Abstract
Most mathematical models of the transport of charged species in battery electrodes require a constitutive relation describing the intercalation of lithium, which is a reversible process taking place on the interface between the electrolyte and the active particle. The most commonly used model is the Butler–Volmer relation, which gives the current density as a product of two expressions: one expression, the exchange current, depends on lithium concentration only, whereas the other expression depends on both lithium concentration and overpotential. We consider an inverse problem where an optimal form of the exchange current density is inferred, subject to minimum assumptions, from experimental voltage curves. This inverse problem is recast as an optimization problem in which the leastsquares error functional is minimized with a suitable Sobolev gradient approach. The proposed method is thoroughly validated, and we also quantify the reconstruction uncertainty. Finally, we identify the universal features in the constitutive relations inferred from the data obtained during charging and discharging at different Crates and discuss how these features differ from the behavior predicted by the standard Butler–Volmer relation. We also identify possible limitations of the proposed approach, mostly related to uncertainties inherent in the material properties assumed to be known in the inverse problem. Our approach can be used to systematically improve the accuracy of mathematical models employed to describe Liion batteries as well as other systems relying on the Butler–Volmer relation.
Original language  English 

Article number  35 
Pages (fromto)  17508–17523 
Number of pages  16 
Journal  The Journal of Physical Chemistry C 
Volume  127 
Issue number  35 
Early online date  25 Aug 2023 
DOIs  
Publication status  Published  7 Sept 2023 
Datasets

Learning optimal forms of constitutive relations characterizing ion intercalation from data in mathematical models of lithiumion batteries
Daniel, L. (Creator), Sahu, S. (Creator), Sanders, K. J. (Creator), Goward, G. R. (Creator), Foster, J. (Creator) & Protas, B. (Creator), The Journal of Physical Chemistry C, 30 Sept 0007
DOI: 10.1021/acs.jpcc.3c02915, https://pubs.acs.org/doi/10.1021/acs.jpcc.3c02915?goto=supportinginfo
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