GALVANOSTATIC CYCLING

Constant current, watch the voltage

constant I → watch V

Push a fixed current in until the voltage hits its upper limit, then pull the same current out until it falls to the lower limit, and repeat. It's the closest test to how a real device gets used, and the usual source of capacitance, resistance, energy, and cycle life.

GCD is the workhorse test for device performance.

THE TRIANGLE

Capacitance from the slope

C = I · Δt / ΔV

At constant current an ideal capacitor's voltage ramps in a straight line, so the charge–discharge curve is a symmetric triangle. On discharge, C = I·Δt/ΔV, where Δt is the discharge time and ΔV the voltage change during it, leaving out the initial drop.

A straight, symmetric line means capacitive. A bent or plateaued line means redox is at work.

READING A GCD CURVE

What the curve's features mean

Straight, symmetric triangle Ideal double-layer behavior

Sudden drop as discharge begins IR drop from series resistance: ESR ≈ ΔV_drop / (2I)

Curved or plateau sections Pseudocapacitive or battery-like reactions

Discharge shorter than charge Charge is being lost, so coulombic efficiency is below 100%

The drop's size, divided by twice the current, gives the resistance directly.

COULOMBIC EFFICIENCY

Does the charge come back?

η = t_dis / t_charge

At constant current, charge is proportional to time, so discharge time divided by charge time is the coulombic efficiency. Near 100% means almost all stored charge is recovered. Well below means side reactions or leakage are eating charge.

A clean triangle and near-100% efficiency signal a healthy device.

UNIT 27 STUDY COMPLETE

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Ready for the Fab Challenge?

You've covered constant-current cycling: capacitance, IR drop, and coulombic efficiency.