Page 258 - Carbon Nanotube Fibres and Yarns

CNT yarn-based supercapacitors 249

electrode in a chosen electrolyte using electrochemical cyclic voltammetry
(CV) to record cyclic voltammograms, from which the capacitance can be
calculated.
When two electrodes, positive electrode with a capacitance C p and neg-
ative electrode with a capacitance C n , are combined into a supercapacitor,
the overall capacitance C T of the entire cell is.
1 = 1 + 1 (10.1)
C T C p C n

If the two electrodes are the same, C p = C n , the supercapacitor is sym-
metric. If C p ≠ C n , the supercapacitor is asymmetric, in which case, C T is
dominated by the electrode with the smaller capacitance.
The specific capacitance of an SC cell can be calculated using the vol-
tammetric charge integrated from its CV curve.
Q ∫ IdV (10.2)
C = =
cell
∆
υ
2 mV 2 m ∆ V
where C cell is the specific capacitance of the cell, Q is the total charge ob-
tained by integrating the positive and negative sweeps in a CV curve, m is
the mass of the active materials in the two electrodes, v is the scan rate, and
ΔV is the potential window between the two electrodes.
Cell capacitance can also be calculated from the galvanostatic charge-
discharge curve.
I × ∆ t
C = (10.3)
cell
m × ∆ V
in which I is the discharge current, m is the total mass of the active materials
in the two electrodes, ΔV is the applied potential, and Δt is the discharge time.
Energy density and power density are two key performance indicators
for SCs. They can be calculated from the discharge curve using the follow-
ing equations:
1
E = C × ∆ V (10.4)
2 cell

E (10.5)
P =
t ∆

where E is the energy density, P is the power density, C cell is the specific
capacitance, ΔV is the applied potential, and Δt is the discharge time.