Theory and Simulation of Space Charge Layers in All Solid State Batteries

Due to their good expected safety properties, Li batteries based on solid electrolytes provide an attractive alternative to conventional liquid systems. However, a number of obstacles have yet to be overcome for all-solid-state batteries to be competitive on the market.  One of the most severe problems in Lithium all solid state batteries is the as yet rather limited power density, which is mainly ascribed to a strongly increased interfacial resistance. The cause of this resistance is the formation of space-charge layers near the electrodes, which go along with very high electric fields. Understanding in detail the mechanisms and parameters involved in the space-charge-layer formation will be an important step towards improved solid-state systems with more favorable properties. However, although experimental studies on this subject are readily available, a mathematically (and thermodynamically) rigorous description of the space-charge regions in a solid electrolyte seems to be still lacking.

In this work, we propose a new mathematical model for ionic transport in a solid electrolyte, which is based on first principles only. To this end, the conservation equations for mass, momentum and energy are augmented by constitutive relations derived from a universal  entropy principle and a free-energy functional which describes the properties of the system on the macroscopic scale. It is important to note that boundary-layer like structures are intrinsically present in our model and do not have to be augmented a posteriori as, e.g., in Gouy-Chapman theory for fluids.

We provide analytical and numerical solutions for a solid electrolyte in contact with metal electrodes, which we evaluate to study the parametric dependencies of the cation and potential distributions under the influence of varying electrode potentials and varying interface properties. We compare our results both with the predictions of classical Poisson-Nernst-Planck theory and with experimental results [1]. Estimates on the width of the space charge regions are given as well as predictions on the behaviour of this region under different conditions.

We observe that there exist some fundamental differences between space-charge layers in fluid and in solid electrolytes. While the space-charge regions are usually symmetric in a fluid, this is not the case in the solid electrolyte, due to an asymmetric distribution of the charge carriers. Furthermore, the space-charge regions tend to be much wider in the solid electrolyte than in a fluid under comparable conditions. Consistent with experiments [2] we find that the space charge regions and thus the distribution of electric fields can be systematically modified by carefully choosing layers of materials with varying dielectric properties. These modifications can be used to decrease considerably interfacial resistances and thus strongly improve the power density of All Solid State Batteries.

[1] K. Yamamoto et al., Angew. Chem. Int. Ed. 49 (2010), pp 4414-4417.

[2] C. Yada, A. Ohmori, K. Ide, H. Yamasaki, T. Kato, T. Saito, et al., Dielectric modification of 5V-class cathodes for high-voltage all-solid-state lithium batteries, Adv. Energy Mater. 4 (2014) 1–5. doi:10.1002/aenm.201301416.