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 [1].  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 (see Fig. 1).

We employ directly the experimental results from [1], corresponding to a silicon thin-film (67 nm) electrode deposited on a copper current collector. CR2032 coin cells were assembled with the Si thin film as the working electrode and a lithium foil as the counter-reference electrode.

To construct the model in [1], a look-up table was employed to evaluate the variation in the open-circuit potential with lithium content.  In the current work, we develop consistent thermodynamic and electrochemical-reaction treatments that capture the salient features of the Li-Si experimental data and should prove to be of general utility for the treatment of substitutional alloys and insertion electrodes [2]. We employ the low-scan-rate voltammetry data reported in [1], which simplifies material balances, as diffusion resistance is negligible, and species concentrations are uniform throughout the film, although they vary with time. Last, we provide a discussion of results, including a perspective on the potential implications of the proposed treatment (with an emphasis on how the thermodynamic treatment influences transport relations based on the Stefan-Maxwell framework) and important open questions.  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; cyclic voltammetry results are shown in Fig. 2.

 

1. M. Verbrugge, D. Baker, X. Xiao, Q. Zhang, and Y-T. Cheng, “Experimental and theoretical characterization of electrode materials that undergo large volume changes and application to the lithium-silicon system,” J. Phys. Chem. C., 119(2015)5341.
2. M. Verbrugge, D. Baker, and X. Xiao, “Formulation for the treatment of multiple electrochemical reactions and associated speciation for the lithium-silicon electrode,” J. Electrochem. Soc., 163(2016)A262-A271.