentration. Equilibrium ion distributions and differential capacitance curves are investigated as functions of electrolyte properties and the surface charge density modulation. This modulation leads to asymmetric differential capacitance curves that can be tuned. More generally, our approach provides a transparent numerical framework for accurately simulating confined nanofluidic systems with new physical properties that may be exploited in novel iontronic circuit elements.