Electrodeposition from a binary electrolyte: new developments and applications

A dynamically equivalent atomistic electrochemical paradigm for the larger-scale experiments

Electrochemical systems possess a considerable part of modern technologies, such as the operation of rechargeable batteries and the fabrication of electronic components, which are explored both experimentally and computationally. The largest gap between the experimental observations and atomic-level simulations is their orders-of-magnitude scale difference. While the largest computationally affordable scale of the atomic-level computations is ∼ns and ∼nm, the smallest reachable scale in the typical experiments, using very high-precision devices, is ∼s and ∼μm. In order to close this gap and correlate the studies in the two scales, we establish an equivalent simulation setup for the given general experiment, which excludes the microstructure effects (i.e., solid-electrolyte interface), using the coarse-grained framework. The developed equivalent paradigm constitutes the adjusted values for the equivalent length scale (i.e., lEQ), diffusivity (i.e., DEQ), and voltage (i.e., VEQ). The time scale for the formation and relaxation of the concentration gradients in the vicinity of the electrode matches for both smaller scale (i.e., atomistic) equivalent simulations and the larger scale (i.e., continuum) experiments and could be utilized for exploring the cluster-level inter-ionic events that occur during the extended time periods. The developed model could offer insights for forecasting experiment dynamics and estimating the transition period to the steady-state regime of operation.

Dendritic propagation on circular electrodes: The impact of curvature on the packing density

The dendritic growth in rechargeable batteries is one of the hurdles for the utilization of high energy-density elements, such as alkaline metals, as the electrode. Herein we explore the preventive role of the curved electrode surface in the cylindrical electrode design versus the flat geometry on the stochastic evolution of the dendritic crystals. In this regard we establish a coarse-grained Monte Carlo paradigm in the polar coordinates (r,θ), which runs in a larger scale of time and space (∼μs,∼nm ) than those of interionic collisions (∼fs, Å). Subsequently we track the density and the maximum reach of the microstructures in real time, and we elaborate on the underlying mechanisms for their correlation of the relative dendrite measure with the electrode curvature. Such quantification of the positive impact of the curvature on suppressing dendrites could be utilized as an effective longevity design parameter, particularly for the cases prone to dendritic propagation.

Observation of Remote Electroconvection and Inert-Cation Concentration Valley within Supporting Electrolytes in a Microfluidic-Based Electrochemical Device

The electrochemical system is playing an increasingly important role in the advanced technology development for drinkable water and energy storage. While the binary electrolyte has been widely studied, such as the associated intriguing interfacial instabilities, multi-component electrolyte is by far less known. Here, based on the classic Cu|CuSO₄ |Cu electrochemical system, the effect of supporting electrolyte is systematically investigated by highlighting the inert cations. In an annulus microfluidic device, the suppression of a previously known electro-osmotic instability and the emergence of an array of the remote electroconvection along the azimuthal direction is found. A distinctive inert-cation concentration valley propagates radially outward at a speed limited by the electromigration velocity. Remarkably, the simultaneous visualization of spatiotemporal evolution demonstrates the correlation of the concentration valley and electroconvection at a microscopic level. The underlying physical mechanism of their correlation is discussed, and the scaling analysis agrees with experiments. This work might inspire more future work on the multi-component electrolyte, such as for the suppression of interfacial hydrodynamic instability and mitigation of dendrite growth, with the technological implications for water treatment and energy storage in batteries.

A fully coupled hybrid lattice Boltzmann and finite difference method-based study of transient electrokinetic flows

Transient electrokinetic (EK) flows involve the transport of conductivity gradients developed as a result of mixing of ionic species in the fluid, which in turn is affected by the electric field applied across the channel. The presence of three different coupled equations with corresponding different time scales makes it difficult to model the problem using the lattice Boltzmann method (LBM). The present work aims to develop a hybrid LBM and finite difference method (FDM)-based model which can be used to study the electro-osmotic flows (EOFs) and the onset of EK instabilities using an Ohmic model, where fluid and conductivity transport are solved using LBM and the electric field is solved using FDM. The model developed will be used to simulate three different problems: (i) EOF with varying zeta-potential on the wall, (ii) similitude in EOF, and (iii) EK instabilities due to the presence of conductivity gradients. Problems (i) and (ii) will be compared with the analytical results and problem (iii) will be compared with the simulations of a spectral method-based numerical model. The results obtained from the present simulations will show that the developed model is capable of studying transient EK flows and of predicting the onset of instability.

