The invention features an electrochemical device which includes at least two capacitor electrodes 16, each of which includes a conductive material characterized in that at least ten percent (10%) of the overall surface area of the conductive material is an edge plane. In contrast to a basal plane, the electric field along an edge plane is distorted so as to exhibit an ‘edge effect or ‘fringe effect. Capacitor electrodes 16 with many edges, points, corners, or fractal surfaces exhibit greater capacitance per unit volume or mass amount of capacitor electrode material, than do materials in which the surface area of the material is predominately basal plane. An electrochemical device of the invention can be, for example, an electrochemical cell, e.g., a battery, a capacitor, or a flow-through capacitor.