Chronoamperometry: Diffusion-Limited Current Decay

Potential Step

Cell Parameters

Bulk concentration C₀ 2.0 mM

Diffusion coefficient D 1.0 ×10⁻⁵ cm²/s

Electrode area A 0.10 cm²

Live Readouts

Current I(t) — Cottrell decay

Current I(t)0.0 µA

Diffusion layer δ(t)0 µm

Charge passed Q(t)0.0 µC

Elapsed time0.00 s

How it works

Chronoamperometry is an analytical electrochemistry technique: the electrode potential is stepped instantly to a value where an analyte is oxidized or reduced the moment it touches the surface, and the resulting current is recorded versus time. Because the reaction is instantaneous, the current is limited entirely by how fast fresh analyte can diffuse in from the bulk solution — this is Fick's second law with an absorbing boundary at the electrode.

Cottrell equation:
I(t) = n F A C₀ √(D / (π t))

Diffusion layer thickness:
δ(t) ≈ √(π D t)

Charge passed (Cottrell–Anson):
Q(t) = 2 n F A C₀ √(D t / π)

n — electrons transferred per molecule (fixed at 1 here), F — Faraday constant (96 485 C/mol), A — electrode area, C₀ — bulk concentration, D — diffusion coefficient.
Apply Potential Step — turns on the surface reaction: every ion that reaches the electrode is instantly consumed and a particle-free "depletion zone" opens up and grows as √t, exactly matching δ(t) above.
The current falls as 1/√t because the depletion zone keeps getting thicker, so each fresh ion has farther to diffuse to reach the surface — this is why the graph curve drops steeply at first and flattens later.
Real-world relevance: this is the working principle behind amperometric biosensors (e.g. the glucose sensor in a glucometer) and is used to measure diffusion coefficients and electrode surface area in analytical labs.

Analyte ions Electrode surface

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