# One law to rule them all: Stretched exponential master curve of capacity fade for Li-ion batteries

## TL;DR

This paper demonstrates that the capacity fade of various Li-ion batteries under different conditions follows a universal stretched exponential master curve, enabling simplified and accurate lifetime predictions.

## Contribution

It introduces a universal capacity fade model based on a stretched exponential curve, applicable across multiple cell types and conditions, supported by a diffusion-to-traps theoretical framework.

## Key findings

- Capacity loss follows a universal master curve.
- The model applies across different cell chemistries and aging conditions.
- The framework enables accurate lifetime predictions.

## Abstract

Li-ion batteries gradually lose their capacity with time and use; therefore, ageing forecasts are key to designs of battery powered systems. So far, cell-type-specific studies without standardised testing practices have lead to a variety of ageing models in which generality, simplicity, and accuracy seem exclusive. Previous studies hint to an interplay of multiple mechanisms leading to capacity loss, which depend on cell chemistry and are affected by temperature, state of charge, and cycling rate. Here we show that, despite this complexity, the time dependence of the actual capacity follows a unique master curve, for several cell types aged under various different conditions. We discuss the statistical origin of this common behaviour, and the testing practice required for the characterisation of a model. The master curve is a stretched exponential that describes many other phenomena in nature and is theoretically justified within a diffusion-to-traps depletion model. These findings provide a simple and broadly applicable framework for accurate life-time predictions.