Mechanism of a morphology transition in ramified electrochemical growth

Formation of magnetic nanowire arrays by cooperative lateral growth

Nanowires typically grow along their longitudinal axis, and the long-range order among wires sustains only when a template exists. Here, we report an unprecedented electrochemical growth of ordered metallic nanowire arrays from an ultrathin electrolyte layer, which is achieved by solidifying the electrolyte solution below the freezing temperature. The thickness of the electrodeposit is instantaneously tunable by the applied electric pulses, leading to parallel ridges on webbed film without using any template. An array of metallic nanowires with desired separation and width determined by the applied pulses is formed on the substrate with arbitrary surface patterns by etching away the webbed film thereafter. This work demonstrates a previously unrecognized fabrication strategy that bridges the gap of top-down lithography and bottom-up self-organization in making ordered metallic nanowire arrays over a large area with low cost.

First Principle Analysis on Pyridine Amide Derivatives’ Adsorption Behavior on the Pt (111) Surface

The reactivity and adsorption behavior of three pyridine amide additives (Nicotinamide, Pyridine-2-formamide and Pyridine-4-formamide) on the Pt (111) surface was studied by First principle methods. The quantum chemical calculations of molecular reactivity show that the frontier orbitals of the three additives are distributed around the pyridine ring, oxygen atom of carbonyl and nitrogen atom of amino, and the nucleophilic and electrophilic active centers are located on the nitrogen atoms of pyridine ring, oxygen atom of carbonyl and nitrogen atom of amino. All three molecules were adsorbed with the chemical adsorption on the Pt (111) surface, and the order of adsorption was Nicotinamide > Pyridine-2-formamide > Pyridine-4-formamide. The C and N atoms of three derivatives forms C-Pt and N-Pt bonds with the Pt atoms of the Pt (111) surface, which makes derivatives stably adsorb on the Pt surface and form a protective film. The protective film inhibits the diffusion of atoms to the surface of the growth center, so as to inhibit the formation of dendrite and obtain a smooth aluminum deposition layer.

Unexpected Propagation of Ultra-Lean Hydrogen Flames in Narrow Gaps

Very lean hydrogen flames were thought to quench in narrow confined geometries. We show for the first time how flames with very low fuel concentration undergo an unprecedented propagation in narrow gaps: H_{2}-air flames can survive very adverse conditions by breaking the reaction front into isolated flame cells that travel steadily in straight lines or split to perform a fractal-like propagation that resembles the pathway of starving fungi or bacteria. The combined effect of hydrogen mass diffusivity and intense heat losses act as the two main mechanisms that explain the experimental observations.

Stabilizing effect of tip splitting on the interface motion

Pattern-forming processes, such as electrodeposition, dielectric breakdown, or viscous fingering, are often driven by instabilities. Accordingly, the resulting growth patterns are usually highly branched fractal structures. However, in some of the unstable growth processes the envelope of the structure grows in a highly regular manner, with the perturbations smoothed out over the course of time. In this paper we show that the regularity of the envelope growth can be connected to small-scale instabilities leading to the tip splitting of the fingers at the advancing front of the structure. Whenever the growth velocity becomes too large, the finger splits into two branches. In this way it can absorb an increased flux and thus damp the instability. Hence, somewhat counterintuitively, the instability at a small scale results in a stability at a larger scale. The quantitative analysis of these effects is provided by means of the Loewner equation, which one can use to reduce the problem of the interface motion to that of the evolution of the conformal mapping onto the complex plane. This allows an effective analysis of the multifingered growth in a variety of different geometries. We show how the geometry impacts the shape of the envelope of the growing pattern and compare the results with those observed in natural systems.

Electrodeposition of aluminium foils on carbon electrodes in low temperature ionic liquid

Schematic illustration of aluminium foils on GC substrate by electrodeposition. It is significant to find the thickness value at which dendrites start occurring on foils at different current densities.

Fractal growth of platinum electrodeposits revealed by in situ electron microscopy

Fractals are commonly observed in nature and elucidating the mechanisms of fractal-related growth is a compelling issue for both fundamental science and technology. Here we report an in situ electron microscopy study of dynamic fractal growth of platinum during electrodeposition in a miniaturized electrochemical cell at varying growth conditions. Highly dendritic growth - either dense branching or ramified islands - are formed at the solid-electrolyte interface. We show how the diffusion length of ions in the electrolyte influences morphology selection and how instability induced by initial surface roughness, combined with local enhancement of electric field, gives rise to non-uniform branched deposition as a result of nucleation/growth at preferred locations. Comparing the growth behavior under these different conditions provides new insight into the fundamental mechanisms of platinum nucleation.

