The Complex Capacitance Model

As described previously, the De Levie model is useful to describe the electrochemical ac (or dc) behavior of a porous electrode. This TLM describes the porous electrode as an interpenetrated network of RC elements, whose contribution depends on the frequency of the ac signal. In other words, the capacitance and the resistance of the EDLC change with the frequency. However, it is difficult to get from these equations the change of the capacitance with the frequency useful to characterize an EDLC electrode. This is why other approaches have been developed and focused more onto the EDLC problematic, with the aim to quantify the change of the porous electrode capacitance (or the EDLC device capacitance) with the frequency of the ac signal. 

An alternative approach between the basic RSC series circuit and the De Levie model (TLM) is to consider a porous electrode as a whole capacitance by simply using the impedance data [20]  

Carbons for Electrochemical Energy Storage and Conversion Systems 

C (co) and C (co) are, respectively, the real part and the imaginary part of the capacitance 

C (co) is the capacitance of the electrode (or the cell) the low frequency value of C (to) is the capacitance obtained during constant current discharge measurements. 

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This complex capacitance model, even if simplified, gives precious quantitative information about the change of the capacitance of an EDLC device versus the frequency. The knowledge of the ac behavior is indeed important since EDLC, as power devices, are often used in ac modes. Finally, it must be precise that improvements of such approach have been recently developed in a series of papers [35,36], where the De Levie TLM is associated with the complex capacitance model to estimate the porous structure of the carbon electrodes using discrete Fourier transformation. 

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