Computational modeling is vital for the fundamental understanding of processes in Li-ion batteries. However, capturing nanoscopic to mesoscopic phase thermodynamics and kinetics in the solid electrode particles embedded in realistic electrode morphologies is challenging. In particular for electrode materials displaying a first order phase transition, such as LiFePO₄, graphite, and spinel Li₄Ti₅O₁₂, predicting the macroscopic electrochemical behavior requires an accurate physical model. Herein, a thermodynamic phase field model is presented for Li-ion insertion in spinel Li₄Ti₅O₁₂ which captures the performance limitations presented in literature as a function of all relevant electrode parameters. The phase stability in the model is based on ab initio density functional theory calculations and the Li-ion diffusion parameters on nanoscopic nuclear magnetic resonance (NMR) measurements of Li-ion mobility, resulting in a parameter free model. The direct comparison with prepared electrodes shows good agreement over three orders of magnitude in the discharge current. Overpotentials associated with the various charge transport processes, as well as the active particle fraction relevant for local hotspots in batteries, are analyzed. It is demonstrated which process limits the electrode performance under a variety of realistic conditions, providing comprehensive understanding of the nanoscopic to microscopic properties. These results provide concrete directions toward the design of optimally performing Li₄Ti₅O₁₂ electrodes.

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The improvement of Li-ion battery performance requires development of models that capture the essential physics and chemistry in Li-ion battery electrode materials. Phase-field modeling has recently been shown to have this ability, providing new opportunities to gain understanding of these complex systems. In this paper, a novel electrochemical phase-field model is presented that captures the thermodynamic and kinetic properties of lithium insertion in TiO2-anatase, a well-known and intensively studied Li-ion battery electrode material. Using a linear combination of two regular solution models, the two phase transitions during lithiation are described as lithiation of two separate lattices with different physical properties. Previous elaborate experimental work on lithiated anatase TiO2 provides all parameters necessary for the phase-field simulations, giving the opportunity to gain fundamental insight in the lithiation of anatase and validate this phase-field model. The phase-field model captures the essential experimentally observed phenomena, rationalizing the impact of C rate, particle size, surface area, and the memory effect on the performance of anatase as a Li-ion battery electrode. Thereby a comprehensive physical picture of the lithiation of anatase TiO2 is provided. The results of the simulations demonstrate that the performance of anatase is limited by the formation of the poor Li-ion diffusion in the Li1TiO2 phase at the surface of the particles. Unlike other electrode materials, the kinetic limitations of individual anatase particles limit the performance of full electrodes. Hence, rather than improving the ionic and electronic network in electrodes, improving the performance of anatase TiO2 electrodes requires preventing the formation of a blocking Li1TiO2 phase at the surface of particles. Additionally, the qualitative agreement of the phase-field model, containing only parameters from literature, with a broad spectrum of experiments demonstrates the capabilities of phase-field models for understanding Li-ion electrode materials, and its promise for guiding the design of electrodes through a thorough understanding of material properties and their interactions.@en