Modeling the Voltage Response of Lithium Symmetric Cells
Authors: Chen Jerry , Subramaniam Akshay , Geise Natalie R , Kasse Robert M , Toney Michael F , Subramanian Venkat R. 
Published: February 2020

The use of Lithium metal as anode material has been regarded as the "Holy Grail" for Lithium batteries. It has a higher theoretical specific capacity (3860 mAh∙g-1) compared to the graphite (372 mAh∙g-1) used in conventional lithium-ion batteries and one of the lowest electrochemical potentials (−3.04 V vs. standard hydrogen electrode).1 However, its commercialization is greatly hampered by the poor electrodeposition of lithium, characterized by the formation of "dead lithium" and dendrites, which cause low coulombic efficiency, reduced cycle life and possible internal short circuits during operation.
Useful insight into lithium electrodeposition dynamics and morphology can be obtained by taking advantage of the simplicity of Li/Li symmetric cells. Electrochemical models can help elucidate these trends in terms of thermodynamics, electrode reactions, and transport phenomena. Models can also help study parametric variations and different operating conditions, giving further information into different electrodeposition regimes and limiting conditions. From a systems perspective, the access to internal state variables (e.g. concentration) can also help capture the complex voltage and current responses that have been observed during Li metal electrodeposition.2,3

These considerations form the motivation for the mathematical model used in this work. The model will include the governing equations for electrolyte transport, ionic current, and electrode reactions. Transport equations are based on the concentrated solution theory.4,5 A modified Ohm’s law for the liquid electrolyte phase is considered and the Butler-Volmer (BV) equation is used for lithium metal deposition and stripping at the electrode. Bulk electrolyte transport is described by Fick’s law. This basic electrochemical model is then extended by modifying the Butler-Volmer equation to incorporate dendrite growth as a parallel electrodeposition pathway on the lines of existing literature.2,6,7 A model for SEI growth will also be incorporated.8 Electrode kinetics equations will be modified to account for external pressure and local stress effects, yielding an integrated model that combines transport and electrode reaction models with SEI growth, external pressure, mechanical effects and heterogeneous plating dynamics.9,10

Efficient simulation techniques will be applied to simulate the model for different parametric combinations and experimentally relevant conditions of galvanostatic cycling. The model will be validated against experimental data in terms of the prediction of electrodeposition trends and cell voltage.

References

J. Qian, W. A. Henderson, W. Xu, P. Bhattacharya, M. Engelhard, O. Borodin and J.-G. Zhang, Nature communications, 6 (2015).

K. N. Wood, E. Kazyak, A.F. Chadwick, K-H. Chen, J-G. Zhang, K. Thornton, and N.P. Dasgupta, ACS Cent. Sci.,
2, 790-801 (2016).

P. Bai, J. Li, F.R. Brushett, and M.Z. Bazant, Energy Environ. Sci., 9, 3221-3229 (2016).

M. Doyle, T. F. Fuller, and J. Newman, J. Electrochem. Soc., 140, 1526–1533 (1993).

S-L. Wu, A.E. Javier, D. Devaux, N.P. Balsara, and V. Srinivasan, Electrochem. Soc., 161, A1836–A1843 (2004).

R. Akolkar, J. Power Sources, 232, 23-28 (2013).

C. Monroe and J. Newman, J. Electrochem. Soc., 150, A1377–A1384 (2003).

M. B. Pinson and M.Z. Bazant, J. Electrochem. Soc.,
160, A243-A250 (2013).

C. Monroe and J. Newman, J. Electrochem. Soc., 151, A880–A886 (2004).

X. Zhang, W. Shyy, and A. M. Sastry, J. Electrochem. Soc., 154, A910–A916 (2007).