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Temperature Effects on Battery Charging: Butler-Volmer Kinetics

About This Model

A battery has a voltage written on the side — 1.2 V for the NiCd cell used here. To push charge back into it, a charger must supply more than that. This model shows how much more, and why the answer depends on temperature.

  • Pick a temperature and a charging current, and read off the voltage the charger must supply
  • See that voltage split into its parts: the cell's own voltage, the extra push each electrode needs, and the loss in the cell's internal resistance
  • Watch the voltage climb as the cell fills up (right graph)
  • Open the kinetics view to see where those extra pushes come from (Butler-Volmer curves)

The idea in one line: a cold electrode reacts more sluggishly, so it needs a bigger extra push — an overpotential — to carry the same current. Both electrodes need one, and the charger pays for both.

Electrode Reactions and Kinetic Parameters:

Negative electrode (cathodic/reduction during charging): Cd(OH)₂ + 2e⁻ → Cd + 2OH⁻

Exchange current density (i₀) at 25°C: 0.01 A/cm² — i₀ measures how briskly a reaction runs when nothing is pushing it. A bigger i₀ means a smaller push is needed.

Positive electrode (anodic/oxidation during charging): Ni(OH)₂ + OH⁻ → NiOOH + H₂O + e⁻

Exchange current density (i₀) at 25°C: 0.001 A/cm² — ten times smaller, which is why this electrode needs the larger push.

These i₀ values are used in the Butler-Volmer equation to calculate overpotentials. Temperature dependence follows Arrhenius relationship.

Charging a 1.2 V NiCd cell

Move a slider to see the voltage this cell needs.

Charging Parameters

20 °C
700 mA
What the words mean
Overpotential (η)
The extra voltage, beyond the cell's own voltage, needed to make a reaction run at the rate you want. Bigger current or colder electrode means bigger η.
Exchange current density (i₀)
How briskly the reaction ticks over when there is no net push. A sluggish reaction has a small i₀ and needs a large η.
iR drop
Voltage lost inside the cell simply because current has to flow through it, like a voltage drop in a wire.
Anodic and cathodic
Anodic means oxidation (electrons leaving the electrode) and is drawn as positive current. Cathodic means reduction and is drawn as negative current.
Butler-Volmer equation
The equation linking current to overpotential at an electrode. Its curve is steep for a fast reaction and flat for a sluggish one.

What the charger must supply

At the start of charge, for a 1.2 V NiCd cell

—

Temperature: 20 °C
Charging current: 700 mA
Charge time: --- h
Voltage at start: --- V
Voltage at full charge: --- V
Positive η (start): --- mV
Negative η (start): --- mV

Why the curve rises: as the cell fills, concentration changes at the electrode surfaces make both overpotentials grow, so the voltage needed climbs throughout the charge. This model uses a simplified treatment of that effect and does not include gas evolution or phase transitions.

Understanding the Butler-Volmer Plot

The kinetics graph shows how each electrode's overpotential (η) relates to current through the Butler-Volmer equation. By electrochemical convention, anodic (oxidation) currents are positive, while cathodic (reduction) currents are negative. The curves are "mirror images" across the origin: the positive electrode shows that positive overpotentials drive positive (anodic) currents for oxidation, while the negative electrode shows that negative overpotentials drive negative (cathodic) currents for reduction.

The horizontal tie line joins the two operating points, so its length is the total overpotential — the sum of the pushes at the two electrodes. Cooling the cell flattens both curves, so the operating points slide outwards and the tie line gets longer.

Why the charge time does not change with temperature

This model holds the charging current fixed, so the same charge goes in per hour whatever the temperature, and the charge time only depends on the current you choose. What temperature changes is the voltage the charger must supply to keep that current flowing. A real charger has a voltage ceiling, so in the cold it would fail to reach the set current and the cell really would charge more slowly.