High volumetric capacitance near the insulator-metal percolation transition

I propose a newtype of capacitor with a very high volumetric capacitance. It is based on the known phenomenon of the sharp increase of the dielectric constant of a metal-insulator composite in the vicinity of the percolation threshold on the insulator side. The optimization suggests that the sizes of the metallic particles should fall within the nanoscale. The distance between planar electrodes should be somewhat larger than the correlation length of the percolation theory and approximate to 10-20 times larger than the size of the particles while the area of the electrodes could be unlimited. The random electric field in the capacitor is calculated and is shown to be larger than the average field corresponding to the potential difference of the electrodes. This random field is potentially responsible for the dielectric breakdown. The estimated breakdown voltage of the capacitor shows that the stored energy density might be significantly larger than that of electrolytic capacitors while the volumetric capacitances might be comparable. The charging and discharging times should be significantly smaller than the corresponding times of batteries and even electrolytic capacitors.