Finite-pulse waves for efficient suppression of evolving mesoscale dendrites in rechargeable batteries

The ramified and stochastic evolution of dendritic microstructures has been a major issue on the safety and longevity of rechargeable batteries, particularly for the utilization of high-energy metallic electrodes. We analytically develop criteria for the pulse characteristics leading to the effective halting of the ramified electrodeposits grown during extensive timescales beyond inter-ionic collisions. Our framework is based on the competitive interplay between diffusion and electromigration and tracks the gradient of ionic concentration throughout the entire cycle of pulse-rest as a critical measure for heterogeneous evolution. In particular, the framework incorporates the Brownian motion of the ions and investigates the role of the geometry of the electrodeposition interface. Our experimental observations verify the analytical developments, where the dimension-free developments allows the application to the electrochemical systems of various scales.

Confined Electroconvective Vortices at Structured Ion Exchange Membranes

In this paper, we investigate electroconvective ion transport at cation exchange membranes with different geometry square-wave structures (line undulations) experimentally and numerically. Electroconvective microvortices are induced by strong concentration polarization once a threshold potential difference is applied. The applied potential required to start and sustain electroconvection is strongly affected by the geometry of the membrane. A reduction in the resistance of approximately 50% can be obtained when the structure size is similar to the mixing layer (ML) thickness, resulting in confined vortices with less lateral motion compared to the case of flat membranes. From electrical, flow, and concentration measurements, ion migration, advection, and diffusion are quantified, respectively. Advection and migration are dominant in the vortex ML, whereas diffusion and migration are dominant in the stagnant diffusion layer. Numerical simulations, based on Poisson-Nernst-Planck and Navier-Stokes equations, show similar ion transport and flow characteristics, highlighting the importance of membrane topology on the resulting electrokinetic and electrohydrodynamic behavior.

Dendrite Suppression by Shock Electrodeposition in Charged Porous Media

It is shown that surface conduction can stabilize electrodeposition in random, charged porous media at high rates, above the diffusion-limited current. After linear sweep voltammetry and impedance spectroscopy, copper electrodeposits are visualized by scanning electron microscopy and energy dispersive spectroscopy in two different porous separators (cellulose nitrate, polyethylene), whose surfaces are modified by layer-by-layer deposition of positive or negative charged polyelectrolytes. Above the limiting current, surface conduction inhibits growth in the positive separators and produces irregular dendrites, while it enhances growth and suppresses dendrites behind a deionization shock in the negative separators, also leading to improved cycle life. The discovery of stable uniform growth in the random media differs from the non-uniform growth observed in parallel nanopores and cannot be explained by classic quasi-steady "leaky membrane" models, which always predict instability and dendritic growth. Instead, the experimental results suggest that transient electro-diffusion in random porous media imparts the stability of a deionization shock to the growing metal interface behind it. Shock electrodeposition could be exploited to enhance the cycle life and recharging rate of metal batteries or to accelerate the fabrication of metal matrix composite coatings.

Suppression of lithium dendrite growth by introducing a low reduction potential complex cation in the electrolyte

A low reduction potential complex cation (LRPCC) N-methyl-N-butylpiperidinium was introduced to the LiPF₆/EC/DEC electrolyte to investigate its effect on the interface properties of a lithium anode.

Morphological instability during steady electrodeposition at overlimiting currents

We present a linear stability analysis of a planar metal electrode during steady electrodeposition. We extend the previous work of Sundstrom and Bark by accounting for the extended space-charge density, which develops at the cathode once the applied voltage exceeds a few thermal voltages. In accordance with Chazalviel's conjecture, the extended space-charge region is found to greatly affect the morphological stability of the electrode. To supplement the numerical solution of the stability problem, we have derived analytical expressions valid in the limit of low and high voltage, respectively.

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.

Dynamics of microvortices induced by ion concentration polarization

We investigate the coupled dynamics of the local hydrodynamics and global electric response of an electrodialysis system, which consists of an electrolyte solution adjacent to a charge selective membrane under electric forcing. Under a dc electric current, counterions transport through the charged membrane while the passage of co-ions is restricted, thereby developing ion concentration polarization (ICP) or gradients. At sufficiently large currents, simultaneous measurements of voltage drop and flow field reveal several distinct dynamic regimes. Initially, the electrodialysis system displays a steady Ohmic voltage difference (ΔV_{ohm}), followed by a constant voltage jump (ΔV_{c}). Immediately after this voltage increase, microvortices set in and grow both in size and speed with time. After this growth, the resultant voltage levels off around a fixed value. The average vortex size and speed stabilize as well, while the individual vortices become unsteady and dynamic. These quantitative results reveal that microvortices set in with an excess voltage drop (above ΔV_{ohm}+ΔV_{c}) and sustain an approximately constant electrical conductivity, destroying the initial ICP with significantly low viscous dissipation.

