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

Lithium garnet solid electrolytes such as Li₇La₃Zr₂O₁₂ (LLZO) are widely regarded as promising candidates for next-generation all-solid-state lithium batteries owing to their high ionic conductivity, wide electrochemical stability window, and superior mechanical stiffness against lithium dendrite penetration. These attributes position LLZO as a key advanced energy material for enabling safe, high-energy-density storage technologies critical to electrified transportation and renewable energy integration. However, despite frequently being approximated as purely Ohmic ionic conductors, growing experimental evidence indicates that transport in LLZO can deviate significantly from ideal electroneutral behavior. In particular, interfacial resistance, thickness-dependent conductivity, and current-induced polarization effects have been reported to limit rate capability and power performance in practical cells.

In this work, we develop a continuum-scale theoretical framework to systematically investigate lithium-ion transport in LLZO under externally applied electric fields. The model is formulated using the coupled Poisson–Nernst–Planck (PNP) equations, capturing the interplay between ionic diffusion, migration, and electrostatic potential evolution. The governing equations are nondimensionalized using physically motivated scaling parameters, revealing that the transport response is governed primarily by a single dimensionless group corresponding to the squared ratio of the Debye screening length to the electrolyte thickness. This scaling provides direct physical insight into when space-charge effects become non-negligible in solid electrolytes.

To resolve the resulting nonlinear boundary-value problem, numerical solutions are obtained using a fully implicit Newton–Raphson scheme, enabling stable and accurate resolution of steep potential gradients and space-charge layers near blocking or reactive interfaces. The simulations reveal pronounced deviations from classical Ohmic conduction in thin electrolytes and under high applied voltages, manifested through charge accumulation, field localization, and nonlinear current–voltage characteristics. These findings demonstrate that polarization losses in LLZO cannot always be attributed solely to microstructural defects or grain boundary resistance but may arise intrinsically from continuum electrostatic effects.

The developed framework establishes a quantitative basis for interpreting experimental impedance and polarization data and provides design guidelines for thickness optimization, interfacial engineering, and composite electrolyte architectures. More broadly, this study highlights the importance of coupled electrochemical–electrostatic modeling in advancing solid-state battery performance and reliability.