Galvanostatic Charge–Discharge (GCD) — run, calculate, report

GCD cycles the cell at constant current between two voltage cut-offs and records the voltage. It is the workhorse test: it gives capacity, Coulombic efficiency, the voltage profile (and thus energy and average voltage), cycle life / retention, and rate capability — and, for capacitors, capacitance and ESR.

This pairs with the Battery reporting checklist (same section): GCD is where most of those numbers come from, so report loading, area, current basis, and cell count alongside them.

What GCD gives you

How to run it — choosing parameters

• Current — state it as a C-rate and a current density (mA cm⁻² or mA g⁻¹), and define 1C (which capacity it is based on).
• Voltage window — the cut-offs; inside the safe range for the chemistry.
• CC vs CC–CV — say whether you hold at the top (constant-voltage step) and give the CV cut-off current; a CC–CV charge adds capacity that a CC-only discharge will not return (affects CE).
• Formation cycles — run a few and report a steady cycle, not the first.
• Rest / relaxation between charge and discharge, if any.
• Temperature (and whether controlled); number of cycles; cell format and mass loading.

Calculations

Capacity, efficiency, energy

Specific capacity   q   = I·Δt / (3.6·m)              [mAh/g]   (I in A, Δt in s, m in g)
Areal capacity      q_A = I·Δt / (3600·A)             [mAh/cm²]
Coulombic eff.      CE  = Q_dis / Q_ch  = Δt_dis/Δt_ch  (constant I)   [%]
Specific energy     E   = I·∫V dt / (3.6·m)           [mWh/g]
Average voltage     V̄   = E / q
Capacity retention  = Q_N / Q_1 × 100 %

Supercapacitors (triangular profile)

Capacitance (discharge slope)   C = I / |dV/dt|        → C_specific = C/m   [F/g]
   (fit dV/dt on the linear 10–90 % of the discharge, EXCLUDING the IR drop)
ESR (from the IR drop at reversal)  ESR = ΔV_IR / (2·I)   [Ω]
Energy  E = ½ C ΔV²        Power  P = E / Δt_dis

Use the discharge branch and a two-electrode cell for device-relevant capacitor numbers.

Running several cycles

• Report which cycle the capacity/CE come from — a steady cycle, not formation.
• Plot capacity vs cycle and CE vs cycle; show voltage profiles at selected cycles (e.g. 1st, 10th, Nth) to reveal how the shape changes.
• Do not point-by-point average voltage profiles across cycles or cells — it smears plateaus. Show a representative profile.

Running several samples

• Fix the current basis, window, protocol, temperature, and mass basis.
• Normalise (per g or per cm²) before comparing.
• Report capacity, CE, retention as mean ± SD with n (≥ 3 cells where feasible); overlay capacity-vs-cycle for all cells (thin) with the mean bold.
• Account for every cell (measured vs included, and why any were excluded).

Presentation

• Voltage vs specific capacity for the profile; capacitors usually voltage vs time (triangles).
• Capacity & CE vs cycle number (twin axes) — with the multi-cell treatment above.
• Rate capability: capacity vs C-rate (and note recovery when the rate returns to low).
• Caption: current / C-rate, window, cycle number, temperature, mass loading, cell type.

Caveats

• CE needs enough significant figures (99.92 %, not “~100 %”); tiny CE losses compound over hundreds of cycles.
• Specific capacity basis must be explicit (per active material vs per electrode/cell).
• Ultra-low loading inflates apparent rate and cycling — report a practical areal capacity.
• CC–CV on charge but CC-only discharge lowers CE for reasons that are protocol, not material.
• Capacitance from GCD ≠ from CV in general; state the method. Exclude the IR drop when fitting.

References to read (start with 1–2)

1. M. D. Stoller & R. S. Ruoff, “Best practical methods for making the most reliable measurements on supercapacitors,” Energy Environ. Sci. 3, 1294 (2010). The standard for capacitor GCD.
2. The lab’s Battery reporting checklist (same Resources section) — what to disclose with any GCD result.
3. A. J. Bard & L. R. Faulkner, Electrochemical Methods, Wiley — fundamentals behind constant- current techniques.
4. BioLogic Application Note 51 — DC (galvanostatic) characterisation of supercapacitors: capacity, energy, ESR, CE.
5. For batteries specifically: the reporting guidelines of Joule, ACS Energy Letters, and Nature Energy cited in the battery checklist.

Script: gcd.py (in the Resources downloads) computes specific capacity, CE, energy, retention, and the supercapacitor C/ESR, and plots the voltage profile + capacity/CE-vs-cycle. Run python gcd.py.