Abstract
Negative capacitance (NC), predicted by various electrical double layer (EDL) theories, is critically reviewed. Physically possible for individual components of the EDL, the compact or diffuse layer, it is strictly prohibited for the whole EDL or for an electrochemical cell with two electrodes. However, NC is allowed for the artificial conditions of σ control, where an EDL is described by the equilibrium electric response of electrolyte to a field of fixed, and typically uniform, surface charge-density distributions, σ. The contradiction is only apparent; in fact local σ cannot be set independently, but is established by the equilibrium response to physically controllable variables, i.e., applied voltage ϕ (ϕ control) or total surface charge q (q control). NC predictions in studies based on σ control signify potential instabilities and phase transitions for physically realizable conditions. Building on our previous study of ϕ control [M. B. Partenskii and P. C. Jordan, Phys. Rev. E 77, 061117 (2008)], here we analyze critical behavior under q control, clarifying the basic picture using an exactly solvable “squishy capacitor” toy model. We find that ϕ can change discontinuously in the presence of a lateral transition, specify stability conditions for an electrochemical cell, analyze the origin of the EDL’s critical point in terms of compact and diffuse serial contributions, and discuss perspectives and challenges for theoretical studies not limited by σ control.