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, (Fe8a3+)[Fe3+Fe2+]16dO4,32e2-, 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.

Magnetite is a known lithium intercalation material, and the loss of active, nanocrystalline magnetite can be inferred from the open-circuit potential relaxation. Specifically, for current interruption after relatively small amounts of lithium insertion, the potential first increases and then decreases, and the decrease is hypothesized to be due to a formation of a surface layer, which increases the solid-state lithium concentration in the remaining active material. Comparisons of simulation to experiment suggest that the reactions with the electrolyte result in the formation of a thin layer of electrochemically inactive material, which is best described by a nucleation and growth mechanism. Simulations are consistent with experimental results observed for 6, 8 and 32-nm crystals. Furthermore, simulations capture the experimental differences in lithiation behavior between the first and second cycles.

Electric energy storage systems such as batteries can significantly impact society in a variety of ways, including facilitating the widespread deployment of portable electronic devices, enabling the use of renewable energy generation for local off grid situations and providing the basis of highly efficient power grids integrated with energy production, large stationary batteries, and the excess capacity from electric vehicles. A critical challenge for electric energy storage is understanding the basic science associated with the gap between the usable output of energy storage systems and their theoretical energy contents. The goal of overcoming this inefficiency is to achieve more useful work (w) and minimize the generation of waste heat (q). Minimization of inefficiency can be approached at the macro level, where bulk parameters are identified and manipulated, with optimization as an ultimate goal. However, such a strategy may not provide insight toward the complexities of electric energy storage, especially the inherent heterogeneity of ion and electron flux contributing to the local resistances at numerous interfaces found at several scale lengths within a battery. Thus, the ability to predict and ultimately tune these complex systems to specific applications, both current and future, demands not just parametrization at the bulk scale but rather specific experimentation and understanding over multiple length scales within the same battery system, from the molecular scale to the mesoscale. Herein, we provide a case study examining the insights and implications from multiscale investigations of a prospective battery material, Fe3O4.