I was looking but I couldn't find answer to this question. My GCD curve at 10 A/g (activated carbon supercapacitor) looks like in the attached file. How should I properly calculate the specific capacitance?
From the slope: which part of the curve should I use to measure the slope? Right after the ohmic drop or should I rather also consider the part at the lower voltage which reflects the resistances related to the porous nature of the electrode? When I measure the slope right after ohmic drop I get the capacitance of 101 F/g. When I integrate the whole discharge region (with Origin integration function) I get 40 F/g. I'm confused...
in best practice, you should measure the slope and then calculate the specific capacitance. I would like to know what formula is used for calculating capacitance.
But the slope varies with the voltage...The formula I use is C=idt/dU, where dt/dU is the reciplocal of the slope.
take the straight line portion of the discharge curve to straight fit .
I have seen your GCD plot. First you need to evaluate IR drop because you need to subtract energy dissipated on the internal resistance.
See Fig. 11 in paper entitled "supercapacitor performance evaluation" for exact calculation of IR drop.
Then, most accurate formula for the capacitance calculation is
C (F/g) = 2*Im* (area under the discharge curve) / (V-IR)2 (square)
'Im' is the specific discharging current in A/g
area under the discharge curve = integral of V.dt (only discharge portion)
.....................................................
Derivation of the above formula:
Energy = 1/2 CV2 = Im * area under the discharge curve
This formula is free from the shape of the discharge curve and gives most reliable value.
Hope this helps.
Arvinder
Dear Dr. Arvinder Singh, I have no access to Willey. Could you please attach the paper you mentioned here or send me via email?
Thank you very much!
I am sorry. I completely missed your message. Today suddenly i come across this message. I hope you had found that paper.
Regards
Arvinder
1. The Ohmic drop does not really add or subtract to your capacitance, as it is recorded over an extremely low time interval (zero-time, in theory). In practice, it will depend on the time step you are using in your GCDC measurement - so, keep it as low as possible for the most reliable result.
2. Yes, your approach of integration is correct, from time-0 where the discharge is starting until the end, where voltage drops to 0.
3. The hidden message (just kidding) in Artur Braun's comment is that you should perform your GCDC over a range of CDC currents, from low to high, to audit the performance of your device over a range of parameters, and to see where it behaves optimally. Your capacitance will always depend on your selected current, with (usually) the highest scores obtained over the lowest currents. This way, you will plot your final capacitance scores over a wide set of currents - and you can also give it in the Ragone format. You can report your capacitance as F/X (X=mass, area, or volume) at the current value where it's measured, but also provide the full plot of capacitance over current. The current value you use for reporting your capacitance needs to make the comparison with other reported scores viable: if most of the papers you are referencing report capacitance at 25mA for example, then report it at that exact value and also give the full plot of capacitance over a wide range of currents in your figures.
PS: there are plenty of papers you can use as example, no need to advertise over here with any of mine.
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