Explaining key properties of lithiation in TiO2 -anatase Li-ion battery electrodes using phase-field modeling

Abstract

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 TiO 2 -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 TiO 2 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 TiO 2 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 Li 1 TiO 2 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 TiO 2 electrodes requires preventing the formation of a blocking Li 1 TiO 2 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.

Multiphase Porous Electrode Theory

“…Active materials with more complex thermodynamics, resulting in multiple stable phases of different equilibrium concentrations, cannot be described, except by certain empirical modifications. Phase separating materials, such as lithium iron phosphate and graphite, can be accommodated by introducing artificial phase boundaries, such as shrinking cores [56] or shrinking annuli [70], respectively, but this approach masks the true thermodynamic behavior.Instead, the open circuit voltage of a battery is an emergent property of multiphase materials, which reflects phase separation in single particles [25,[71][72][73] and porous electrodes [40,44,65]. It can only be predicted by modeling the free energy functional, rather than the voltage directly, and consistently defining electrochemical activities, overpotentials, and reaction rates using variational nonequilibrium thermodynamics [74,75].…”

“…First, we incorporate the standard description of transport in concentrated electrolytes based on Stefan-Maxwell coupled fluxes and chemical diffusivities [5,85]. Second, we capture the continued development by our group of phase field models for the active solid materials [25, 44, 71-74, 76, 86, 87], which have increasingly been validated by direct experimental observations of phase separation dynamics [38,44,73,75,77,88,89]. Third, we provide alternatives to the empirical Butler-Volmer model of Faradaic reaction kinetics [5,[90][91][92], based on the quantum mechanical theory of electron transfer pioneered by Marcus [93-96] and extended here for concentrated solutions [97], motivated by recent battery experiments [98].…”

“…Instead, the open circuit voltage of a battery is an emergent property of multiphase materials, which reflects phase separation in single particles [25,[71][72][73] and porous electrodes [40,44,65]. It can only be predicted by modeling the free energy functional, rather than the voltage directly, and consistently defining electrochemical activities, overpotentials, and reaction rates using variational nonequilibrium thermodynamics [74,75].…”

Ab Initio Study of Sodium Insertion in the λ-Mn2O4 and Dis/Ordered λ-Mn1.5Ni0.5O4 Spinels

“…56 Therefore, the inserted spinel system will be more susceptible to suppression of phase separation. Suppression of the phase separation mechanism can be achieved either by high currents 57−60 or by reducing the particle size to the thickness of the phase interface layer, 55 as simulated and shown experimentally for LFP and anatase TiO 2 electrodes. Thus, given the correct conditions, partial mixing of the end-member phases (solid solution) might be possible, leading to a sloping voltage curve.…”

“…The phase transition between Li 0.5 TiO 2 and LiTiO 2 shows a clear plateau during extremely slow cycling and/or for very small particle sizes, while during standard cycling conditions, a slope is seen due to kinetically induced overpotentials. 55 A thick phase interface layer is also linked with a large gradient penalty (κ), penalizing the coexistence of two phases. 56 Therefore, the inserted spinel system will be more susceptible to suppression of phase separation.…”