Phase-Field Modeling of Transport-Limited Electrolysis in Solid and Liquid States

Abstract

A phase-field model of electrochemical interface dynamics is developed to study cathode shape and topology change in transportlimited electrolysis in two and three dimensions under conditions of rapid charge redistribution. A case study for the binary model is carried out for an Fe-FeO system. Stability behavior of the model is in good agreement with linear stability theory for small amplitude sinusoidal perturbation in electrodeposition. When there is no convection, a high electric field and low surface tension cause the cathode interface to be unstable, leading to growth of dendrites which break into powders. When the electrodes and electrolyte are low-viscosity fluids, flow provides an additional mechanism for stabilizing the interface. A new stability criterion for this liquid situation based on the Schmidt number is derived from dimensional analysis and model results. For an unstable cathode interface, a streamer morphology ͑liquid dendrites͒ is observed in two and three dimensions. This binary model is extended to a ternary system and a representative case is carried out for the Ti-Mg-Cl system. One-and two-dimensional ternary simulations show qualitatively correct interface motion and electrical potential behavior.Electrochemical interactions are ubiquitous in the field of materials, from fuel cells and batteries, to smelting or refining of metals, to corrosion, to electromigration in electronic interconnects. In order to maximize the performance of these materials and systems, one must understand the role of electrochemistry in the migration of phase boundaries. The complexity of interface shape and topology changes and coupled chemical and electrical driving forces makes these systems very difficult to comprehend, let alone engineer. For example, the cathodic reduction of ions to metal exhibits a MullinsSekerka instability due to an ion-depleted layer at the cathode/ electrolyte interface. Any perturbation on the cathode surface leads to the formation of solid dendrites or liquid streamers, affecting the process efficiency as well as resulting in a rough surface or porous deposit.The governing equations which describe this process are well understood, such as the Poisson equation for electrical potential, charge conservation, and ion diffusion driven by electric and chemical potential gradients. Many investigators have used these equations in the limit of small perturbations in order to study the stability of cathodic interfaces. 1-9 Haataja et al. classify previous works on linear stability analysis into unsupported 1-8 and fully supported electrolytes, 3-5 then extend this analysis to arbitrary supporting electrolytes. 9 These analyses demonstrate that the interface perturbation growth is faster with increasing deposition rates, increasing spectator ion concentrations, increasing perturbation wavelengths and amplitudes, and decreasing ohmic resistances due to charge transfer. Qualitatively, these predictions correlate well with experimental observation.The shape and topology of the interface, however, ...

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Phase field modeling of phase boundary motion due to transport-limited electrochemical reactions

“…When the Schmidt number is large, high viscosity prevents flow, and stability behavior approaches the case without flow. When it is small, the interface becomes more stable, as described in further detail in ref [6].…”

“…A phase field formulation for coupled fluid flow, diffusion, electromigration, and transport-limited electrochemical reactions was developed by Dussault [8], and expanded by Pongsaksawad and Powell [6]. This model begins with a dimensionless concentration variable C which is zero in the FeO slag and one in the iron metal, and uses a very simplistic polynomial function for the homogeneous free energy with minima at zero and one:…”

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