The Tortuosity of Graded Electrodes: Electrochemical Impedance and Microstructure-Aware Cell Models

Microstructure design of battery electrodes is key to enable fast charge and higher capacity in next-generation lithium and sodium ion batteries. While porous-electrode (Doyle–Fuller–Newman-type) models capture the coupled transport–reaction physics governing cell performance, they typically treat the electrode as a homogenized medium and encode microstructure only through fitted, scalar “effective” parameters (e.g., Bruggeman-type tortuosity). This assumption is often adequate for uniform electrodes, but it breaks down for modern architectures with graded porosity, binder migration, bimodal particle distributions, or bilayer designs, where transport resistance is heterogeneous and reaction rates localize, leading to non-uniform utilization and premature rate limitations. Here we introduce an approach that efficiently bridges 3D image-based electrode simulations and microstructure-aware cell-scale modelling using volume-averaged microstructure descriptors. We compute spatially resolved, directional tortuosity factors τ(x) along with spatial porosity ε(x) and specific surface area a(x) and embed these closures directly into DFN-type cell models. This replaces ad hoc, globally fitted transport factors with architecture-dependent descriptors that can represent graded and bilayer electrodes in a physically interpretable way. We further show that common characterization and parameter-identification workflows implicitly assume electrode homogeneity, and can therefore misattribute microstructure-driven limitations to “material” kinetics when applied to structured electrodes. By preserving the computational efficiency of porous electrode models while injecting microstructure information, the proposed workflow runs in seconds to minutes per design, enabling rapid screening and sensitivity analyses under fast (dis)charge. Combined with generative AI methods, this pipeline enables high-throughput exploration of electrode microstructure space for both Li- and Na-ion chemistries, accelerating the discovery of architectures that simultaneously improve transport, reaction uniformity, and capacity utilization.