TY - JOUR

T1 - Learning optimal forms of constitutive relations characterizing ion intercalation from data in mathematical models of lithium-ion batteries

AU - Daniels, Lindsey

AU - Sahu, Smita

AU - Sanders, Kevin J.

AU - Goward, Gillian R.

AU - Foster, Jamie M.

AU - Protas, Bartosz

N1 - Appendices are supplementary information available at:
https://pubs.acs.org/doi/10.1021/acs.jpcc.3c02915

PY - 2023/9/7

Y1 - 2023/9/7

N2 - 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 least-squares 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 C-rates 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 Li-ion batteries as well as other systems relying on the Butler–Volmer relation.

AB - 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 least-squares 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 C-rates 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 Li-ion batteries as well as other systems relying on the Butler–Volmer relation.

U2 - 10.1021/acs.jpcc.3c02915

DO - 10.1021/acs.jpcc.3c02915

M3 - Article

SN - 1932-7447

VL - 127

SP - 17508

EP - 17523

JO - The Journal of Physical Chemistry C

JF - The Journal of Physical Chemistry C

IS - 35

M1 - 35

ER -