Intercalation kinetics in multiphase layered materials

Abstract

Many intercalation compounds possess layered structures or inter-penetrating lattices that enable phase separation into three or more stable phases, or "stages," driven by competing intra-layer and inter-layer forces. While these structures are often well characterized in equilibrium, their effects on intercalation kinetics and transport far from equilibrium are typically neglected or approximated by empirical solid solution models. Here, we formulate a general phase-field model with thermodynamically consistent reaction kinetics and cooperative transport to capture the dynamics of intercalation in layered materials. As an important case for Li-ion batteries, we model single particles of lithium intercalated graphite as having a periodic two-layer structure with three stable phases, corresponding to zero, one, or two layers full of lithium. The electrochemical intercalation reaction is described by a generalized Butler-Volmer equation with thermodynamic factors to account for the flexible structure of the graphene planes. The model naturally captures the "voltage staircase" discharge curves as a result of staging dynamics with internal "checkerboard" domains, which cannot be described by solid-solution models based on Fickian diffusion. On the other hand, the two-layer model is computationally expensive and excludes low-density stable phases with longer-range periodicity, so we also present a reduced model for graphite, which captures the high-density stages while fitting the low-density voltage profile as an effective solid solution. The two models illustrate the general tradeoff between the explicit modeling of periodic layers or lattices and the needs for computational efficiency and accurate fitting of experimental data.

References in corpus (4)

• Theory of Chemical Kinetics and Charge Transfer based on Nonequilibrium Thermodynamics
• A Finite Strain Model of Stress, Diffusion, Plastic Flow and Electrochemical Reactions in a Lithium-ion Half-cell
• Charge Transfer Kinetics at the Solid-Solid Interface in Porous Electrodes
• Revisiting the domain model for lithium intercalated graphite

Cited by in corpus (9)

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• Explaining key properties of lithiation in TiO${}_2$-anatase Li-ion battery electrodes using phase-field modelling
• Robust high-fidelity DFT study of the lithium-graphite phase diagram
• DFTB modelling of lithium intercalated graphite with machine-learned repulsive potential
• Interplay between Phase Transformation Instabilities and Spatiotemporal Reaction Heterogeneities in Particulate Intercalation Electrodes
• In-plane staging in lithium-ion intercalation of bilayer graphene
• Interfacial resistive switching by multiphase polarization in ion-intercalation nanofilms
• Spinodal decomposition and domain coarsening in a multi-layer Cahn-Hilliard model for lithium intercalation in graphite
• Asymptotic reduction, solution, and homogenisation of a thermo-electrochemical model for a lithium-ion battery