The value and interpretation of dynamic electrochemical impedance spectroscopy (DEIS) during the charging and discharging of lithium-ion batteries is examined using the Doyle-Fuller-Newman pseudo-two-dimensional (P2D) lithium-ion battery model with parameters for a lithium-cobalt-oxide/graphite cell. Two computational approaches are explored to balance accuracy, speed, and interpretability: (i) A brute force time domain calculation of the full nonlinear equation set subject to direct current (DC) plus superimposed sinusoidal modulation of frequency ω 1, followed by post-processing with short-time Fourier transforms to track the dynamic impedance signal at the modulation frequency during charge and discharge; (ii) A fast-computing time-separated method that solves the C-rate dependent P2D equations for the DC charge/discharge transients occurring on the slow time-scales, t b ∼ O(3600 s/C), followed by solutions to linearized frequency domain equations derived for direct computation of the dynamic impedance signal. The time-separated method is rigorously correct in the limit 1/(t b ω 1) → 0. Key physics that drives differences between stationary and dynamic EIS signals is easily explored with the time-separated method. C-rate dependent studies show that DEIS signals are selectively sensitive to interfacial processes in ways that may be promising for real-time diagnostics and control of the negative electrode at high states-of-charge (SOC) and the positive electrode at low SOCs.

A survey of physical phenomena in the modeling literature and challenges for accelerating development of LiS batteries using continuum models.

Electrochemical impedance spectroscopy (EIS) is an established technique for monitoring and testing of electrochemical systems, including batteries. Parameters related to electrochemical phenomena such as charge-transfer kinetics and mass transport can be estimated from the impedance response over a range of frequencies1. The classical description for impedance of an electrochemical system, subjected to a periodic input perturbation, depends upon achieving a steady periodic output state2. However, there may be value in analyzing the joint time-frequency response of a dynamic impedance-like output signal under conditions that are not steady periodic3. For example, it has been shown that using a dynamic impedance-like response allows parameter estimation to be carried out in shorter times than waiting for a steady periodic state to be reached4. This may be particularly valuable for accessing low frequency (slow) phenomena such as thermodynamic and diffusion effects. As a result, dynamic impedance-like signals may be a valuable tool for real time diagnostics of battery degradation processes. The objective of this study is to develop time and frequency dependent solutions for existing battery models to further investigate the full dynamic response of the system. Devan et al. has performed transient voltage analysis for a porous electrode model5 and short-time current density response for an intercalation particle model4. A comparison to the steady periodic response for parameter estimation and the choice of optimum frequencies for measurements will be explored. While the analysis will begin with a simple physics-based model, the goal is to develop a fast and efficient tool for porous electrode 2D models. In particular, the focus will be on the gain in estimating parameters with specific confidence intervals, and mechanism validation from using the transient data compared to steady state models. References Yu, B. N. Popov, J. A. Ritter, and R. E. White, Journal of The Electrochemical Society, 146, 8 (1999). Ceder, M. Doyle, P. Arora, and Y. Fuentes, MRS Bulletin, 27, 619–623 (2002). Doyle and J. Newman, in Tutorials in Electrochemical Engineering—Mathematical Modeling, edited by R.F. Savinell, J.M. Fenton, A.C. West, S.L. Scanlon, and J. Weidner (The Electrochemical Society, Seattle, 1999) p. 144. Devan and R. E. White, Journal of The Electrochemical Society, 154(2007). Devan, V. R. Subramanian, and R. E. White, Journal of The Electrochemical Society, 152 (2005).

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Time domain physics-based models for lithium sulfur have been developed with mechanisms of the reaction cascade and precipitation reactions, allowing for a deeper understanding of internal states of the battery.1 Such models are able to capture voltage curves well during discharge. However, there have been challenges to reproduce charging curves accurately. It has been suggested that the charge and discharge reaction pathways are different,2 and/or precipitation rates and expressions to take into account numerical instability associated with dissolution when charging need to be improved.3,4 Since it is challenging for existing physics-based models to demonstrate macro-reversibility, we aim to see if there is evidence of micro-reversibility as impedance modeling would require these mechanistic models to work over much smaller changes in state-of-charge. Applying such models to the frequency domain can also give us detailed insight on proposed mechanisms and processes that occur across a larger range of timescales that are not available during a slow charge/discharge. Fronczek and Bessler5 have simulated electrochemical impedance spectroscopy (EIS) spectra based on mechanisms in the widely accepted one-dimensional model developed by Kumaresan et al..1 They are the first to demonstrate this with a physics-based modeling approach using a potential step in the time domain and performing FFT on the current relaxation to obtain the impedance. We aim to extend this further by comparing to experimental trends seen in the literature6,7 and explore qualitative features in the EIS spectra based on physical processes. We use a different computational approach by transforming the governing equations in the Kumaresan model to the frequency domain. We present this system of linearized ordinary differential equations and solve them in a manner consistent with numerical approaches demonstrated previously.8 Acknowledgement This work was supported by the Advanced Battery Material Research (BMR) Program (Battery 500 Consortium). References K. Kumaresan, Y. Mikhaylik, and R. E. White, J. Electrochem. Soc., 155, A576 (2008). Q. Wang et al., J. Electrochem. Soc., 162, A474–A478 (2015). K. Yoo, M.-K. Song, E. J. Cairns, and P. Dutta, Electrochimica Acta, 213, 174–185 (2016). N. Kamyab, P. T. Coman, S. K. Madi Reddy, S. Santhanagopalan, and R. E. White, J. Electrochem. Soc., 167, 130532 (2020). D. N. Fronczek and W. G. Bessler, Journal of Power Sources, 244, 183–188 (2013). S. Waluś, C. Barchasz, R. Bouchet, and F. Alloin, Electrochimica Acta, 359, 136944 (2020). Z. Deng et al., J. Electrochem. Soc., 160, A553–A558 (2013). M. Pathak et al., J. Electrochem. Soc., 165, A1324–A1337 (2018).