Evolution of the space-charge layer during electrochemical deposition with convection

Electroconvective instability near an ion-selective surface: A mesoscopic lattice Boltzmann study

Direct numerical simulations of electroconvection instability near an ion-selective surface are conducted using a mesoscopic lattice Boltzmann method (LBM). An electrohydrodynamic model of ion transport and fluid flow is presented. We numerically solve the Poisson-Nernst-Planck equations for the electric field and the Navier-Stokes equations for the flow field. The results cover Ohmic, limiting, and overlimiting current regimes, and they are in good agreement with the asymptotic analytical solution for the relationship between current and voltage. The influences of different ion transport mechanisms on the voltage-current relationship are discussed. The results reveal that the electroconvection mechanism is as important as other ion transport mechanisms in electrohydrodynamic flow. By comparing the contribution of different regions in the numerical domain, we find that the flow in the extended space charge layer is dominated by electroconvection. We also study the influences of multiple driving parameters, and the electrohydrodynamic coupling constant plays a dominant role in triggering convective instability. The flow pattern and ion concentration distribution are described in detail. Moreover, the route of flow from steady state to periodic oscillation and then to chaos is discussed.

Suppression of dendrite growth by cross-flow in microfluidics

Formation of rough, dendritic deposits is a critical problem in metal electrodeposition processes and could occur in next-generation, rechargeable batteries that use metallic electrodes. Electroconvection, which originates from the coupling of the imposed electric field and a charged fluid near an electrode surface, is believed to be responsible for dendrite growth. However, few studies are performed at the scale of fidelity where root causes and effective strategies for controlling electroconvection and dendrite growth can be investigated in tandem. Using microfluidics, we showed that forced convection across the electrode surface (cross-flow) during electrodeposition reduced metal dendrite growth (97.7 to 99.4%) and delayed the onset of electroconvective instabilities. Our results highlighted the roles of forced convection in reducing dendrite growth and electroconvective instabilities and provided a route toward effective strategies for managing the consequences of instability in electrokinetics-based processes where electromigration dominates ion diffusion near electrodes.

Spontaneous and field-induced crystallographic reorientation of metal electrodeposits at battery anodes

The propensity of metal anodes of contemporary interest (e.g., Li, Al, Na, and Zn) to form non-planar, dendritic morphologies during battery charging is a fundamental barrier to achievement of full reversibility. We experimentally investigate the origins of dendritic electrodeposition of Zn, Cu, and Li in a three-electrode electrochemical cell bounded at one end by a rotating disc electrode. We find that the classical picture of ion depletion-induced growth of dendrites is valid in dilute electrolytes but is essentially irrelevant in the concentrated (≥1 M) electrolytes typically used in rechargeable batteries. Using Zn as an example, we find that ion depletion at the mass transport limit may be overcome by spontaneous reorientation of Zn crystallites from orientations parallel to the electrode surface to dominantly homeotropic orientations, which appear to facilitate contact with cations outside the depletion layer. This chemotaxis-like process causes obvious texturing and increases the porosity of metal electrodeposits.

Random Spacing between Metal Tree Electrodeposits in Linear DLA Arrays

When we examine the random growth of trees along a linear alley in a rural area, we wonder what governs the location of those trees, and hence the distance between adjacent ones. The same question arises when we observe the growth of metal electro-deposition trees along a linear cathode in a rectangular film of solution. We carry out different sets of experiments wherein zinc trees are grown by electrolysis from a linear graphite cathode in a 2D film of zinc sulfate solution toward a thick zinc metal anode. We measure the distance between adjacent trees, calculate the average for each set, and correlate the latter with probability and entropy. We also obtain a computational image of the grown trees as a function of parameters such as the cell size, number of particles, and sticking probability. The dependence of average distance on concentration is studied and assessed.

Sharp-interface model of electrodeposition and ramified growth

We present a sharp-interface model of two-dimensional ramified growth during quasisteady electrodeposition. Our model differs from previous modeling methods in that it includes the important effects of extended space-charge regions and nonlinear electrode reactions. The electrokinetics is described by a continuum model, but the discrete nature of the ions is taken into account by adding a random noise term to the electrode current. The model is validated by comparing its behavior in the initial stage with the predictions of a linear stability analysis. The main limitations of the model are the restriction to two dimensions and the assumption of quasisteady transport.

