Formulation for the Treatment of Multiple Electrochemical Reactions and Associated Speciation for the Lithium-Silicon Electrode

Abstract

We develop a theory and commensurate equations to model the thermodynamics, electrochemistry, and species transport of substitutional alloys subject to multiple electrochemical reactions, and we apply the treatment to the lithium-silicon (Li-Si) system. The approach is general in that we expect it is applicable to simulate the electrochemical-reaction behavior of known substitutional-alloy and insertion-electrode materials of interest relative to today's and near-future electrode materials. Central to the approach is the treatment of slow-scan voltammetry to gather information usually obtained by data differentiation associated with differential voltage spectroscopy; we show that the approach taken here allows for an accurate description of very low-rate behavior (0.01 mV/s), which we refer to as dynamic equilibrium. Treatment of the dynamic equilibrium data leads to speciation and activity coefficients for the solid state, which are then employed in the development of equations describing interfacial reactions and diffusion within the host material. The model is shown to compare favorably with experimental results obtained from thin-film Li-Si electrodes conducted at moderate potential-scan rates, with irreversible behavior governed by charge-transfer (interfacial) resistance. We conclude with a section addressing the potential implications of the proposed model, particularly with regard to the Stefan-Maxwell form of the diffusion equations, and open questions.