I probably can answer the send part of your question, about the capacitive contribution calculation from CV curves. Actually this has been done for a lot of materials, not only limited to capacitor materials. The basic theory is that: for diffusion controlled processes, the current at any point on CV curves is proportional to the squire root of scan rate; for non-diffusion controlled processes, usually double layer capacitance and pseudocapacitance, the  current is proportional to scan rate v. If conduct several CV scans at various scan rates, the contribution from both reactions can be roughly estimated, as expressed in this euqation: i(V)=k1 v+k2 v^(1/2). where k1υ represents the non-diffusion controlled charge storage and k2υ1/2 represents the diffusion controlled charge storage. B. Dunn is the pioneer to use this equation, then later a lot of research utilized this method to calculate the capacitive contribution. Here are some example literatures:

1. Augustyn, V., Simon, P. and Dunn, B., 2014. Pseudocapacitive oxide materials for high-rate electrochemical energy storage. Energy & Environmental Science, 7(5), pp.1597-1614.

 5. Yu, P., Li, C. and Guo, X., 2014. Sodium storage and pseudocapacitive charge in textured Li4Ti5O12 thin films. The Journal of Physical Chemistry C, 118(20), pp.10616-10624.

 6. Zhao, K., Liu, F., Niu, C., Xu, W., Dong, Y., Zhang, L., Xie, S., Yan, M., Wei, Q., Zhao, D. and Mai, L., 2015. Graphene Oxide Wrapped Amorphous Copper Vanadium Oxide with Enhanced Capacitive Behavior for High‐Rate and Long‐Life Lithium‐Ion Battery Anodes. Advanced Science, 2(12).

 7. Dong, S., Shen, L., Li, H., Nie, P., Zhu, Y., Sheng, Q. and Zhang, X., 2015. Pseudocapacitive behaviours of Na2Ti3O7@ CNT coaxial nanocables for high-performance sodium-ion capacitors. Journal of Materials Chemistry A, 3(42), pp.21277-21283.

 8. Chen, Z., Augustyn, V., Jia, X., Xiao, Q., Dunn, B. and Lu, Y., 2012. High-performance sodium-ion pseudocapacitors based on hierarchically porous nanowire composites. ACS nano, 6(5), pp.4319-4327.

 9. Lim, E., Jo, C., Kim, M.S., Kim, M.H., Chun, J., Kim, H., Park, J., Roh, K.C., Kang, K., Yoon, S. and Lee, J., 2016. High‐Performance Sodium‐Ion Hybrid Supercapacitor Based on Nb2O5@ Carbon Core–Shell Nanoparticles and Reduced Graphene Oxide Nanocomposites. Advanced Functional Materials, 26(21), pp.3711-3719.

 10. Lim, E., Jo, C., Kim, H., Kim, M.H., Mun, Y., Chun, J., Ye, Y., Hwang, J., Ha, K.S., Roh, K.C. and Kang, K., 2015. Facile Synthesis of Nb2O5@Carbon Core–Shell Nanocrystals with Controlled Crystalline Structure for High-Power Anodes in Hybrid Supercapacitors. ACS nano, 9(7), pp.7497-7505.

 11. Cook, J.B., Kim, H.S., Yan, Y., Ko, J.S., Robbennolt, S., Dunn, B. and Tolbert, S.H., 2016. Mesoporous MoS2 as a Transition Metal Dichalcogenide Exhibiting Pseudocapacitive Li and Na‐Ion Charge Storage. Advanced Energy Materials.

 12. Zhu, Y., Peng, L., Chen, D. and Yu, G., 2015. Intercalation Pseudocapacitance in Ultrathin VOPO4 Nanosheets: Toward High-Rate Alkali-Ion-Based Electrochemical Energy Storage. Nano letters, 16(1), pp.742-747.

In addition, here is a  new publication that questioning this calculation method.

13. Opitz, M., Yue, J., Wallauer, J., Smarsly, B. and Roling, B., 2015. Mechanisms of Charge Storage in Nanoparticulate TiO2 and Li4Ti5O12 Anodes: New Insights from Scan rate-dependent Cyclic Voltammetry. Electrochimica Acta, 168, pp.125-132.

I think this is a novel work to make a electrode through the supercapacitor materials.

I probably can answer the send part of your question, about the capacitive contribution calculation from CV curves. Actually this has been done for a lot of materials, not only limited to capacitor materials. The basic theory is that: for diffusion controlled processes, the current at any point on CV curves is proportional to the squire root of scan rate; for non-diffusion controlled processes, usually double layer capacitance and pseudocapacitance, the  current is proportional to scan rate v. If conduct several CV scans at various scan rates, the contribution from both reactions can be roughly estimated, as expressed in this euqation: i(V)=k1 v+k2 v^(1/2). where k1υ represents the non-diffusion controlled charge storage and k2υ1/2 represents the diffusion controlled charge storage. B. Dunn is the pioneer to use this equation, then later a lot of research utilized this method to calculate the capacitive contribution. Here are some example literatures:

1. Augustyn, V., Simon, P. and Dunn, B., 2014. Pseudocapacitive oxide materials for high-rate electrochemical energy storage. Energy & Environmental Science, 7(5), pp.1597-1614.

 5. Yu, P., Li, C. and Guo, X., 2014. Sodium storage and pseudocapacitive charge in textured Li4Ti5O12 thin films. The Journal of Physical Chemistry C, 118(20), pp.10616-10624.

 6. Zhao, K., Liu, F., Niu, C., Xu, W., Dong, Y., Zhang, L., Xie, S., Yan, M., Wei, Q., Zhao, D. and Mai, L., 2015. Graphene Oxide Wrapped Amorphous Copper Vanadium Oxide with Enhanced Capacitive Behavior for High‐Rate and Long‐Life Lithium‐Ion Battery Anodes. Advanced Science, 2(12).

