Phase-field modeling for electrodeposition process

Abstract

A novel phase-field model for electrochemical processes, in which cations were driven by an electrostatic potential coupled with a thermodynamic potential, was formulated from a variation of the Ginzburg-Landau free-energy functional. Using this model, an electrodeposition process of copper deposits from copper-sulfate solution was studied using a phase-field simulation. The dependence of the growth velocity of the electrode on the applied voltage was examined in a one-dimensional system. Then, the morphological transition of the electrodeposits as functions of the applied voltage and the composition ratio of copper ion in electrolyte was examined using a two-dimensional system. Thin and dense branches were observed at a low applied voltage. The shape of the branches became more complicated as the composition ratio was lowered. r

Sharp-interface model of electrodeposition and ramified growth

“…In principle, the phase-field models are superior to our model in this aspect since they do not have this limitation. However, it is not of practical relevance, as all of the published phase-field simulations are for systems so short that the quasi-steady-state assumption is valid anyway [25][26][27].…”

“…Over the years, many experimental, theoretical, and numerical studies have been devoted to increasing the understanding of this ramified growth regime [12][13][14][15][16][17][18][19][20]. Big contributions to our understanding of the growth process have come from diffusion-limited aggregation (DLA) models [21,22] and, more recently, phasefield models similar to those that have successfully been applied to solidification problems [23][24][25][26][27][28][29]. However, while both of these approaches capture parts of the essential behavior of ramified growth, they have some fundamental shortcomings when applied to the electrodeposition problem.…”

A phase-field simulation of uranium dendrite growth on the cathode in the electrorefining process

“…In addition to the above numerical models, a phase-field model (PFM) [9,10], which can treat a free boundary in a biphasic system, has also been adopted to investigate various electrode reactions [11][12][13][14][15][16][17][18][19][20][21] focusing on complex morphologies of the electrode surface. For example, Guyer et al [12,13] solved distributions of components and obtained an electric double layer by solving Poisson's equation in the one-dimensional (1D) system.…”

“…Han et al [15] examined Li diffusion in secondary battery electrodes using a phasefield model and discussed the diffusion coefficient on the basis of Galvanostatic and Potentiostatic Intermittent Titration Technique (GITT and PITT). Moreover, we have studied electrochemical processes such as bridge formation and disappearance in the atomic switch [16][17][18] and electrodeposition of copper from copper sulfate solution [19][20][21], where a morphological diagram of the copper deposits was summarized as functions of the applied voltage and the concentration of metal ion in the electrolyte.…”

Computational Model of Magnesium Deposition and Dissolution for Property Determination via Cyclic Voltammetry

“…Guyer et al 40,41 reported a thermodynamically derived one-dimensional (1D) phase-field model of metal deposition that included charge-separation effects in the double layer and was able to recover the behavior described by Butler-Volmer kinetics. Additional phase-field models have also been derived in two or three dimensions to examine deposition of copper, 42 lithium, [43][44][45] zinc, 46 and, most recently, magnesium. 25 All of these models have increased scientific understanding of the rich set of phenomena observed during electrodeposition and electrodissolution.…”