Supercapacitor characterisation: CV, GCD, EIS and the Ragone plot
1 Theory
Storage mechanisms
Electrical double-layer capacitors (EDLC) store charge electrostatically at the porous carbon/electrolyte interface; since there is no Faradaic reaction they offer hundreds of thousands of cycles and high power. Pseudocapacitors (RuO₂, MnO₂, conducting polymers, MXenes) show capacitive-looking behaviour through fast surface redox reactions; they lie between batteries and supercapacitors. Hybrid systems (Li-ion capacitors) combine the two kinds of electrode.
How is capacitance calculated?
In CV from the area of the rectangular curve, C = ∫i·dE/(2·v·ΔE); in GCD from the slope of the discharge curve, C = I·Δt/ΔV (excluding the iR drop); in EIS from the low-frequency imaginary part, C = −1/(2πf·Z″). Since the three methods probe different time scales the values may differ; in porous electrodes in particular the capacitance measured at low rate is higher. For specific capacitance (F/g) the active mass and, in a two-electrode symmetric cell, the relation C_cell = C_electrode/4 must be taken into account — a common source of error in the literature.
Equivalent series resistance and time constant
ESR is found from the instantaneous voltage jump seen in GCD when the current direction changes (ΔV/2I) or from the high-frequency intercept of EIS; it limits the power density (P = V²/4·ESR). The transmission-line behaviour of the porous electrode appears as a 45° region in the Nyquist plot; the characteristic time constant τ₀ (the inverse of the frequency at which half the capacitance is reached) is the measure of power capability. The Ragone plot is obtained from constant-power discharges and allows comparison between devices.
Self-discharge and life
Leakage current and self-discharge are measured by following the current at constant voltage after full charge, or the voltage drop at open circuit. In life testing, 'floating' (holding at constant voltage) at high voltage and temperature gives faster ageing than cycling; capacitance loss and ESR rise are the indicators.
2 Application in measurement
Capacitance is determined in three ways: CV (C = i/v), galvanostatic charge-discharge (C = I·Δt/ΔV; the most reliable) and EIS (C = −1/(2πf·Z'')). As Stoller and Ruoff warned, single-electrode and two-electrode (cell) capacitance must not be confused, and energy and power density must be reported separately for cell mass/volume.
ESR (equivalent series resistance) is read from the IR drop at the start of discharge or from the high-frequency intercept of EIS; the time constant is determined from the complex-capacitance (C', C'') representation. The Ragone plot is built by constant-power discharge (CPW).
In pseudocapacitive materials the CV shape and scan-rate dependence are used to separate the Faradaic contribution.
Key equations
E = ½·C·V²; P = V²/(4·ESR)
3 Applicability
Where it applies
- Electrode material development (carbons, pseudocapacitive oxides), device validation (ESR, Ragone), life and self-discharge tests.
Limits and caveats
- Three-electrode half-cell measurements exaggerate device performance; final values should be given in a two-electrode full cell.
- At very high scan rates (>1 V/s) ohmic drop and instrument bandwidth distort the curve.
4 What did the application notes find?
- Supercapacitor AN33 — Shows the calculation of capacitance, ESR and efficiency by constant-current charge/discharge, and the monitoring of the power response with current pulses.
- Supercapacitor AN34 — Explains the determination of the time constant by potentiostatic/potentiodynamic and EIS methods; interpretation of the transmission-line region and the low-frequency capacitance.
- Supercapacitor AN51 — Shows EDLC characterisation by the galvanostatic polarisation method and measurement of leakage current/self-discharge.
- Electrochemistry AN6 — Shows the set-up of the constant-power technique and building the Ragone plot from successive power levels.
5 Which instruments perform this measurement?
References
- article M. D. Stoller, R. S. Ruoff. Best practice methods for determining an electrode material's performance for ultracapacitors. Energy Environ. Sci. 3, 1294–1301, 2010. doi:10.1039/c0ee00074d
- book B. E. Conway. Electrochemical Supercapacitors: Scientific Fundamentals and Technological Applications. Springer, 1999.
- article A. Ch. Lazanas, M. I. Prodromidis. Electrochemical Impedance Spectroscopy — A Tutorial. ACS Meas. Sci. Au 3, 162–193, 2023. doi:10.1021/acsmeasuresciau.2c00070 open access