Solid state electrolytes are becomingly increasingly attractive due to their improved safety, lower self-discharge, and higher power densities over the more commonly used liquid electrolyte [1,2]. Solid electrolytes are a relatively new material in the field of lithium-ion batteries, therefore there is considerably less mathematical investigation and analysis into these materials, compared with their liquid counterparts.

We review a model for a solid electrolyte from thermodynamics principles [3]. We non-dimensionalise and scale the model to identify small parameters, where we identify a scaling that widens the boundary layer in the electrolyte compared to previous literature. We consider an Li2O solid electrolyte which is attached on each end by blocks of solid lithium. We fix a potential difference across the electrolyte and consider different charge flux conditions. We present asymptotic analysis and numerical solutions for both the zero-charge flux equilibrium and for the non-zero charge flux equilibrium problems. We consider numerical simulations of the full-time dependent problem and show that there are two important time scales in the problem, an early transient timescale where the boundary layers first approach their equilibrium followed by a longer timescale where we observe the transience in the bulk of the solution.

We briefly talk about the application of a solid electrolyte to cylindrical nanowire electrodes. Recent advances in electrode chemistry have allowed for cylindrical nanowire geometries exhibiting low-capacity fade. However, the performance of these electrodes is very sensitive to experimental conditions and early charge behavior and thus it is important to understand the lithium transport process in these systems. Following from this work, we will combine the solid electrolyte model with a nanowire electrode in order to investigate these processes.

References

[1] A. Manthiram, X. Yu, Xingwen, and S. Wang. Lithium battery chemistries enabled by solid-state electrolytes, Nature Reviews Materials, Nature Publishing Group, 2(4), 1-16, 2017.

[2] Z. Chen, G. Kim, Z. Wang, D. Bresser, B. Qin, D. Geiger, U. Kaiser, X. Wang, Z.X. Shen, and S. Passerini.
4-V flexible all-solid-state lithium polymer batteries, Nano Energy, Elsevier, 64, 103986, 2019.

[3] S. Braun, C. Yada, and A. Latz. Thermodynamically consistent model for space-charge-layer formation in a solid electrolyte, The Journal of Physical Chemistry C, 119(39), 22281-22288, 2015.