Theory of Work Function and Potential of Zero Charge for Metal Nanostructured and Rough Electrodes

Abstract

We developed a general theory for the work function and potential of zero charge of arbitrary shaped nanostructured and rough metal. Theory accounts for the influence of adsorbed solvent layer, i.e., partial to full solvent coverage, on work function (WF). We show that the change in local WF is due to redistribution of surface charge caused by local surface curvature and adsorbing dipoles. Special cases of spherical and ellipsoidal geometries are obtained from the generic curvature-dependent WF equation to illustrate the size and shape effects. Theory predicts increase in WF of immersed nanoparticles with decrease in their size, while change in shape causes nonuniform WF over the surface. Theory shows anomalous fluctuations in WF for a surface with multiscale roughness, viz., the Weierstrass–Mandelbrot function as a surface. Ensemble or surface averaged work function of randomly curved rough surface is predicted to depend on average mean and Gaussian curvatures. The intrinsic field of various metals regul...