Complex impedance spectra of porous electrode with fractal structure

Transmission line model (TLM) is often used for the analysis of porous electrode since the current distribution in the pore can be calculated. In the present paper, the TLM is applied to the impedance analysis of complicated porous electrode with fractal structure. Activated carbon is used as electrode material for electric double layer capacitor and its pore has branch structure. Considering the fractal structure of the activated carbon, we proposed new equivalent circuit with TLM for three sizes of pores: macropore, mesopore and micropore. In this model, we defined the ratio ξ of electric double layer parts in whole inner wall of the pore because the inner wall is separated to electrolyte/electrode interface and branch base parts. Calculated electrochemical impedance of blocking electrode shows the lumped constant region in low frequency range and the distributed constant region in low frequency range. General TLM yields the straight line with slope of 45° in the distributed constant region on the Nyquist plots. In the present analysis, it was found that the slope was 22.5° at ξ = 0 in the case of double-pores (macropore and mesopore) and 11.25° at ξ = 0 in the case of triple-pores (macropore, mesopore and micropore).