capacitance is capacity per voltage. if the capacity at different voltage is different, for example in faradaic charge transfer, then it is more appropriate to use capacity only. Capacitance should be used for linear change in voltage with time during charge discharge, which only happens in non faradaic Edlc system.

If you are not sure about the difference between EDLCs, psuedo, and battery, I would highly recommend the short paper by Gogotsi et al.

"Energy Storage in Nanomaterials – Capacitive, Pseudocapacitive, or Battery-like?"

https://pubs.acs.org/doi/abs/10.1021/acsnano.8b01914?mi=aayia761&af=R&AllField=nano&target=default&targetTab=std

It explains the differences between 3 types and what their electrochemical testing results should look.

capacitance is capacity per voltage. if the capacity at different voltage is different, for example in faradaic charge transfer, then it is more appropriate to use capacity only. Capacitance should be used for linear change in voltage with time during charge discharge, which only happens in non faradaic Edlc system.

What we know now is that charge storage on electrode can proceed in three ways, namely (1) electric double layer capacitive storage (EDL capacitance, or EDLC), (2) Capacitive Faradaic storage (pseudocapacitance), and (3) Non-capacitive Faradaic storage (battery-like), or more precisely, Nernstian storage. The CVs of (1) and (2) should be the same or very similar, i.e. rectangular, but that of (3) is peak-shaped. Therefore, it is unclear to only specify Faradaic storage, which can be either capacitor-like or battery-like.

I shall point out that it is impossible to distinguish between (1) and (2) by CVs (or GCDs) even though these two are different in charge storage mechanism. It is however possible to tell if the process involves charge transfer reactions (i.e. Faradaic) by using spectroscopic method in situ, such as electron spin resonance (ESR). The following picture is cropped from a paper reporting the CV of polyaniline (a pseudocapacitive material) and simultaneously recorded ESR response (esrogram) that confirms electron transfer reaction during the course of recording the CV of polyaniline. The CV shows capacitive behavior at more positive potentials (i.e. 0.15 V to 0.3 V), but the esrogram indicates charge transfer reactions occuring in this potential window. This is evidence that charge storage in polyaniline in the potential range from 0.15 to 0.30 V is dominantly capacitive Faradaic or pseudocapacitive in nature, instead of EDLC. At less positive potentials (-0.25 to 0.15 V), the CV shows current peaks, indicating Nernstian storage and discharge.

Meenu Sharma You may read our papers on the similarities and differences between battery, supercapacitor and supercapattery.

(Open Access) Chen GZ, Supercapacitor and supercapattery as emerging electrochemical energy stores, Int. Mater. Rev., 62(4) (2017) 173–202. http://dx.doi.org/10.1080/09506608.2016.1240914

(Open Access) Akinwolemiwa B, Chen GZ*, Fundamental consideration for electrochemical engineering of supercapattery, J. Brazilian Chem. Soc., 29(5) (2018) 960-972. http://dx.doi.org/10.21577/0103-5053.20180010 

sir George Zheng Chen kindly tell me about possible diffusion effect of a proton inside the electrode of cerium doped cobalt ferrite. However, I used electrolyte is 1M KOH for those electrodes. The concentration of protons should be negligible in such a strong alkaline electrolyte .

1 M KOH means the bulk solution is alkaline, but it does not mean (1) no proton in the electrolyte, and (2) the same at the interface between the electrode surface and the contacting electrolyte. For example, if your electrode material has a greater basicity than that of the electrolyte, proton diffusion into the electrode can surely proceed. It his the relative activity that determines the flow of proton direction.

The supercapattery refers to a hybrid energy storage device with one supercapacitor electrode (EDLC or faradic) and one battery electrode.