Battery knowledge · Aging and degradation
Arrhenius law
The rule that a rate constant is proportional to exp(−Ea/RT), so a thermally activated reaction speeds up steeply with temperature. Near room temperature many degradation reactions roughly double their rate for every +10 °C. [1]
- Relationship
- k = A·exp(−Eₐ/RT)
Example
Compare reaction-rate factors
For an illustrative activation energy of 40 kJ/mol, increasing temperature from 25 °C to 35 °C multiplies the modeled rate by about 1.69. Convert both temperatures to kelvin before evaluating the exponential.
Interpretation & limits
- A reaction-rate factor alone is not a prediction of battery lifetime.
Explore the graph
Compare an activated process with its rate at 25 °C.
At 25 °C: 1×. At 35 °C: 1.924×. At 45 °C: 3.554×.
k(T)/k(T_ref) = exp[(Eₐ/R)(1/T_ref − 1/T)]
Illustrative model. The equation uses kelvin. One activated process is represented, not lifetime.
Use in Lemonergy
Lemonergy Core equation
Compare reaction rates
Lemonergy Core evaluates this relation.
Equation or tool to use
- arrhenius_factor
Core equation
Inputs & settings
- Temperature (°C)
- Reference temperature (°C)
- Activation energy (J/mol)
This overview identifies the components to use. Follow the example in Lemonergy for their connections and settings.
- Open the lesson and inspect the equation.
- Change one input while holding the others fixed.
Example. At an illustrative 50 kJ/mol activation energy, raising temperature from 25 °C to 35 °C gives a rate factor about 1.92.
Observe. Compare the result with the equation and units.
This factor alone does not predict lifetime or capacity loss.
Open the worked lesson →References & further reading
Technical references
- Arrhenius equation
IUPAC Gold Book · 2025
Technical reference · Temperature dependence of reaction-rate constants and the assumptions about activation energy.
Further reading on this topic
These sources provide broader context; they are not presented as citations for every statement in this entry.
- Lithium ion battery degradation: what you need to know
Physical Chemistry Chemical Physics · 2021
Topic background · Degradation mechanisms, modes, operational effects and their interactions.