Crossover from compact to branched films in electrodeposition with surface diffusion

Reis, F. D. A. Aarão; Caprio, Dung Di; Taleb, Abdelhafed

doi:10.1103/physreve.96.022805

Cited by 11 publications

(17 citation statements)

References 69 publications

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“…First, consider the film morphology for G = 5 × 10 4 and four values of ϵ, as shown in Figure . In all cases, we observe a thick wetting layer on the electrode, as shown in ref . For ϵ ≤ 0.05, dendrites with leaf-like shape are formed, which propagate in (±1,±1,1) directions, as observed for smaller G .…”

Section: Resultssupporting

confidence: 80%

“…We performed numerical simulations of a model of thin-film electrodeposition, which is designed to describe the effects of diffusion of the adsorbed material. This model was introduced in ref , which analyzed the growth of a wetting layer at short times and the crossover to a regime of porous film growth. Here, we analyzed the film structure in this second regime and addressed the conditions for dendrite formation, which is a morphology of interest for several applications.…”

Section: Discussionmentioning

confidence: 99%

“…In a recent work, an electrodeposition model with diffusion of adsorbed atoms was proposed, and the formation of a nonporous wetting layer on the electrode was studied . Here, we extend the simulations of that model to study the properties of the porous films that grow on the wetting layer, with special interest in the conditions for the growth of hierarchically organized structures, that is, the dendrites.…”

Section: Introductionmentioning

confidence: 99%

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Effect of Adsorbate Diffusion on the Dendritic Morphology of Electrodeposited Films

2018

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We study the formation of deposits with dendritic morphology using numerical simulations of a model of electrodeposition and diffusion of the adsorbed material. The model considers a diffusive flux of cations in solution, the instantaneous adsorption and reaction in contact with the film surface, and random walks of mobile atoms on that surface, with a maximum of G hops per atom and a detachment probability ϵ per neighbor at the current position. For low temperature or large current, which corresponds to small G, the deposits are similar to the diffusion-limited aggregates growing from the flat electrode; for high temperature or very small current, which is represented by large G or ϵ, the deposits have thick rounded columns with sporadic ramification. In these conditions, the growth direction is controlled by the orientation of the electrode and of the cation flux. For the balanced conditions of adsorbate diffusion and current (typically 102 ≲ G ≲ 104 and ϵ ≲ 0.1, but also for larger G and very small ϵ), the films have a hierarchical dendritic morphology with the shape of maple leaves. The dendrite tips propagate in directions forming 45° with the electrode and are formed by three concurrent terraces, as a consequence of the simulations in a simple cubic lattice. The average dendrite size increases as a power law of G and is consequently expected to decrease with the applied current. The lowest energy configurations (terraces) are shown to be stable within the timescale of crystallization of an atomic layer, but the weakly bonded atoms have sufficiently large mobility to create those configurations. Thus, the dendritic morphology depends on the interplay between the energetics of the crystal and the electric current, which may help the interpretation of dendrite growth with other crystalline structures. The dendrite shape obtained here resembles those observed in some electrodeposited films of gold, zinc, and palladium, and the effect of the electric current on the dendrite size agrees with the observations in the electrodeposition of silver and gold. Assuming that the adsorbate diffusion is thermally activated, we propose that the average dendrite size is a ratio between an Arrhenius factor and a power law of the current; this suggests a method to estimate the microscopic energy barrier of diffusion, which may differ from the macroscopic activation energy.

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Section: Resultssupporting

confidence: 80%

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Effect of Adsorbate Diffusion on the Dendritic Morphology of Electrodeposited Films

2018

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“…Quantitative relations are expected to be predicted by simulations of improved models which account for details of particular growth processes. Possible extensions may consider the effects of non-collimated particle flux and longer diffusion lenghts of the adsorbed species, as shown in recent models that reproduce morphological properties of dendritic films [66][67][68] . In these cases, the dendrite orientations and the porosity variations that are expected due to the growth instabilities should affect the pore diffusivity.…”

