Molecular interaction model for frequency-dependence of double layer capacitors

Electric double layer capacitances at electrodes exhibit frequency-dependence, decreasing with the frequency in accordance with the power law even at frequency as low as 1 Hz. Since the capacitance is mainly caused by orientation of dipoles of solvent molecules in the Helmholtz layer, the frequency dependence may be associated with the rate of the orientation. The frequency of the orientation on molecular scale is of the order of GHz, whereas the observed frequency domain is less than 10 kHz. The difference implies that the frequency dependence should not be controlled by simple flips of the dipoles but be caused by a slow process induced by the orientation. This belongs to a cooperative phenomenon. We consider here as the inducing causes the solvent-solvent interaction, the image force of the dipoles to the electrode and the orientation by the external field. The energy balance indicates that most dipoles are confined regularly on the electrode surface as a 2D phase. The 2D-Monte Carlo simulation similar to that for the Ising model is performed in the light of the competition of the interaction and the orientation. The simulation demonstrates aggregation of the oriented dipoles which are hindered by the interaction. The aggregation and hence the capacitance grow gradually with the time of voltage application. The increasing rate obeys the experimentally observed power law.