 7. Dong, S., Shen, L., Li, H., Nie, P., Zhu, Y., Sheng, Q. and Zhang, X., 2015. Pseudocapacitive behaviours of Na2Ti3O7@ CNT coaxial nanocables for high-performance sodium-ion capacitors. Journal of Materials Chemistry A, 3(42), pp.21277-21283.

 8. Chen, Z., Augustyn, V., Jia, X., Xiao, Q., Dunn, B. and Lu, Y., 2012. High-performance sodium-ion pseudocapacitors based on hierarchically porous nanowire composites. ACS nano, 6(5), pp.4319-4327.

 9. Lim, E., Jo, C., Kim, M.S., Kim, M.H., Chun, J., Kim, H., Park, J., Roh, K.C., Kang, K., Yoon, S. and Lee, J., 2016. High‐Performance Sodium‐Ion Hybrid Supercapacitor Based on Nb2O5@ Carbon Core–Shell Nanoparticles and Reduced Graphene Oxide Nanocomposites. Advanced Functional Materials, 26(21), pp.3711-3719.

 10. Lim, E., Jo, C., Kim, H., Kim, M.H., Mun, Y., Chun, J., Ye, Y., Hwang, J., Ha, K.S., Roh, K.C. and Kang, K., 2015. Facile Synthesis of Nb2O5@Carbon Core–Shell Nanocrystals with Controlled Crystalline Structure for High-Power Anodes in Hybrid Supercapacitors. ACS nano, 9(7), pp.7497-7505.

 11. Cook, J.B., Kim, H.S., Yan, Y., Ko, J.S., Robbennolt, S., Dunn, B. and Tolbert, S.H., 2016. Mesoporous MoS2 as a Transition Metal Dichalcogenide Exhibiting Pseudocapacitive Li and Na‐Ion Charge Storage. Advanced Energy Materials.

 12. Zhu, Y., Peng, L., Chen, D. and Yu, G., 2015. Intercalation Pseudocapacitance in Ultrathin VOPO4 Nanosheets: Toward High-Rate Alkali-Ion-Based Electrochemical Energy Storage. Nano letters, 16(1), pp.742-747.

In addition, here is a  new publication that questioning this calculation method.

13. Opitz, M., Yue, J., Wallauer, J., Smarsly, B. and Roling, B., 2015. Mechanisms of Charge Storage in Nanoparticulate TiO2 and Li4Ti5O12 Anodes: New Insights from Scan rate-dependent Cyclic Voltammetry. Electrochimica Acta, 168, pp.125-132.

Thanx Chunhui Chen sir

Hi Mr. Chunhui Chen, appreciate a lot for the information. But, do you know how to plot the scan rate dependance graph to determine the k1 and k2? The paper is didn't explain clearly on the current they used for the y-axis.

I posted today (16 May 2019) an answer to another question which is relevant to this post. (https://www.researchgate.net/post/Ambiguity_b_value_and_Dunns_equation_for_battery-type_materials)

In brief, it is incorrect or misleading to use this equation, i(V) = av + bv1/2, to differentiate or separate capacitive current from non-capacitive current as claimed by those papers listed above.

Capacitive charging/discharging , either EDLC or pseudocapacitive, still involves charge balancing counter ions from or into the liquid electrolyte, and hence can become diffusion controlled under some experimental conditions, such as a too fast potential scan, a relatively dense and/or thick coating of the capacitive material on the electrode.

On the other hand, a battery electrode material, if applied as a sufficiently thin coating on the electrode, can also lead to CVs (peak shaped) on which the proportionality exists between the CV current and the scan rate, i.e. i(V) = av (i.e. no diffusion control). In a more general case of a battery electrode, diffusion control is often present, and this equation, i(V) = av + bv1/2, is valid as well.

' b value of close to 1 between 1.2 and 1.7 V before decreasing to ∼0.6 at 1.8 V. '

Article Designing Pseudocapacitance for Nb2O5/Carbide-Derived Carbon...

Subrata Ghosh Do you mean the b value is not a constant, but potential dependent?

Hello Prof. Chen,

Thank you for your previous answers.

In response to your question, the potential dependent b-value is shown in Fig. 4(c) in that article.

Hello Professor George Zheng Chen ,

Following is another report on carbon structures where b-value changes with respect to the potential. The fact is attributed to the ion-intercalation into the carbon. I will be grateful if you provide in-depth understanding.

Thank you

(V)=k1 v+k2 v^(1/2). 

Chunhui Chen Thank you for pointing out the 2015 EA paper by Opitz and co-workers that questioned, actually, criticized the use of the equation for differentiation of psuedocapacitance from EDL capacitance.

Hi Thanh Tuan Nguyen

sorry for the late response.

I had never seen any negative k1 and k2 values in my systems (most for battery). For your case, if the absolute value of k1 is not near 0, you'd better double check your calculation. However, if the absolute value is near 0, that may just be the error in the system and indicating your current is mainly from k2.

For this calculation method, if you look into how you develop the equation, you may find out they have lots of assumptions, even for the liner relationship and squire root relationship. So without meet all these assumptions but using this method, you can only get a rough estimation of each contribution.

Another point, if you are working with battery or the system are more likely work in the diffusion controlled process, you'd better shift the CV curve (to align the peak) at each scan rate, do this especially when you want to do the whole CV curve calculation (shade area in the curve in some paper).If you don't do this, you may have some negative k1 or k2 values at the two end of the CV scan range.

Hope this helps.