Section: Discussionmentioning

confidence: 99%

Effects of the growth kinetics on solute diffusion in porous films

Correa,

Almeida,

Reis

2021

Preprint

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For the development of porous materials with improved transport properties, a key ingredient is to determine the relations between growth kinetics, structure, and transport parameters. Here we address these relations by studying solute diffusion through three-dimensional porous films produced by deposition models with controlled thickness and porosity. A competition between pore formation by lateral particle aggregation and surface relaxation that favors compaction is simulated by the lattice models of ballistic deposition and of random deposition with surface relaxation, respectively, with relative rates proportional to p and 1 − p. Effective diffusion coefficients are determined in steady state simulations with a solute source at the basis and a drain at the top outer surface of the films. For a given film thickness, the increase of the relative rate of lateral aggregation leads to the increase of the effective porosity and of the diffusivity, while the tortuosity decreases. With constant growth conditions, the increase of the film thickness always leads to the increase of the effective porosity, but a nontrivial behavior of the diffusivity is observed. For deposition with p ≤ 0.7, in which the porosity is below 0.6, the diffusion coefficient is larger in thicker films; the decrease of the tortuosity with the thickness quantitatively confirms that the growth continuously improves the pore structure for the diffusion. Microscopically, this result is associated with narrower distributions of the local solute current at higher points of the deposits. For deposition with p ≥ 0.9, in which the films are in the narrow porosity range ∼ 0.65 − 0.7, the tortuosity is between 1.3 and 2, increases with the thickness, and has maximal changes near 25%. Pairs of values of porosity and tortuosity obtained in some porous electrodes are close to the pairs obtained here in the thickest films, which suggests that our results may be applied to deposition of materials of technological interest. Noteworthy, the increase of the film thickness is generally favorable for diffusion in their pores, and the exceptions have small losses in tortuosity.

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“…Quantitative relations are expected to be predicted by simulations of improved models which account for details of particular growth processes. Possible extensions may consider the effects of noncollimated particle flux and longer diffusion lengths of the adsorbed species, as shown in recent models that reproduce morphological properties of dendritic films. − In these cases, the dendrite orientations and the porosity variations that are expected because of the growth instabilities should affect the pore diffusivity.…”

Section: Discussionmentioning

confidence: 99%

Effects of the Growth Kinetics on Solute Diffusion in Porous Films

2020

View full text Add to dashboard Cite

For the development of porous materials with improved transport properties, a key ingredient is to determine the relations between growth kinetics, structure, and transport parameters. Here, we address these relations by studying solute diffusion through three-dimensional porous films produced by deposition models with controlled thickness and porosity. A competition between pore formation by lateral particle aggregation and surface relaxation that favors compaction is simulated by the lattice models of ballistic deposition and of random deposition with surface relaxation, respectively, with relative rates proportional to p and 1 − p. Effective diffusion coefficients are determined in steadystate simulations with a solute source at the basis and a drain at the top outer surface of the films. For a given film thickness, the increase in the relative rate of lateral aggregation leads to the increase in the effective porosity and the diffusivity, while the tortuosity decreases. Under constant growth conditions, the increase in the film thickness always leads to the increase in the effective porosity, but a nontrivial behavior of the diffusivity is observed. For deposition with p ≤ 0.7, in which the porosity is below 0.6, the diffusion coefficient is larger in thicker films; the decrease in the tortuosity with the thickness quantitatively confirms that the growth continuously improves the pore structure for diffusion. Microscopically, this result is associated with narrower distributions of the local solute current at higher points of the deposits. For deposition with p ≥ 0.9, in which the films are in the narrow porosity range ∼0.65−0.7, the tortuosity is between 1.3 and 2, increases with the thickness, and has maximal changes near 25%. Pairs of values of porosity and tortuosity obtained in some porous electrodes are close to the pairs obtained here in the thickest films, which suggests that our results may be applied to deposition of materials of technological interest. Noteworthy, the increase in the film thickness is generally favorable for diffusion in their pores, and the exceptions have small losses in tortuosity.

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Crossover from compact to branched films in electrodeposition with surface diffusion

Cited by 11 publications

References 69 publications

Effect of Adsorbate Diffusion on the Dendritic Morphology of Electrodeposited Films

Effect of Adsorbate Diffusion on the Dendritic Morphology of Electrodeposited Films

Effects of the growth kinetics on solute diffusion in porous films

Effects of the Growth Kinetics on Solute Diffusion in Porous Films

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