Space-Charge Effects in Lithium Garnet Solid Electrolytes: A Continuum Modeling Study Using the Poisson–Nernst–Planck Framework

For next-generation solid-state micro-batteries, lithium garnet solid electrolytes like Li 7 La 3 Zr 2 O 12 (LLZO) are considered a promising material because of their high ionic conductivity, electrochemical stability, and mechanical robustness. Experimental data indicates that interfacial resistance, thickness-dependent conductivity, and currentinduced polarization can considerably restrict their performance, even though they are frequently regarded as Ohmic ionic conductors. Based on the coupled Poisson-Nernst-Planck (PNP) equations, we create a continuum-scale model in this work to study the transport of lithium ions in LLZO under applied potential difference. Physically motivated scales are used to nondimensionalize the governing equations, demonstrating that the problem is governed by a single dimensionless parameter: the squared ratio of the electrolyte thickness to the Debye length. Space-charge layers and nonlinear transport regimes can be resolved steadily by the use of an implicit Newton-Raphson approach to get numerical solutions. The findings underscore the significance of spacecharge effects in solid-state electrolytes by showing departures from electroneutral Ohmic behavior in thin electrolytes and under reduced electrolyte thickness. The framework offers a quantitative foundation for comprehending phenomena and for creating composite or interfacially designed electrolytes that perform better.