Linear and non-linear pseudocapacitances with or without diffusion control

Pseudocapacitance is an important reversible charge storage mechanism in many electrode materials. Although the concept was first proposed in early 1960s, it has been more widely studied following the observation of rectangular cyclic voltammograms (CVs) when testing some transition metal oxides and electronically conducting polymers, and the association with supercapacitor. However, interpretation of pseudocapacitance is inconsistent in the literature. Although all agree that materials are pseudocapacitive if they undergo Faradaic reactions and exhibit rectangular CVs, some have regarded any surface confined Faradaic reactions which may present non-rectangular or even peak-shaped CVs to be pseudocapacitive. In the case of rectangular CVs, the amount of charge stored in the electrode is a linear function of the electrode potential, whilst for non-rectangular or peak-shaped CVs, the relationship is non-linear. It is shown in this article that only linear pseudocapacitance is of relevance to supercapacitor, but non-linear pseudocapacitance may find applications in rechargeable battery and supercapattery. Further, it is clarified that the equation i ​= ​k1v ​+ ​k2v1/2 is useful in analysis of electrode kinetics in terms of surface confinement and diffusion control. However, this kinetic equation is blind to the thermodynamically determined charge storage mechanisms as shown by experimental evidence, and should not be used to differentiate non-capacitive Faradaic processes from pseudocapacitance, either linear or non-linear.