Micromechanics of Nanoporous Alloying Electrodes
Nanostructured electrodes with voids or interconnected pores accommodate large volume changes, shorten ion diffusion pathways, and enhance the structural reversibility of alloying electrodes. While these nanoporous features improve the performance of architected electrodes over bulk electrodes, they also act as geometric irregularities that localize and concentrate internal stresses. In this work, we investigate the hierarchical interplay between phase boundaries and nanoporous features at the microstructural scale and their collective role in mitigating chemo-mechanical failure at the engineering scale. Using Sb$\to$Li$_2$Sb$\to$Li$_3$Sb as a model system, we develop a continuum framework coupling lithium diffusion and reaction kinetics with the finite deformation of alloying electrodes. We analytically show that the interfacial stresses (and not volume changes alone) induce fracture during the Sb $\to$ Li$_2$Sb transformation. Nanoporous geometries accommodate volume changes and in turn lower these interfacial stresses that are detrimental to the structural stability of architected electrodes. We analytically study the elastic-plastic deformation accompanying the Sb $\to$ Li$_2$Sb transformation, and develop a micromechanical model using a hyperelastic neo-Hookean material law to predict the deformations accompanying the Li$_2$Sb$\to$Li$_3$Sb transformation. Our results reveal how diffusion and reaction kinetics shape phase boundary morphology, predict stress concentrations at defects, identify crack geometries likely to propagate, and show how carefully architected electrodes relieve stresses. These findings highlight critical design principles to optimize electrode lifespan and demonstrate a potential application of our continuum model as an electrode design tool.