The black circles represent actual measurements done in 0.9% saline solution. The red curve is the best fit to a Constant Phase Element (CPE) in series with a resistor. The resistor accounts for the bulk resistivity of the solution and the usually negligible resistance of the lead conductor.
Electrochemists have come with multiple and occasionally rather elaborate schemes to explain the frequency-dependence of the double-layer capacitance. For our purpose, the easiest one - the CPE model - suffices. The main difference between a CPE and an ideal capactor is the phase shift between voltage and current. For an ideal capacitor, the phase shift is \(90^{\circ}\); whereas, for a CPE, it is constant but less than \(90^{\circ}\) (hence the name constant phase element). By definition, the reactance of a CPE is calculated as $$ Z_{\text{CPE}}(f) = \frac{1}{(2\pi f)^{\alpha} Q}, $$ where \(Q\) quantifies the capacitance and the power \(\alpha\) ranges from 0 to 1. Note that for \(\alpha=1\), the formula for a CPE is equivalent to the one for an ideal capacitor. We are particularly interested in the value of \(\alpha\), as it is dependent on the heterogeneity of the electrode surface. For a polished metallic surface, \(\alpha\) is 0.75-0.9. But for fractal surfaces, \(\alpha\) assumes smaller values. On the graph, you see the values of the CPE model:
The presented data and the red curve are total impedance, not just the reactance. The red curve at each frequency is calculated as $$ Z_{\text{TOT}}(f) = \sqrt{\left(R+Z_{\text{CPE}}(f)\cos(\theta)\right)^2 + \left(Z_{\text{CPE}}(f)\sin(\theta)\right)^2}. $$ For an ideal capacitor, \(\alpha=1\) and \(\theta=90^{\circ}\), therefore the total impedance reduces to the classic equation $$ Z_{\text{TOT}}(f) = \sqrt{R^2 + Z_{\text{CAP}}^2}. $$