Mechanics of the Ideal Double-Layer Capacitor

Abstract

The mechanical state within a parallel-plate electrolytic capacitor is examined by appending a local momentum balance to a quasielectrostatic theory that describes charge screening in both the electrolyte and the electrodes. A classical diffuse-double-layer model, which treats the capacitor’s separator as a dilute electrolytic solution, is augmented to include metal electrodes, modelled as electron gases. When accounted for in this way, the electrodes are found to impact the interfacial capacitance significantly, as well as exerting compressive stress on the electrolyte. Nonlinear and quadratically perturbed theories are explored, the former around a single plate and the latter around the entire capacitor. Perturbation reveals several mechanical scaling laws generally applicable to capacitive metal/electrolyte interfaces. The two-plate model rationalizes the exponential decay of disjoining pressure between voltage-biased plates as their separation distance grows, as well as retrieving the well-known properties of a dielectric capacitor when the plate separation is small. This was Paper 1964 presented at the Dallas, Texas, Meeting of the Society, May 26-May 30, 2019.