Nature of inclined growth in thin-layer electrodeposition under uniform magnetic fields

Electrochemical deposition (ECD) in thin cells in a vertical position relative to gravity, subject to an external uniform magnetic field, yields a growth pattern formation with dense branched morphology with branches tilted in the direction of the magnetic force. We study the nature of the inclined growth through experiments and theory. Experiments in ECD, in the absence of magnetic forces, reveal that a branch grows by allowing fluid to penetrate its tip and to be ejected from the sides through a pair of symmetric vortices attached to the tip. The upper vortices zone defines an arch separating an inner zone ion depleted and an outer zone in a funnel-like form with a concentrated solution through which metal ions are carried into the tip. When a magnetic field is turned on, vortex symmetry is broken, one vortex becoming weaker than the other, inducing an inclination of the funnel. Consequently, particles entering the funnel give rise to branch growth tilted in the same direction. Theory predicts, in the absence of a magnetic force, funnel symmetry induced through symmetric vortices driven by electric and gravitational forces; when the magnetic force is on, it is composed with the pair of clockwise and counterclockwise vortices, reducing or amplifying one or the other. In turn, funnel tilting modifies particle trajectories, thus, growth orientation.

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.

The Role of Coulombic Forces in Quasi-Two Dimensional Electrochemical Deposition

Recent work demonstrates the relevant influence of convection during growth pattern formation in thin-layer electrochemical deposition. Convection is driven mainly by coulombic forces due to local charges at the tip of the aggregation and by buoyancy forces due to concentration gradients. Here we study through physical experiments and numerical modeling the regime under which coulombic forces are important. In the experimental measurements fluid motion near the growing tips of the deposit is visualized with neutrally buoyant latex spheres and its speed measured with videomicroscope tracking techniques and image processing software. The numerical modeling consists in the solution of the 2D dimensionless Nernst-Planck equations for ion concentrations, the Poisson equation for the electric field and the Navier-Stokes equations for the fluid flow, and a stochastic growth rule for ion deposition. A new set of dimensionless numbers governing electroconvection dominated flows is introduced. Preliminary experimental measurements and numerical results indicate that in the electroconvection dominated regime coulombic forces increase with the applied voltage, and their influence over growth pattern formation can be assessed with the magnitude of the dimensionless electric Froude number. It is suggested that when this number decreases the deposit morphology changes from fractal to dense branching.

Monodisperse, micrometer-scale, highly crystalline, nanotextured Ag dendrites: rapid, large-scale, wet-chemical synthesis and their application as SERS substrates

In this letter, we report on our interesting finding that the direct mixing of aqueous AgNO(3) and NH(2)OH solutions at room temperature leads to rapid, high-yield production of monodisperse, micrometer-scale, highly crystalline, nanotextured Ag dendrites. The surface-enhanced Raman scattering (SERS) effect of these Ag dendrites was evaluated by using 4-aminothiophenol (p-ATP) as the Raman probe and the results demonstrate that they exhibit strong SERS effects.

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.

Electro-convective versus electroosmotic instability in concentration polarization

Electro-convection is reviewed as a mechanism of mixing in the diffusion layer of a strong electrolyte adjacent to a charge-selective solid, such as an ion exchange (electrodialysis) membrane or an electrode. Two types of electro-convection in strong electrolytes may be distinguished: bulk electro-convection, due to the action of the electric field upon the residual space charge of a quasi-electro-neutral bulk solution, and convection induced by electroosmotic slip, due to electric forces acting in the thin electric double layer of either quasi-equilibrium or non-equilibrium type near the solid/liquid interface. According to recent studies, the latter appears to be the likely source of mixing in the diffusion layer, leading to 'over-limiting' conductance in electrodialysis. Electro-convection near a planar uniform charge selective solid/liquid interface sets on as a result of hydrodynamic instability of one-dimensional steady state electric conduction through such an interface. We compare the results of linear stability analysis obtained for instabilities of this kind appearing in the full electro-convective and limiting non-equilibrium electroosmotic formulations. The short- and long-wave aspects of these instabilities are discussed along with the wave number selection principles.

