Could anyone tell me how to calculate specific capacitance or (specific capacity) for battery like materials electrode. I read some paper say that for battery like materials the appropriate way to measure the amount of charge stored in the electrode is specific capacity in terms of C g−1 or mAhg−1 rather than the (specific capacitance Fg−1). My question which equations should I use to calculate specific capacity ( in term of C g−1 and mAhg−1 ). My electrode is LaMnO3 perovskite (look at CD curve as attached Fig). the CD was cycled in potential rage from (-1 to +0.56 V) . The initial voltage drop is about 0.02V. and discharging time is about 727 s.
So of course mAh/g is a measure of stored charge and is some times called specific capacity, and C/g is clearly specific charge. These quantities are measures of how many ions and electrons can be accepted in a certain mass generally intercalated into a crystalline solid inside an electrode. Neither of those measures are specific capacitance which measures the amount of charge which can be accommodated as layers of opposing charges on the surface of the mass at a given voltage difference. The question of method and units may possibly come from the fact capacitance and capacity sound pretty much the same but are not at all alike in batteries.
Assuming you want specific capacity (not specific capacitance) you then need to define the voltage limits because capacity is typically given for a voltage range; at that point you can get the Ah count off your cell cycler or whatever equipment you are using to measure voltage and current and simply divide by mass. If you are building cells to test your materials then a good set of sources for cell measurements and the associated calculations are the USABC manuals, which you can find at: http://www.uscar.org/guest/article_view.php?articles_id=86
Be sure to use plenty of the counter electrode in this test so that your capacity is not artificially limited.
Dear Scott W, many thanks for your help . according to that, I calculated the specific capacity using this equation Cs= I*T/3.6m
and I got Cs = 1 *727/3.6 = 201.9 mAh (727 C/g) at 1A/g, am I right ?.
Another question, is it good I idea to calculate specific capacity from CV for this materials and make a comparison between these two values of capacity (from CV @ from CD)?
If its ok please tell me how ? (look at the attached Fig).
If your charge discharge was done at 1 amp continuous current then that would work. (current * seconds / 3600 ) will give you Ah at constant current, so dividing by 3.6 will obviously give you mAh. However, with most materials the first cycle is a little different from the following cycles since irreversible reactions take place. This gives a high value of capacity relative to the reversible capacity, so be sure to calculate the capacity you want. With many Si electrodes for example the impact is enormous. So you might want to do some cyclic voltametry on the material till the curve settles down to repeating itself, and then measure your capacity at constant current as you have done (or as I think you have done, at least). You may also want to do your capacity calculation as a function of current what impact that has. If there is high inherent resistance in the material it could be very meaningful.
CV is usually done at a fixed voltage scan rate. Accordingly if you integrate the current over a voltage window and then divide by the scan rate and divide that by 3600 s/hr you will get the capacity in Ah over that voltage window, be careful about the sign as it changes in your data. CV is typically pretty slow so this will be the best capacity you can get. Again do a few CV cycles until they start to fall on top of each other or you will only get the first cycle capacity.
You can fabricate battery electrode or supercapacitive electrode. Its upto you.
mainly for battery elecctrode, specific capacity has been calculated. But for supercapacitive electrode specific capacitance has been calculated.
your CD curve shows faradic behavior which shows pseudocapacitive electrode behavior.
Above readers have discussed to calculate specific capacity as I can see.
so, here I'm giving the method to calculate specific capacitance from cyclic voltammetry (CV) and charge-discharge(CD):
Specific capacitance calculated from CV
C=∫Idv/2mv(Vf-Vi)
where, ‘∫Idv’ implies area under the CV curve, ‘m’ signifies mass (g) of active electrode, ‘v’ specifies the scan rate, ‘(Vf-Vi)’ is an functional potential frame.
For, linear/triangular CD curve (EDLC based supercapacitor)
C=I∆t/m(Vf-Vi)
where, , ‘I’ implies current intensity, '∆t' is discharge time.
but for non-linear CD curve (pseudocapacitance based supercapacitor) as per your case:
C=2I∫Vdt/m(Vf-Vi)2
'∫Vdt’ symbolizes the area under the discharge curve only.
For further information, you can see my publications as well.
https://www.nature.com/articles/srep43430
http://www.sciencedirect.com/science/article/pii/S0013468617309817
This paper reported some important issues on capacitance and capacity
http://jes.ecsdl.org/content/162/5/A5185.figures-only?related-urls=yes&legid=jes;162/5/A5185
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