Experimental and Theoretical Characterization of Electrode Materials That Undergo Large Volume Changes and Application to the Lithium-Silicon System

The life and performance of lithium-ion batteries is related to the mechanical expansion and contraction of the active materials, particularly for silicon-enhanced negative electrodes. In this work, we develop a theory and commensurate equations to describe how lithium diffuses within lithiated silicon, and we include the influence of active material expansion (upon lithiation) and contraction (upon delithiation). We employ thin-films of vapor-deposited Si to construct our electrodes. This allows us to isolate our analysis to the active material and avoids the necessity of treating binders, conductive diluents, and complicated geometries associated with conventional porous electrodes used in most practical lithium-ion batteries and in the construction and modeling of a Li-Si porous electrode. The model is shown to compare favorably with experimental results.

We have derived an equation system for the treatment of electrode materials that undergo large volume changes during operation. The approach is applied to a thin-film Li-Si system, wherein a volume change of about 270% is observed relative to pure Si and Li3.75Si. Good agreement is obtained when the model calculations are compared with experimental data obtained from Li-Si thin film electrodes (67-nm thickness) subjected to linear-sweep voltammetry experiments over current and potential ranges of interest for many applications, including electrified vehicles.

We ignore the influence of stress on the thermodynamics and transport of the Li-Si thin films. Instead, we use a one-dimensional model which assumes that stress does not impact the chemical potential, because the stresses are negligible within the infinitely thin film that is unconstrained at its interface with the electrolyte. However, the local expansion and contraction of the film, as a function of lithium content, is taken into consideration, and this leads to a moving boundary value problem, where the position of the film surface must be calculated.