Bulk electroconvective instability at high Péclet numbers

Bulk electroconvection pertains to flow induced by the action of a mean electric field upon the residual space charge in the macroscopic regions of a locally quasielectroneutral strong electrolyte. For a long time, controversy has existed in the literature as to whether quiescent electric conduction from such an electrolyte into a uniform charge-selective solid, such as a metal electrode or ion exchange membrane, is stable with respect to bulk electroconvection. While it was recently claimed that bulk electroconvective instability could not occur, this claim pertained to an aqueous, low-molecular-weight electrolyte characterized by an order-unity electroconvection Péclet number. In this paper, we show that the bulk electroconvection model transforms into the leaky dielectric model in the limit of infinitely large Péclet number. For the leaky dielectric model, conduction of the above-mentioned type is unstable, and so it is in the bulk electroconvection model for sufficiently large Péclet numbers. Such instability is sensitive to the ratio of the diffusivity of the cations to the anions. For infinite Péclet number, the case with equal ionic diffusivities is a bifurcation point separating stable and unstable regimes at the low-current limit. Further, for a cation-selective solid, when the Péclet number is finite and the anions are much more diffusive than the cations, an unreported bulk electroconvective instability is possible at low current. At higher currents and large Péclet numbers, we found that the system is unstable for all cation-to-anion diffusivity ratios, but passes from a monotonic instability to an oscillatory one as this ratio passes through unity.

Novel preparation of snowflake-like dendritic nanostructures of Ag or Au at room temperature via a wet-chemical route

In this letter we describe a novel but effective wet-chemical route for the simple preparation of snowflake-like dendritic nanostructures of Ag, which are homogeneous in size, carried out by directly mixing AgNO3 and p-phenylenediamine (PPD) aqueous solutions at room temperature. It reveals that such dendrites are aggregates of nanoparticles and highly crystalline in nature. It is found that the molar ratio of [PPD]/[Ag+] influences the final morphologies of the structures formed and that excessive PPD (the molar ratio of [PPD]/[Ag+] is higher than 1:1) is crucial to achieving dendrites. The possible dendritic growth mechanism is also predicted. This method can also be extended to the preparation of Au dendrites.

Long-range ordering effect in electrodeposition of zinc and zinc oxide

In this paper, we report the long-range ordering effect observed in the electro-crystallization of Zn and ZnO from an ultrathin aqueous electrolyte layer of ZnSO4 . The deposition branches are regularly angled, covered with random-looking, scalelike crystalline platelets of ZnO. Although the orientation of each crystalline platelet of ZnO appears random, transmission electron microscopy shows that they essentially possess the same crystallographic orientation as the single-crystalline zinc electrodeposit underneath. Based on the experimental observations, we suggest that this unique long-range ordering effect results from an epitaxial nucleation effect in electrocrystallization.

Bulk electroconvection in electrolyte

Bulk electroconvection pertains to flow induced by the action of the mean electric field upon the residual space charge in the macroscopic regions of a locally quasielectroneutral strong electrolyte. There existed a long time controversy in the literature as to whether quiescent electric conduction from such an electrolyte into a uniform charge selective solid, such as a metal electrode or an ion exchange membrane, is stable with respect to bulk electroconvection and whether bulk electroconvection at a nonuniform solid of this type may develop into a fully fledged flow. Numerical results reported in this paper confirm previous conclusions of a linear stability analysis concerning the nonexistence of bulk electroconvective instability, while we suggest that bulk electroconvection at a nonuniform charge selective solid results in a fully fledge flow on the length scale of nonuniformity of the surface.

Electroconvective instability in concentration polarization and nonequilibrium electro-osmotic slip

This paper concerns the comparison of electroconvective instability in concentration polarization at an ion-selective membrane with previously reported nonequilibrium electro-osmotic instability. Electro-osmotic formulation represents an asymptotic limit case of the electroconvective one. An improved nonequilibrium electro-osmotic slip formula is derived. Linear stability analysis for various nonequilibrium electro-osmotic formulations is carried out, including the analytic studies of the short- and long-wave limits. The obtained results are compared with those for a full electroconvective formulation. It is observed that the shortwave singularity typical for the nonequilibrium electro-osmotic instability is removed in the full electroconvective formulation. The effect of ionic diffusivities ratio on stability is discussed.

