(Keynote) Battery Archeology: Using Physics-Based Models to Unearth (Quantitative) Battery Aging Artifacts
Authors: Schwartz Daniel T. 
Published: September 2023

A key question any battery modeler must grapple with is how much physics to include in a physics-based model. An ideal approach was articulated by Albert Einstein as “everything should be made as simple as possible, but not simpler.” Yet, a quick review of the electrochemical literature suggests an alternative is to embrace the Grateful Dead lyric, “too much of everything is just enough.” Finding the right balance between model complexity and experimental complexity is critical for rigorous model-data convergence, and remains an on-going challenge for nearly every battery chemistry.[1]
The publications of honoree Ralph White often resolve this dilemma by incorporating impressively comprehensive physics in a model, along with equally impressive mathematical analysis, so a careful reader can determine, for themselves, what physics matters for the situation they care about. An elegant example of this is the analytical solution for the electrochemical impedance spectroscopy (EIS) response of the pseudo-two-dimensional (P2D) model of a porous insertion electrode [2]. Numerical solutions of the P2D model for linear or nonlinear EIS of a battery, as we have shown,[3-5] allows one to capture the behavior of an experimental battery system, but parameter identification challenges do not always allow rigorous validation of the essential physics. Analytical models such as given in [2] can help sort out what parameters, or clustering of parameters, matter.
In this talk we tackle the question of model-data convergence, where the goal is modeling that meets Einstein’s ideal so that quantitative physics-based insights can be extracted and interpreted from experimental data. Just as with modeling, experimental measurements should embrace Einstein’s notion of being simple, but not too simple, if we hope to extract meaningful parameters from real batteries. A key experimental concept introduced in this talk is measurement signal parity in full-cell datasets. We show that a single physics-based model simultaneously fit to two datasets (of opposite signal parity) can help discern half-cell processes from full-cell data. We illustrate this, first, using slow cycling data from commercial NMC|C 18650 cells to non-destructively estimate half-cell thermodynamic parameters from the commercial cells as they cycle and age. The cornerstone of our thermodynamic modeling is adaptation of half-cell methods developed at General Motors,[6] but implemented here for full-cell analysis.[7] We also look at second harmonic nonlinear EIS as a negative parity complement to linear EIS (positive parity) data, but we step back from our prior use of computed P2D models;[3, 5] for our current state of knowledge, P2D models may be closer to the Grateful Dead end of second harmonic EIS battery modeling than Einstein’s ideal. To better align our understanding and ability to extract meaningful parameters, we attempt to thoughtfully build up the physics of nonlinear EIS from a basic physical chemistry description of the electrified interface – a Helmholz double layer and Butler-Volmer charge transfer kinetics – while progressively adding solid state transport and electrode geometry to increasingly capture more of the variance of linear (positive parity) and second harmonic nonlinear (negative parity) EIS experimental data without over-fitting. In both the thermo and EIS examples, one appropriate physics-based model is simultaneously fit to two datasets of opposite parity. Working with battery aging data, we show how this approach for aligning modeling physics to complementary datasets of opposite parity can be used to quantify half-cell physicochemical processes that evolve with cycle aging of an engineered commercial full-cell.
[1] M. Cornish and M. Marinescu, Toward rigorous validation of Li-S Battery Models, J.E.S.
169 060531 (2022)
[2] G. Sikha and R. White, Analytical expression for the impedance response of an insertion electrode cell, J.E.S.
154(1) A43 (2007).
[3] M.D. Murbach and D.T. Schwartz, Extending Newman’s P2D lithium-ion battery impedance approach to include the nonlinear harmonic response, J.E.S.
164(11) E3311 (2017).
[4] M.D. Murbach and D.T. Schwartz, Analysis of Li-ion battery electrochemical impedance spectroscopy data: an easy-to-implement approach for physics-based parameter estimation using an open-source tool, J.E.S.
165(2) A297 (2018).
[5] M.D. Murbach, V.W. Hu, and D.T. Schwartz, Nonlinear electrochemical impedance spectroscopy of lithium-ion batteries: experimental approach, analysis, and initial finding, J.E.S.
165(11) A2758 (2018).
[6] M. Verbrugge, D. Baker, B. Koch, X-C Xiao, and W-T. Gu, Thermodynamic model for substitutional materials: Application to lithiated graphite, spinel MnO, LFP, NMC, J.E.S.
164(11) E3243 (2017).
[7] V.W. Hu and D.T. Schwartz, Low error estimation of half-cell thermodynamic parameters from whole-cell li-ion battery experiments: Physics-based model formulation, experimental demonstration, and an open software tool, J.E.S.
169(3) 030539 (2022).