Interface capacitance of nano-patterned electrodes

By employing numerical solutions of the Poisson–Boltzmann equation we have studied the interface capacitance of flat electrodes with stripes of different potentials of zero charge ?_pzc. The results depend on the ratio of the width of the stripes l to the dielectric screening length in the electrolyte, the Debye length d_Debye, as well as on the difference Δ?_pzc in relation k_BT/e. As expected, the capacitance of a striped surface has its minimum at the mean potential of the surface if l/d_Debye << 1 and displays two minima if l/d_Debye >> 1. An unexpected result is that for Δ?_pzc ? 0.2V, the transition between the two extreme cases does not occur when l ? d_Debye, but rather when l > 10d_Debye. As a consequence, a single minimum in the capacitance is observed for dilute electrolytes even for 100 nm wide stripes. The capacitance at the minimum is however higher than for homogeneous surfaces. Furthermore, the potential at the minimum deviates significantly from the potential of zero mean charge on the surface if l > 3d_Debye and Δ?_pzc is larger than about 4k_BT/e. The capacitance of stepped, partially reconstructed Au(11n) surfaces is discussed as an example. Consequences for Parsons–Zobel-plots of the capacitances of inhomogeneous surfaces are likewise discussed.