Roughness effects on the double-layer charge capacitance: the case of Helmholtz layer induced roughness attenuation

For electrical double layers, the presence of a Helmholtz layer could lead to electrode roughness attenuation. The latter is assumed of self-affine type which is characterized by the roughness amplitude w, the correlation length ξ, and the roughness exponent H. For sufficiently rough metal electrode surfaces (H≪1 and/or ratios w/ξ⩾0.1) the diffuse/Helmholtz layer interface would not have the same roughness parameters with the metal electrode surface. If the latter is smoothened at lateral length scales smaller than a healing length Λ (≪ξ), the diffuse charge capacitance decreases and approaches values close to that of the Gouy–Chapman theory for flat electrodes.