Power law for frequency-dependence of double layer capacitance of graphene flakes

• Double layer capacitance of graphene decreases with an increase in ac-frequency.
• The frequency-dependence is given by the power law of the frequency.
• The capacitance is proportional approximately to the thickness of graphene films.
• Resistance-like voltammograms at thick films are caused by frequency-dispersion.

The double layer capacitance per weight of graphene (GN) flakes in aqueous solution at the polarized potential increases with a decrease in the ac-frequency, obeying the inverse of the power law of the frequency. The power law is demonstrated to be equivalent to the constant phase element. The frequency-dependence increases with the thickness of the GN films. Thus, the lower the frequency and the thinner the film is, the larger is the capacitance density per weight. This is confirmed by cyclic voltammetry for several thickness of GN films and several scan rates. Resistance-like voltammograms at thick films are caused by frequency-dispersion. The overall capacitive properties of the GN films are as follows: the thickness of one GN flake is estimated to be 2 nm in average from the comparison of the thickness with the capacitances at the HOPG, which is consistent with values by the STM and AFM images.