Fundamental Electrochemistry of Pseudocapacitance

Assuming that the redox material particles and/or reaction sites are uniformly distributed in the electrode layer and both the oxidant (Of) and the reductant (RJ) are insoluble in the electrolyte, the redox process can be expressed as 

Equation (3.3) indicates that when the electrode potential E changes over time, for example, in a linear potential scan experiment, the concentration of oxidant will change accordingly, resulting in a current flow through the electrode [19]. The current density (x, A/cm ) passing through the electrode can be expressed as 

Equation (3.6) is for the case of an ideal reversible redox reaction. However, due to the electrode matrix structure, the distribution of reaction redox centers may not be uniform and the interaction between the centers may cause a quasi-reversible behavior of the redox reaction. To take care of this quasi-reversible behavior, we may introduce a factor as did Conway and Gileadi [20]. This factor can be written as 

Actually, the pseudocapadtance expressed by Equation (3.9) is the momentary capacitance, which is a function of electrode potential. For the intrinsic pseudocapacitance (Qp, F/g) of fhe redox reacfion, an average value may make more sense and may be defined using fhe following equation by combining with Equation (3.9)  

Note that because the value of E -E is normally small ( 0.3 V), the obtained intrinsic pesudocapacitance of the redox reaction is normally much higher 

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