This interactive tool shows how Butler-Volmer kinetics at two electrodes determine battery performance. The Battery Operation and Electrode Reactions panels (above the graph) are key - they translate the abstract curves into real battery behavior. Watch how the voltage changes as you adjust current and kinetics!
New to this? Start with the Quick setups buttons and read the sentence above the graph each time. The shaded band on the graph is the battery's voltage: watch it narrow as you draw more current, and widen when you charge.
Nickel-Metal Hydride (NiMH) Battery Example:
Positive Electrode: Ni(OH)₂/NiOOH at E₀ = +0.49 V (typically i₀ ~ 10 mA/cm²)
Negative Electrode: Metal Hydride (MH) at E₀ = -0.83 V (typically i₀ ~ 1 mA/cm², often rate-limiting)
Open Circuit Voltage: 0.49 - (-0.83) = 1.32 V (when no current flows)
The two electrodes are called positive and negative here rather than anode and cathode, because anode and cathode swap places between charging and discharging. Positive and negative do not.
Try This: Start with default values and increase the current slider. Watch the Battery Operation panel show voltage dropping (discharge) or rising (charge). The Electrode Reactions panel shows which reactions occur at each electrode!
Key Concept: As current flows, each electrode moves away from its equilibrium potential. The cell voltage is always the difference between the two electrode potentials. Better kinetics (higher exchange current density) means smaller deviations!
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Drawing 10.0 mA/cm² pulls the positive electrode down 0.044 V and pushes the negative electrode up 0.135 V, so the battery delivers 1.14 V instead of 1.32 V. Most of that 0.179 V loss is at the negative electrode, so it is the bottleneck.
Controls
050 mA/cm²
none → trickle → normal → fast
SlowFast
how readily this electrode reacts
SlowFast
how readily this electrode reacts
Cell Voltage1.14 V
Current Density10.0 mA/cm²
Power Density11.4 mW/cm²delivered by the cell
What You're Seeing
Shaded band: The gap between the two electrode potentials. Its width is the cell voltage - what the battery delivers on discharge, or what you must supply to charge it
Above and below the zero line: Current above the line is oxidation (the electrode gives up electrons); below the line is reduction (the electrode takes electrons in). This is why one operating point sits above the line and the other below
Battery Operation Panel (above graph): Shows current battery state - voltage delivered (discharge), voltage required (charge), or open circuit voltage (idle)
Electrode Reactions Panel (above graph): Shows which reactions occur at each electrode based on charge/discharge mode
Two Butler-Volmer curves: Each electrode has its own curve showing current vs. potential relationship — the positive electrode is red and the negative electrode is blue. In high contrast both curves are white, so the positive electrode is drawn as a solid line with round operating points and the negative electrode as a dashed line with square operating points.
Operating points (dots): Show where each electrode operates at the chosen current density
Vertical dotted lines: Drop from operating points to x-axis, showing actual electrode potentials (E+ and E−)
Key Learning Points
Discharge: As current increases, battery voltage drops below OCV (1.32 V) due to kinetic losses
Charge: As current increases, required voltage rises above OCV to overcome kinetic barriers
Slow kinetics = bigger losses: The electrode with slower kinetics (lower i₀) deviates more from its E₀
Watch the panels update: They show exactly how Butler-Volmer kinetics translate to real battery performance!
Rate-limiting electrode: In NiMH, the negative electrode (MH) typically has slower kinetics and limits performance
A Sense of Scale
Current density is current spread over electrode area. A cell with roughly 100 cm² of electrode running at 10 mA/cm² draws about 1 A - similar to charging a phone. At 50 mA/cm² the same cell is pulling around 5 A, which is a hard, fast discharge.