Solid-State Transport of Lithium in Lithium-Ion-Battery Positive Electrodes

Abstract

mportant to all systems that utilize lithium-ion batteries is the characterization of the irreversibilities associated with solid-state lithium transport limitations that exist within the materials comprising the battery electrodes. Essential to this characterization is an accurate description of the flux of lithium, which necessarily involves the lithium diffusivity. The theory for an appropriate description of the lithium flux is detailed and ultimately used to demonstrate the importance of this description via comparisons of measured to calculated voltage responses in batteries specifically designed for hybrid electric vehicles. An analytic expression for the solid-state excess Gibb's free energy associated with a secondary reference state of full lithiation is developed, which is appropriate for present-day positive-electrode materials that cannot be operated at low degrees of lithiation. Expressions for the thermodynamic open-circuit voltage, the thermodynamic factor, and activity coefficients are also derived. The approach preserves thermodynamic consistency in dilute and in full occupancy and circumvents difficulties that can arise with the differentiation of discrete experimental data points. Variations in previously reported chemical diffusivities over a significant range of lithiation are shown to be explained by the inclusion of both the thermodynamic factor and the flux of lithium due to bulk motion of material.