Electro-osmotic pumping and ion-concentration polarization based on conical nanopores

A numerical investigation is performed into the characteristics of an electro-osmotic pump consisting of a negatively charged conical nanopore. It is shown that the dependence of the flow rectification effect on the bias direction is the reverse of that of the ion current rectification effect. Moreover, the nozzle mode (i.e., the bias is applied from the base side of the nanopore to the tip side) has a higher flow rate compared to the diffuser mode (i.e., the bias is applied from the tip side of the nanopore to the base side). The results showed that the ion-concentration polarization effect occurred inside the conical nanopore, resulting in surface conduction dominating in the ionic current. The ions inside the nanopore are depleted and enriched under the nozzle mode and the diffuser mode, respectively. As a result, the electro-osmotic pump yields a greater pumping pressure, flow rate, and energy conversion efficiency when operating in the nozzle mode. In addition, we also investigated the flow rate rectification behavior for the conical nanopore. The best flow rate rectification factor in this work is 2.06 for an electrolyte concentration of 10(-3) M.

Equilibrium electroconvective instability

Since its prediction 15 years ago, hydrodynamic instability in concentration polarization at a charge-selective interface has been attributed to nonequilibrium electro-osmosis related to the extended space charge which develops at the limiting current. This attribution had a double basis. On the one hand, it has been recognized that neither equilibrium electro-osmosis nor bulk electroconvection can yield instability for a perfectly charge-selective solid. On the other hand, it has been shown that nonequilibrium electro-osmosis can. The first theoretical studies in which electro-osmotic instability was predicted and analyzed employed the assumption of perfect charge selectivity for the sake of simplicity and so did the subsequent studies of various time-dependent and nonlinear features of electro-osmotic instability. In this Letter, we show that relaxing the assumption of perfect charge selectivity (tantamount to fixing the electrochemical potential of counterions in the solid) allows for the equilibrium electroconvective instability. In addition, we suggest a simple experimental test for determining the true, either equilibrium or nonequilibrium, origin of instability in concentration polarization.

Over-limiting current and control of dendritic growth by surface conduction in nanopores

Understanding over-limiting current (faster than diffusion) is a long-standing challenge in electrochemistry with applications in desalination and energy storage. Known mechanisms involve either chemical or hydrodynamic instabilities in unconfined electrolytes. Here, it is shown that over-limiting current can be sustained by surface conduction in nanopores, without any such instabilities, and used to control dendritic growth during electrodeposition. Copper electrodeposits are grown in anodized aluminum oxide membranes with polyelectrolyte coatings to modify the surface charge. At low currents, uniform electroplating occurs, unaffected by surface modification due to thin electric double layers, but the morphology changes dramatically above the limiting current. With negative surface charge, growth is enhanced along the nanopore surfaces, forming surface dendrites and nanotubes behind a deionization shock. With positive surface charge, dendrites avoid the surfaces and are either guided along the nanopore centers or blocked from penetrating the membrane.

Dynamics of Lithium Dendrite Growth and Inhibition: Pulse Charging Experiments and Monte Carlo Calculations

Short-circuiting via dendrites compromises the reliability of Li-metal batteries. Dendrites ensue from instabilities inherent to electrodeposition that should be amenable to dynamic control. Here, we report that by charging a scaled coin-cell prototype with 1 ms pulses followed by 3 ms rest periods the average dendrite length is shortened ∼2.5 times relative to those grown under continuous charging. Monte Carlo simulations dealing with Li(+) diffusion and electromigration reveal that experiments involving 20 ms pulses were ineffective because Li(+) migration in the strong electric fields converging to dendrite tips generates extended depleted layers that cannot be replenished by diffusion during rest periods. Because the application of pulses much shorter than the characteristic time τc ∼ O(∼1 ms) for polarizing electric double layers in our system would approach DC charging, we suggest that dendrite propagation can be inhibited (albeit not suppressed) by pulse charging within appropriate frequency ranges.

Overlimiting current and shock electrodialysis in porous media

Most electrochemical processes, such as electrodialysis, are limited by diffusion, but in porous media, surface conduction and electroosmotic flow also contribute to ionic flux. In this article, we report experimental evidence for surface-driven overlimiting current (faster than diffusion) and deionization shocks (propagating salt removal) in a porous medium. The apparatus consists of a silica glass frit (1 mm thick with a 500 nm mean pore size) in an aqueous electrolyte (CuSO4 or AgNO3) passing ionic current from a reservoir to a cation-selective membrane (Nafion). The current-voltage relation of the whole system is consistent with a proposed theory based on the electroosmotic flow mechanism over a broad range of reservoir salt concentrations (0.1 mM to 1.0 M) after accounting for (Cu) electrode polarization and pH-regulated silica charge. Above the limiting current, deionized water (≈10 μM) can be continuously extracted from the frit, which implies the existence of a stable shock propagating against the flow, bordering a depleted region that extends more than 0.5 mm across the outlet. The results suggest the feasibility of shock electrodialysis as a new approach to water desalination and other electrochemical separations.

