Battery knowledge · Aging and degradation
Square-root-of-time law
The observation that SEI-driven capacity loss in storage grows roughly with the square root of time, because the growing film slows its own growth. A cell that lost 4 % in its first year will lose about 1.7 % more in the second. [1]
- Relationship
- Q_loss ∝ √t
Example
Compare equal time intervals
If an illustrative diffusion-limited loss is 1% after 100 h and follows only a square-root law, it is 2% after 400 h. Reaching twice the modeled loss takes four times the elapsed time.
Explore the graph
Four times the elapsed time gives twice the film thickness in this model.
At four reference time units, thickness is 2× the reference thickness.
δ / δ_ref = √[(t / t_ref) A]
Illustrative model. Normalized analytical relation, not a capacity-loss or SOH prediction.
Use in Lemonergy
Lemonergy Core equation
Explore film growth
Lemonergy Core evaluates this relation.
Equation or tool to use
- parabolic_film_thickness
Core equation
Inputs & settings
- Reference thickness
- Elapsed and reference time
- Acceleration factor
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 a factor of one, 10 nm at 1 h becomes 20 nm at 4 h and 30 nm at 9 h.
Observe. Compare the result with the equation and units.
This does not identify SEI chemistry or fit state of health.
Open the worked lesson →References & further reading
Technical references
- Lithium ion battery degradation: what you need to know
Physical Chemistry Chemical Physics · 2021
Technical reference · Degradation mechanisms, modes, operational effects and their interactions.