THERMODYNAMICS OF ROUGH COLLOIDAL SURFACES

In Debye-Huckel theory, the free energy of an electric double layer near a colloidal (or any other) surface can be related to the statistics of random walks near the surface. We present a numerical method based on this correspondence for the calculation of the double-layer free energy for an arbitrary charged or conducting surface. For self-similar surfaces, we propose a scaling law for the behavior of the free energy as a function of the screening length and the surface dimension. This scaling law is verified by numerical computation. Capacitance measurements on rough surfaces of, e.g., colloids can test these predictions.