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A Thermodynamically Consistent Model for Electric Double Layers in Li All-Solid-State Batteries
A Thermodynamically Consistent Model for Electric Double Layers in Li All-Solid-State Batteries
Friday, 13 June 2014
Cernobbio Wing (Villa Erba)
Due to their expected improved safety properties, Li all-solid-state batteries provide an attractive alternative to conventional battery systems. However, as yet their performance is strongly limited, since the relevant transport restrictions in the solid electrolyte are still not sufficiently understood. Of great importance in this context are space charge regions at the boundaries between active particles and the electrolyte, similar to the electric double layers in liquid electrolytes. Gaining knowledge about the behavior of this region and the factors that influence it will be a significant step towards a better understanding of the transport properties of a solid electrolyte.
In this work, we propose a new, mathematically rigorous model for a Li solid electrolyte. Whereas literature on the modeling of liquid electrolytes is abundantly available, the situation is very different for solid electrolytes. The number of theoretical treatments on this topic is very limited [1], and existing work does not always treat transport and equilibrium properties consistently. We overcome this problem by carefully developing a thermodynamically fully consistent model on the basis of first principles only, using the method of rational thermodynamics. To this end, the laws of continuum mechanics are supplemented by constitutive equations, which can be derived from a free-energy functional that describes the properties of the system on the macroscopic scale (i.e., beyond ~10 interatomic distances). An important step is to identify the proper free-energy functional for the solid electrolyte. Basing our theory on a functional that describes Li ion hopping on a fixed anion lattice containing defects, we analyze the charge and potential distributions in a solid electrolyte in contact with a metal electrode under the influence of varying electrode potential differences. The resulting differential equations are solved numerically as well as analytically in the limit of small electrode potential differences.
In this work, we propose a new, mathematically rigorous model for a Li solid electrolyte. Whereas literature on the modeling of liquid electrolytes is abundantly available, the situation is very different for solid electrolytes. The number of theoretical treatments on this topic is very limited [1], and existing work does not always treat transport and equilibrium properties consistently. We overcome this problem by carefully developing a thermodynamically fully consistent model on the basis of first principles only, using the method of rational thermodynamics. To this end, the laws of continuum mechanics are supplemented by constitutive equations, which can be derived from a free-energy functional that describes the properties of the system on the macroscopic scale (i.e., beyond ~10 interatomic distances). An important step is to identify the proper free-energy functional for the solid electrolyte. Basing our theory on a functional that describes Li ion hopping on a fixed anion lattice containing defects, we analyze the charge and potential distributions in a solid electrolyte in contact with a metal electrode under the influence of varying electrode potential differences. The resulting differential equations are solved numerically as well as analytically in the limit of small electrode potential differences.
References:
[1] M. Landstorfer et al, Phys. Chem. Chem. Phys. 13, 12817-12825 (2011).