Self-affine and mound roughness effects on the double-layer charge capacitance

Abstract

In this article, we investigate the influence of self-affine and mound roughness on the charge capacitance of double layers. The influence of self-affine roughness is more significant for small roughness exponents (H<0.5) and/or large roughness ratios w/ξ, as well as small charge and counter charge separations in electrolyte plasma as described by the Debye length λD(<ξ). On the other hand, mound roughness has a more complex influence on the charge capacitance, when the system correlation length ζ is larger than the average mound separation λ. In this case, the charge capacitance oscillates as a function of the parameters λ and ζ before it approaches the Gouy–Chapman [G. Gouy, J. Phys. (Paris) 9, 457 (1910); D. L. Chapman, Philos. Mag. 25, 475 (1913)] asymptotic limit for smooth interfaces. Furthermore, the oscillation magnitude is larger for relatively small Debye lengths λD(<ζ,λ).