Rate-Dependent Morphology of Li2O2 Growth in Li-O2 Batteries

Compact solid discharge products enable energy storage devices with high gravimetric and volumetric energy densities, but solid deposits on active surfaces can disturb charge transport and induce mechanical stress. In this Letter, we develop a nanoscale continuum model for the growth of Li2O2 crystals in lithium-oxygen batteries with organic electrolytes, based on a theory of electrochemical nonequilibrium thermodynamics originally applied to Li-ion batteries. As in the case of lithium insertion in phase-separating LiFePO4 nanoparticles, the theory predicts a transition from complex to uniform morphologies of Li2O2 with increasing current. Discrete particle growth at low discharge rates becomes suppressed at high rates, resulting in a film of electronically insulating Li2O2 that limits cell performance. We predict that the transition between these surface growth modes occurs at current densities close to the exchange current density of the cathode reaction, consistent with experimental observations.

Fractal structures in two-metal electrodeposition systems II: Cu and Zn

In this second part of our study on fractal co-electrochemical deposition, we investigate the Cu-Zn system. Macroscopic and microscopic inspection shows a sensitive dependence of the morphology of the final pattern on initial concentrations. The pattern is seen to undergo a transition from classical dendrites to randomly ramified deposits, with each slight increase in [Cu(2+)](0), while [Zn(2+)](0) is maintained constant. The variational trends in chemical composition, growth velocity, and fractal dimension with increasing [Cu(2+)](0) are analyzed. The latter is seen to generally increase with copper (II) ion concentration. In contrast, the growth rate of the deposits is seen to decrease with increasing concentration of Cu(2+) ions. A new probe of dense ramified morphology, the pattern density, is introduced and seen to increase with [Cu(2+)](0). XRD measurements reveal that the observed properties correlate with the birth of copper-rich nuclei, which disrupt the crystalline anisotropy of the two-metal alloy.

Deionization shocks in microstructures

Salt transport in bulk electrolytes is limited by diffusion and advection, but in microstructures with charged surfaces (e.g., microfluidic devices, porous media, soils, or biological tissues) surface conduction and electro-osmotic flow also contribute to ionic fluxes. For small applied voltages, these effects lead to well known linear electrokinetic phenomena. In this paper, we predict some surprising nonlinear dynamics that can result from the competition between bulk and interfacial transport at higher voltages. When counterions are selectively removed by a membrane or electrode, a "deionization shock" can propagate through the microstructure, leaving in its wake an ultrapure solution, nearly devoid of coions and colloidal impurities. We elucidate the basic physics of deionization shocks and develop a mathematical theory of their existence, structure, and stability, allowing for slow variations in surface charge or channel geometry. Via asymptotic approximations and similarity solutions, we show that deionization shocks accelerate and sharpen in narrowing channels, while they decelerate and weaken, and sometimes disappear, in widening channels. These phenomena may find applications in separations (deionization, decontamination, biological assays) and energy storage (batteries, supercapacitors) involving electrolytes in microstructures.

Overlimiting current in a microchannel

We revisit the classical problem of diffusion-limited ion transport to a membrane (or electrode) by considering the effects of charged sidewalls. Using simple mathematical models and numerical simulations, we identify three basic mechanisms for overlimiting current in a microchannel: (i) surface conduction carried by excess counterions, which dominates for very thin channels, (ii) convection by electro-osmotic flow on the sidewalls, which dominates for thicker channels, and (iii) transitions to electro-osmotic instability on the membrane end in very thick channels. These intriguing electrokinetic phenomena may find applications in biological separations, water desalination, and electrochemical energy storage.

Potential-induced copper periodic micro-/nanostructures by electrodeposition on silicon substrate

We demonstrate the fabrication of large scale nano- and micropatterned copper periodic structures on a silicon substrate without imposed templates. In the electrodeposition process, we employ a periodic variation voltage in an ultrathin layer of concentrated CuSO(4) electrolyte. The pattern can be controlled by varying the frequency of the applied potential. We suggest that the observed periodic micro-/nanostructures are caused by the lag of the migrating ion concentration profile versus the applied voltage profile near the tip of the growth.