Role of electro-osmosis in the impedance response of microchannel-nanochannel interfaces

The influence of net fluid flow on the low-frequency ac response of a microchannel-nanochannel interface under dc bias is studied theoretically using a simple 1D model based on the Poisson-Nernst-Planck-Stokes equations. The model describes cross-sectional averaged transport wherein the electro-osmotic flow is controlled by the magnitude of the dc bias and captures essential features of the problem related to the micro-nano interface, specifically geometric focusing effects and nanochannel control of the net fluid flow. This model predicts behavior which differs from that predicted by a purely electrodiffusive formulation. The high-frequency edge of the Warburg branch of the complex impedance plot has a slope which deviates from the π/4 Warburg value, decreasing with increasing bias, and there are corresponding changes in the overall phase as seen in the Bode plots. This can be attributed to a streaming contribution to the capacitive reactance of the device as well an increase in the conductance of the depleted region, both due to net fluid flow. The increase in conductance, corresponding to reduced interfacial depletion, also permits dc currents above the classical electrodiffusive limit.

Recent Progress in Electrochemical Deposition without Supporting Electrolyte

Electrochemical deposition (ECD) of metals is a very old subject[l], which has considerable applications in the context of electroshaping or electroplating. Electrochemists and chemical engineers have long known the different growth conditions of these metal aggregates and the different parameters which drive morphological changes, at least empirically [2-4]. However, in the recent years, after the introduction of the concept of fractal aggregation[5,6], in the field of non-linear pattern formation[7,8], a lot of work has been devoted to the specific problem of growth of electrodeposits from binary electrolytes [9-51] (i.e. without supporting electrolyte). These studies aimed at understanding the morphology, on the large scale (∼1cm) of the deposits and, more specifically, the transitions between morphologies. It is the aim of this paper to review the progress which has been achieved in the past five years on this question.

A Growth Model For Ramified Electrochemical Deposition

We introduce a macroscopic model for the description of growth pattern formation in ramified electrochemical deposition. The theoretical model is formulated as a 2D time-dependent problem consisting in the Nernst-Planck equations for the concentration of the solute (cations and anions), coupled to a Poisson equation for the electrostatic potential and the Navier-Stokes equations for the solvent, with a moving boundary. A dimensional analysis is performed and a new set of dimensionless numbers governing the flow regime is derived. A 2D discrete version of these equations in a DBM scheme with a random moving boundary constitutes the computational model. We present numerical results which show that our growth model, with a proper variation of the set of dimensionless numbers, gives a reasonable picture of the interplay of the electroconvective, migration and diffusive motion of the ions near the growing tips.

Simulations of transport regime in electrodeposition in different viscosity scenarios

In this work we study the effects of viscosity variations in thin-layer electrochemical deposition (ECD) under galvanostatic conditions through experimental measurements and theoretical modeling. The theoretical model, written in terms of dimensionless quantities, describes diffusive, migratory and convective ion transport in a fluid under galvanostatic conditions. Experiments reveal that as viscosity increases, convection decreases when the cell resistance remains constant. Our numerical model predicts that as viscosity increases, electroconvection becomes less relevant and concentration and convective fronts slow down. The time scaling of this phenomenon is studied and compared to previously reported low viscosity solution studies.

Transition from gravito- to electroconvective regimes in thin-layer electrodeposition

The transition from gravitoconvective to electroconvective prevailing regimes in thin-layer electrochemical deposition is analyzed through variations of electrolyte viscosity at constant cell thickness. The distribution of velocity directions at the deposit front is a measure of the relative weight of electroconvection versus gravitoconvection, and a signature of that transition. The experiments are carried out under galvanostatic conditions in convection prevailing regimes. Particle image velocimetry reveals that at low viscosities, buoyancy driven convection dominates; as viscosity increases, electrically driven convection becomes more important, eventually prevailing. The transition is observed at 1.5 times the viscosity of water. The theoretical model presented reveals that an increase of the Poisson and Reynolds numbers and a decrease of the Peclet and electric Grashof numbers, when viscosity increases, makes the electroconvective motion relatively more important. The model predicts a transition at approximately two times the viscosity of water. We may conclude that, in a physicochemical hydrodynamic flow involving ions, under galvanostatic conditions, increasing viscosity damps gravitoconvection and enhances electroconvection.

Internal structure of dense electrodeposits

We report experimental investigations of the structure of dense patterns obtained during electrochemical deposition of copper in thin cells. The deposit correlation function reveals the periodic structuration of the patterns but shows that the primary spacing is not steady during the growth and that moreover it is not simply related to the diffusion length. Another measurable quantity is the occupancy ratio of the fingers in the cell. Its variation as a function of the experimental parameters is interpreted from specific properties of electrochemical growth. The results are discussed with respect to the well-known behavior of cellular solidification fronts.