Equilibria and Rate Phenomena from Atomistic to Mesoscale: Simulation Studies of Magnetite

Batteries are dynamic devices composed of multiple components that operate far from equilibrium and may operate under extreme stress and varying loads. Studies of isolated battery components are valuable to the fundamental understanding of the physical processes occurring within each constituent element. When the components are integrated into a full device and operated under realistic conditions, it can be difficult to decouple the physical processes that occur across multiple interfaces and multiple length scales. Thus, the physical processes studied in isolated components may change in a full battery setup or may be irrelevant to performance. Simulation studies on many length scales play a key role in the analysis of experiments and in the elucidation of the relevant physical processes impacting performance. In this Account, we aim to highlight the use of modeling on multiple length scales to identify rate limiting phenomena in lithium-ion batteries. To illustrate the utility of modeling, we examine lithium-ion batteries with nanostructured magnetite, Fe₃O₄, as the positive electrode active material against a solid Li⁰ negative electrode. Due to continuous operation away from equilibrium, batteries exhibit highly nonideal behavior, and a model that aims to reproduce behavior under realistic operating conditions must be able to capture the physics occurring on the length scales relevant to the performance of the system. It is our experience that limiting behavior in lithium-ion batteries can be observed on the atomic scale and up through the electrode scale and thus, predictive models must be capable of integrating and communicating physics across multiple length scales. Magnetite is studied as an electrode material for lithium-ion batteries, but it is found to suffer from slow solid-state transport of lithium, slow reaction kinetics, and poor cycling. Magnetite (Fe₃O₄) is a material capable of undergoing multiple electron transfers (MET), and can accept up to eight lithium per formula unit (Li₈Fe₃O₄). Magnetite, (Fe_8a³⁺)[Fe³⁺Fe²⁺]_16dO_4,32e^2-, has a close-packed inverse spinel structure and undergoes intercalation, structural rearrangement, and conversion reactions upon full lithiation. (1) To overcome solid-state transport resistances, magnetite can be nanostructured to decrease Li⁺ diffusion lengths, and this has been shown to increase capacity. Additionally, unique architectures incorporating both carbon and Fe₃O₄ have shown to alleviate transport and cycling issues in the material. (2) Here, we solely address traditional composite electrodes, in which Fe₃O₄ is synthesized as nanoparticles and combined with additives to fabricate the electrode. In the case of nanoparticulate magnetite, it has been found that the electrode fabrication process results in the formation of micrometer-sized agglomerates of the Fe₃O₄ nanoparticles, introducing a secondary structural motif. The agglomerates may form in one or more fabrication processes, and their elimination may not be straightforward or warranted. Here, we highlight the impact of these secondary formations on the performance of the Fe₃O₄ lithium-ion battery. We illustrate how simulations can be used to design experiments, prioritize research efforts, and predict performance.