RANDOM-NETWORK SIMULATION OF AN ULTRACAPACITOR BASED ON METAL-SOLID-ELECTROLYTE COMPOSITE

A random-network model of a dense (pore-free) metal-solid-electrolyte composite is developed. Real and imaginary parts of admittance are sim ulated as a function of frequency and composition by means of the tran sfer matrix algorithm on a cubic lattice. For a composite without a so lid-electrolyte membrane in the middle (insulating with respect to ele ctronic current) the results predict the capacity maximum at the perco lation threshold in three dimensions and two maxima in two dimensions as a function of composition; they are compared with the predictions o f the effective medium theory. For a composite with an insulating memb rane in the middle, typical for ultracapacitors, the maximum of capaci tance in three dimensions is at equal portion of metal and solid-elect rolyte particles. In contrast to metal dielectric mixtures there are n o giant enhancement effects in static capacitance as a function of com position: the upper estimates of the enhancement factor are proportion al to the ratio of the size of the sample to the size of the grains.