Electrocapillary coupling at rough surfaces

We investigate the impact of the surface roughness on the experimental value of the electrocapillary coupling coefficient, zeta. This quantity relates the response of electrode potential, E, to tangential elastic strain, e, and also measures the variation of the surface stress, f, with the superficial charge density, q. We combine experiments measuring the apparent coupling coefficient zeta(eff) for gold thin film electrodes in weakly adsorbing electrolyte with data for the surface roughness determined by atomic force microscopy and by the capacitance ratio method. We find that even moderate roughness has a strong impact on the value of zeta(eff). Analyzing the mechanics of corrugated surfaces affords a correction scheme yielding values of zeta that are invariant with roughness and that agree with expectations for the true coupling coefficient on ideal, planar surfaces. The correction is simple and readily applied to experiments measuring zeta(eff) from surface stress changes in cantilever bending studies or from the potential variation in dynamic electrochemo- mechanical analysis.