Architecture-influenced stress and diffusion for hierarchical 3D thick electrodes with multi-layer nanosheets

Hierarchical 3D thick electrodes with multi-layer nanosheets represent an important step in the advancement of electrode design and fabrication that allows more efficient charge transport beyond the limits of traditional electrodes. However, there is still a lack of systematic theoretical investigations of microstructure and kinetic diffusion on the stress development for such electrode at the mesoscale. Therefore, in this work, we propose a comprehensive modeling framework with a light by using plate theory together with a mechanical concept model based on structure constraint that can fully address the chemo-mechanical environment accounting for the failure of electrodes. Through extracting the basic building block of thick electrode, the model can describe the typical characteristics of the elaborated 3D architectures with a compliant backbone. Bilayer and three-layer sandwich-like nanosheets with different mechanical constraints reflecting structure flexibility are considered. Theoretical investigations reveal the influences of the mechanical constraint and heterogeneous electrochemistry on the stress evolution in thick electrodes. Although the analysis of transient ion diffusion in composite solids has been developed for almost 50 years, an exact closed-form solution for general electrochemical conditions is lacking owing to the mathematical difficulty. Here, for transient diffusion in bilayer and three-layer slab under both galvanostatic and potentiostatic charging, theoretical solutions giving a complete description of the spatial and temporal variation of lithium concentration and allowing ion exchange between each layer are derived by using the natural eigenfunction expansion method, which is particularly convenient. Such investigation has potential avenues for guiding design of high performance 3D thick electrodes and catching sight of the under-lying mechanisms in the view of mechanics and diffusion considerations.