Revisiting the t^0.5 Dependence of SEI Growth

SEI growth in lithium-ion batteries is commonly assumed to scale with t^0.5, in line with simple models of diffusion-limited surface layer growth. As a result, this model is widely used for empirical predictions of capacity fade in lithium-ion batteries. However, the t^0.5 model is generally not theoretically sufficient to describe all of the various SEI growth modes. Furthermore, previous literature has not convincingly demonstrated that this model provides the best fit to measurements of SEI growth. In this work, we discuss the theoretical assumptions of the t^0.5 model, evaluate claims of t^0.5 dependence in six previously published datasets and one new dataset, and compare the performance of this model to that of other models. We find that few of the purported t^0.5 fits in literature are statistically justified, although t^0.5 generally describes SEI growth during storage better than SEI growth during cycling. Finally, we evaluate how the fitted exponents in the power-law models vary as a function of time, and we illustrate the limitations of using t^0.5 for prediction without validating its applicability to a particular dataset. This work illustrates the theoretical and empirical limitations of the t^0.5 model and highlights alternatives for more accurate estimates and predictions of SEI growth.