I strongly believe that two commonly used methods in the literature such as, (i) the first method (Trasatti method) differentiates b/w double layer and pseudocapacitance, but gives very high value of pseudocapacitance for activated carbons and (ii) Second method (Dunn's method) differentiates charge storage through capacitive and diffusion controlled processes.

Md. Faruque Hossain thank you for your comment. But that doesn't answer the question.

Hi, Muhammad Bilal , before answering your question, I think it is necessary to clarify a confusion in the literature that misleadingly claims that electric double layer (EDL) capacitance contributes to surface controlled current (i = av), and pseudocapacitance results from diffusion controlled current (i = bv0.5).

The truth is that both the EDL capacitance and pseudocapacitance CAN be either surface or diffusion controlled, or both. In other words, a pure EDL charging process can be diffusion controlled if, for example, the EDL material is used as a thick coating or the CV scan rate is sufficiently high, whilst a pure pseudocapacitive charging can be surface controlled if the material used is very thin, and/or the CV scan rate is sufficiently low.

In fact, the equation i = av + bv0.5 and its rearranged form, i/v0.5 = av0.5 + b, which were possibly first used in a 1988 paper [T.-C. Liu, W. G. Pell, B. E. Conway, J. Electrochem. Soc., 145 (1988) 1882] for analysis capacitive cyclic voltammograms, are NOT able to differentiate between EDL capacitance and pseudocapacitance. The correct derivation of information is the relative contribution of diffusion (either EDL or pseudo) to the dis-/charging of the electrode.

In principle, in cyclic voltammetry, any charge storage process in a solid electrode material (including EDL and pseudocapacitive materials, and also battery-type materials) is surface controlled at low scan rate and/or thin coating. When the scan rate and/or coating thickness increase, the process then becomes influenced by diffusion in a way of mixed control, and eventually, diffusion controlled.

Now, about your question "Is there any method to separate diffusion controlled double layer capacitance and normal double layer capacitance?" My answer is that there is not such as a concept of "diffusion controlled EDL capacitance", but only EDL capacitance. However, diffusion can affect the EDL capacitance value as measured by CVs, particularly when coating is thick and/or scan rate is high. You can use the equation, i = av + bv0.5 to analyse the relative contributions of surface and diffusion processes to the measured overall current and hence the overall electrode capacitance. Coverall = i/v.

On your second question, "is there any way to find how much double layer capacitance is coming from micropores and mesopores?", there is not yet any study on using an electrochemical method to do this. However, it is possible to derive such information from the porous structure analysis such as the BET method that can determine the pore size distribution, specific area and volume proportions of micropores and mesopores, from which the relative contribution of each may be estimated.

Note that experimentally measured capacitance is dependent on the properties of the electrolyte ions, which means both the micro- and mesopores may be accessed by small ions, but not the large ones. Although one may use such differently sized ions to explore the pore information of the electrode (material), caution is needed to compare the capacitance values measured from using differently sized ions.

Thank you for your comprehensive discussion George Zheng Chen . The equation i = av + bv^0.5 used to separate capacitive and diffusion controlled currents, now commonly called Dunn's method (after Dunn et al. Journal of Physical Chemistry C 2007, 111, (40), 14925-14931) is time-intensive and needs the current values from a large number of CVs at different scan rates. On the other hand, I found the Trasatti method (after Trasatti et al. Electrochimica Acta 1990, 35, (1), 263-267) to be less time-intensive and instead of differentiating surface and diffusion controlled capacitance, it claims to tell the minimum value of double layer and maximum value of pseudocapacitance at low scan rates window using equations C^-1 = Rv^0.5 + CT^-1 and C = Rv^-0.5 + CDL. It has been used by Lee et al. Journal of Power sources 2013, 227, 300-308, Do you think it's incorrect?

According to Convey and others, activated carbon-based supercapacitors, so-called electric double-layer capacitors, exhibit 5-10% of charge storage due to pseudocapacitance, depending on surface functionalities. What should be the best method to differentiate? There is a recent EIS study that differentiates Double-Layer, Psuedocapacitance, and Battery-like mechanisms (ACS Appl. Mater. Interfaces 2020, 12, 12, 14071–14078). Maybe it can be helpful for some readers.

If one knows the microporous surface area from BET, how can he/she quantitatively find the capacitance contribution from micropores?

Muhammad Bilal As I already stated, this equation, i = av + bv0.5, and its application in analysis of cyclic voltammograms were possibly first proposed in the paper of [T.-C. Liu, W. G. Pell, B. E. Conway, J. Electrochem. Soc., 145 (1988) 1882] in relation with a pseudocapacitive material, but was later used and misinterpreted or misunderstood in the paper of [J. Wang, J. Polleux, J. Lim, B. Dunn. J. Phys. Chem. C, 111(2007) 14925]. Unfortunately, it was the latter paper that has presented a largely incorrect interpretation, and misled many in the supercapacitor community.

The method reported in the paper of [S. Ardizzone, G. Fregonara, S.Trasatti, Electrochim. Acta, 35, (1990) 263] also aims to correlate the diffusion control and surface control with the charge transfer (charging or discharging) process. Like the Liu-Pell-Conway method, the Ardizzone-Fregonara-Trasatti method is also blind to, and should not be used to judge if a process is based on EDL capacitance or pseudocapacitance, nor to differentiate (separate) the two.

In brief, these two methods are themselves useful in analysis of electrode kinetics in terms of surface and diffusion controls, but they both have not been developed to differentiate EDL capacitance and pseudocapacitance. The problem is the later misinterpretation or misunderstanding that surface control results from EDL capacitance, and diffusion control is related to pseudocapacitance. It is unfortunate that the original authors did NOT interpret their methods according to EDL capacitance or pseudocapacitance, but a few others who later made the mistakes which were unfortunately followed by many.

It is worth noting that EDL capacitance and pseudocapacitance are electrically the same, i.e. they both behave like a capacitor, which is why it is difficult, if not impossible, to differentiate them by an electrical or electrochemical method. In principle, an EDL electrode should be dis-/charged at a higher rate than a pseudocapacitive electrode, which means these two types of electrodes may respond differently to stimulants of different frequencies, which makes EIS a possible option for differentiation. However, what has been reported in the paper of [ Ko et al., ACS Appl. Mater. Interfaces 12 (2020) 14071] does not show EIS to be more informative than CV or GCD.

However, there is a major difference between EDL capacitance and pseudocapacitance: the latter involves chemical changes but not the former. Therefore, differentiation between EDL capacitance and pseudocapacitance is possible by combining the electrochemical analysis with an in situ spectroscopic method that is capable of monitoring the variation of element valence or chemical bonding.

(The followings are added on 03 May 2022)

Regarding your last question, the specific microporous surface area from BET can be used to calculate/estimate the specific capacitance by the following simple relation with an assumption (actually fact) that the true areal capacitance, Cdl, of carbon is 10 to 30 uF/cm2. For example, if the BET area, SBET, is 800 m2/g, the specific capacitance, Csp, is calculated/estimated as follows.

Csp = Cdl x SBET = (10~30) x 10-6 x 800 x 104 = 80 ~ 240 F/g