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Fuel Cell Electrode Kinetics: Butler-Volmer

About This Visualisation

This interactive tool shows how Butler-Volmer kinetics at the anode and cathode determine fuel cell performance. The key insight is the enormous asymmetry between the two electrode reactions:

  • Anode — Hydrogen Oxidation (HOR): H₂ → 2H⁺ + 2e⁻ at E₀ = 0.00 V vs SHE. Extremely fast on Pt (i₀ ~ 0.1 A/cm²)
  • Cathode — Oxygen Reduction (ORR): O₂ + 4H⁺ + 4e⁻ → 2H₂O at E₀ = 1.229 V vs SHE. Very sluggish, even on Pt (i₀ ~ 10⁻⁵ A/cm²)
  • Open Circuit Voltage: 1.229 − 0.00 = 1.229 V

Start with the Simple view to see where the voltage goes, then switch to the Kinetics view to see why. Try This: Select different catalyst materials for each electrode and increase the current — nearly all the kinetic loss comes from the cathode!

Anode Catalyst (HOR)
What is exchange current density?Exchange current density (i₀) is how fast the reaction already runs on that catalyst when nothing is pushing it. A big i₀ means the reaction is eager and needs only a small nudge; a tiny i₀ means you have to push hard, and that push is voltage you never get back.

Operating current 0.0 A/cm²

How hard you are working the cell. Drag it up and watch the voltage fall.

Cathode Catalyst (ORR)
What is exchange current density?Exchange current density (i₀) is how fast the reaction already runs on that catalyst when nothing is pushing it. Notice how much smaller every cathode value is than every anode value — that is the whole problem with oxygen reduction.

Nothing is being drawn from the cell yet, so no voltage is lost. Drag the current slider to make it deliver power.

Fuel Cell Operation

Idle — no current drawn, both electrodes at equilibrium.

Open circuit voltage
What is open circuit voltage?Open circuit voltage (OCV) is the voltage when you draw no current at all. It is the best this cell could ever do. The moment you ask it for current, you start paying some of that voltage away.
 1.229 V
Voltage lost 0.000 V

Where the Voltage Goes
What is overpotential?Overpotential (η) is the extra voltage you have to give up to make a reaction go at the rate you are asking for. A sluggish reaction needs a big push, so it costs more voltage. That voltage leaves as heat instead of reaching your circuit.

Anode η (HOR) 0.000 V
Cathode η (ORR) 0.000 V
Cathode share of the loss —

Cell Output

Cell voltage 1.229 V
Voltage efficiency 100%
Power density 0.0 W/cm²

Electrode Reactions

Anode (Oxidation)
H₂ → 2H⁺ + 2e⁻
Cathode (Reduction)
O₂ + 4H⁺ + 4e⁻ → 2H₂O

What You're Seeing

  • Simple view: The 1.229 V you start with, split into what is lost at each electrode and what the cell actually delivers
  • Anode curve (solid, blue): Positive current — rate of hydrogen oxidation. Steep curve = fast kinetics, small overpotential
  • Cathode curve (dashed, orange): Negative current — rate of oxygen reduction. Shallow curve = sluggish kinetics, large overpotential
  • Operating points (dots): Where each electrode operates at the chosen current density
  • Vertical dotted lines: Show how far each electrode deviates from E₀ — the overpotential
  • Thick line on the x-axis: Vcell = Ecathode − Eanode

Key Learning Points

  • The ORR is the bottleneck: Even on Pt, the cathode i₀ is ~10,000× smaller than the anode. Nearly all kinetic loss is at the cathode
  • Try switching cathode to Carbon: Watch the voltage collapse — this is why catalysts are essential for the ORR
  • The anode is almost "free": Even at high currents, the HOR overpotential on Pt is tiny
  • Exchange current density (i₀): The single most important parameter distinguishing fast from slow electrode reactions. It depends on both the reaction and the catalyst material
  • This model shows kinetic losses only. A real cell also loses voltage to electrolyte resistance and to reactant supply at high current