Learning the Material Physics of Graphite Electrodes through Image Inversion
Authors: Degnan-Morgenstern Samuel , Gopal Rajeev , Bai Peng , Bazant Martin Z. 
Published: December 2024

Graphite is the predominant commercial anode chemistry due to its high capacity, affordability, reversible intercalation reactions, and low lithiation potential [1]. Despite its prevalence, the fundamental material physics in graphite remain poorly understood due to the complex interplay of the layered thermodynamics, lithium-ion transport, and reaction kinetics, which introduce many interacting timescales during a dynamic (dis)charge process. Agrawal and Bai employed operando optical microscopy to visualize the dynamic phase transformations and many particle effects out of equilibrium [2]. Their study highlighted the challenges in experimental estimation of kinetic and transport properties for systems of many phase separating particles such as graphite. The lack of quantitative assessment underscores a need for model-based approaches to improve our theoretical understanding of operational limitations. Recent success in the work of Zhao et al. demonstrates the potential to infer physically-interpretable dynamical electrochemical models directly from experimental imaging data [3]. By employing these techniques, we develop a framework to quantitatively characterize the operando optical microscopy data stream by combining approaches in image processing, physics-based modeling, and scientific machine learning (ML).
In this study, we create a software pipeline to (1) quantitatively process colorimetric optical microscopy movies of graphite electrodes, (2) model the reactive population dynamics of a many-particle graphite system using a high-performance numerical scheme, and (3) solve an inverse problem to extract the kinetic and thermodynamic behavior from the optical microscopy dataset. Image data provides a rich dataset on the heterogeneous spatiotemporal dynamics of electrochemical systems that can be harnessed with proper data processing techniques. To achieve this goal, we develop an open-source platform for ML-assisted particle segmentation, size estimation, and local state of charge quantification to prepare this data for model-based assessment. To model this system, we employ a Fokker-Planck equation to describe the distribution of concentration and size dependence in an ensemble of many reacting graphite particles [4]. Finally, we employ image inversion to extract the nonlinear exchange current density and free energy landscape through physically-constrained ML. The estimation of these constitutive relationships offers unique insights into the limiting behavior of graphite by refining our understanding of the underlying asymmetrical phase transformations caused by autocatalysis and the breakdown of driven thermodynamic stability. Successful quantitative characterization of the material properties in graphite will lay the groundwork for future model-based design and optimization of particulate intercalation electrodes. Our approach establishes a novel open-source pipeline for future ML-based characterization of lithium intercalation materials from economical operando optical microscopy experiments that can be readily applied to new electrochemical systems.
References
[1] B. Scrosati and J. Garche. Lithium batteries: Status, prospects and future. Journal of Power Sources, 195(9):2419–2430, 2010.
[2] S. Agrawal and P. Bai. Dynamic interplay between phase transformation instabilities and reaction heterogeneities in particulate intercalation electrodes. Cell Reports Physical Science, 3(5):100854, May 2022.
[3] H. Zhao, H. Dean Deng, A. E. Cohen, J. Lim, Y. Li, D. Fraggedakis, B. Jiang, B. D. Storey, W. C. Chueh, R. D. Braatz, and M. Z. Bazant. Learning heterogeneous reaction kinetics from X-ray videos pixel by pixel. Nature, 621(7978):289–294, September 2023.
[4] H. Zhao and M. Z. Bazant. Population dynamics of driven autocatalytic reactive mixtures. Physical Review E, 100(1):012144, July 2019.