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Chapters / Chapter 3, Supercapacitors / Lesson 3.2

3.2 Measuring and reporting supercapacitors

Three- versus two-electrode cells, capacitance from charge–discharge and CV, mass loading, energy and power, rate capability and cycling, with calculators for each.

About 30 minutesOpen to everyoneQuiz at the end

Three electrodes or two

A three-electrode cell measures one electrode against a reference, so it shows how a material behaves over a chosen potential window. It is the right tool for studying a material. A two-electrode cell, a coin cell or a pouch with two electrodes and a separator, measures a device. Energy and power only mean something for a device.

The factor of fourIn a symmetric two-electrode cell the two electrodes are in series, so the cell capacitance is half that of one electrode. Per gram of one electrode, with mtotal the mass of both, Csp = 4 Ccell / mtotal. Stoller and Ruoff (2010) showed how often this factor is mixed up.

Capacitance from charge and discharge

Galvanostatic charge and discharge (GCD) at constant current is the closest test to real use. For a capacitive material the discharge is a straight line, and the capacitance follows from its slope.

C = I·Δt / (ΔV − VIR)I discharge current, Δt discharge time, ΔV window, VIR the sudden drop at the start of the discharge. The drop also gives the equivalent series resistance, ESR ≈ VIR/(2I).

For a curved discharge, integrate the energy instead, E = I∫V dt, and use C = 2E/ΔV². For battery-type materials, report the capacity Q = I·Δt in mAh/g.

Capacitance from a CV

The charge stored in one sweep is the area enclosed by the CV divided by twice the scan rate. Dividing by the window gives the capacitance. Report the scan rate, because the capacitance usually falls as the scan gets faster.

Numbers that compare fairly

  • Mass loading and thickness. Give mg per cm² and the electrode thickness. Thin films with tiny loadings can show very high F/g that do not survive at practical loadings, as Gogotsi and Simon (2011) pointed out. Report areal (F/cm²) and volumetric (F/cm³) values too.
  • Which mass. Say whether specific values are per gram of active material, of the whole electrode, or of both electrodes in a cell.
  • Rate capability. Give the capacitance at several current densities, from slow to fast, and the share kept at the highest rate.
  • Energy and power from a two-electrode cell, shown on a Ragone plot of energy density against power density. Do not combine the energy of one electrode with the power of another test.
  • Cycling. Several thousand cycles at a stated current, with capacitance retention and Coulombic efficiency. An early increase in capacitance often comes from slow wetting or activation, so describe it.
  • Impedance. The ESR from the high-frequency intercept, and the frequency at which the Nyquist plot turns almost vertical, which shows how fast the device behaves as a capacitor (Lesson 1.3).

Check your understanding

Quiz for lesson 3.2

Pick one answer per question. You see the explanation straight away.

References and further reading

  1. M. D. Stoller, R. S. Ruoff, Best practice methods for determining an electrode material's performance for ultracapacitors, Energy Environ. Sci. 3 (2010) 1294–1301. doi:10.1039/c0ee00074d
  2. Y. Gogotsi, P. Simon, True performance metrics in electrochemical energy storage, Science 334 (2011) 917–918. doi:10.1126/science.1213003
  3. P. Simon, Y. Gogotsi, Materials for electrochemical capacitors, Nat. Mater. 7 (2008) 845–854. doi:10.1038/nmat2297
  4. T. Brousse, D. Bélanger, J. W. Long, To be or not to be pseudocapacitive?, J. Electrochem. Soc. 162 (2015) A5185.
  5. A. J. Bard, L. R. Faulkner, Electrochemical Methods: Fundamentals and Applications, 2nd ed., Wiley, 2001, chapters 1 and 13.