Effect of interfacial reaction rate on the morphogenesis of nanostructured coatings in a simulated electrodeposition process

Brownian dynamics simulations (BDSs) are performed to investigate the influence of interfacial electrochemical reaction rate on the evolution of coating morphology on circular fibres. The boundary condition for the fluid phase concentration, representing the balance between the rates of interfacial reaction and transport of ions by bulk diffusion, is incorporated into the BDS by using a reaction probability, P(s). Different modes of growth, ranging from diffusion limited ([Formula: see text]) to reaction controlled [Formula: see text], are studied. It is found that, consistent with experimental observations, two distinct morphological regimes exist, with a dense and uniform structure for [Formula: see text] (reaction limited deposition (RLD)) and an open and porous one as [Formula: see text] (diffusion limited deposition (DLD)). An analysis of the fractal dimension indicates that this morphological transition occurs at P(s)≈0.3. Long-time power-law scalings for the evolution of thickness [Formula: see text] and roughness (ξ) of the coating exist, i.e. [Formula: see text] with 0.86≤α≤0.91 and 0.56≤β≤0.93 for 0.01≤P(s)≤1. These values are different from those reported for sequential, pseudo-time lattice simulations on planar surfaces, signifying the importance of multiparticle dynamics and surface curvature. The internal structure and porosity of the coating are characterized quantitatively by the radial density profile, pair correlation function, two-point probability function, void distribution function and pore area distribution. For RLD the radial density, ρ(n), remains nearly constant, while for DLD ρ(n) follows a power law, [Formula: see text]. The coating exhibits short ranged order in the RLD regime while a long range order is created by DLD. The void distribution function becomes broader with increasing P(s), indicating that in the RLD regime the coating consists of small and spherical pores, while in the DLD regime large and elongated pores are obtained. The pore area distribution shows narrower distributions in DLD for small pores, while the area of the largest pore increases by nearly three orders of magnitude as one moves from the RLD to the DLD regime. Such morphological diversity could be potentially exploited for applications such as percolation, catalysis and surface protection.

Absence of bulk electroconvective instability in concentration polarization

The problem of bulk electroconvective stability of quiescent electric conduction from an electrolyte solution into a charge-selective solid (ion-exchange membrane) has been revised. It is shown through a numerical solution of the linear stability problem that previously reported bulk electroconvective instability does not exist. This numerical result is supported by the short wave asymptotic analysis. Our comprehensive study confirms the result of an earlier, less detailed, report by Buchanan and Saville.

Chirality of electrodeposits grown in a magnetic field

Electrodeposits grown around a point cathode in a flat, horizontal electrochemical cell have fractal form. When grown in the presence of a perpendicular applied magnetic field, the deposits develop a spiral structure with chirality which reverses on switching the field direction. These structures are modeled numerically using biased variants of the diffusion limited aggregation (DLA) model. The effects of electric and magnetic fields are modeled successfully by varying the probabilities that a random walker will move in a given direction as a result of a Coulomb force and the Lorentz force-induced flow of electrolyte past the deposit surface. By contrast, a numerical model which considers only the effect of the Lorentz force on individual ions, without reference to the surface of the growing deposit, produces spiral structures with incorrect chirality. The modified DLA model is related to the differential equations for diffusion, migration, and convection. Length scales in the problem are understood by associating the step length of the random walker with the diffusion layer thickness, the lookup radius with the hydrodynamic boundary layer thickness and a point on the numerical deposit with a nucleation center for growth of a crystallite.

Three-dimensional nature of ion transport in thin-layer electrodeposition

A generalized three-dimensional model for ion transport in electrodeposition is introduced. Ion transport is mainly governed by diffusion, migration, and convection. When convection prevails, in particular, in the limiting case of gravity-driven convection, the model predicts concentration shells and convection rolls and their interaction mode with a deposit tip: shell and roll bend and surround the tip forming a three-dimensional envelope tube squeezed at the deposit tip. In the limiting case of electrically driven convection, a vortex ring and an electric spherical drop crowning the deposit tip are predicted. When gravity and electric convection are both relevant, the interaction of ramified deposits, vortex tubes and rings, and electric spherical drops, leading to complex helicoidal flow, is predicted. Many of these predictions are experimentally observed, suggesting that ion transport underlying dendrite growth is remarkably well captured by our model.

Formation of nanostructured copper filaments in electrochemical deposition

In this paper, we report in detail the studies of a different self-organized copper electrodeposition carried out in an ultrathin layer of CuSO4 electrolyte. On a macroscopic scale, the morphology of the electrodeposit is fingerlike. Microscopically, each fingering branch consists of long, straight copper filaments with periodic corrugated nanostructures. Branching rate of the electrodeposit is significantly decreased, compared with the patterns grown in conventional systems. Detailed information of the growth environment in the ultrathin electrodeposition system is provided, the formation mechanism of the periodic nanostructures on the deposit filaments is explored, and the origin of the significant descent of branching rate of the electrodeposit is discussed.

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.

Growth pulsations in symmetric dendritic crystallization in thin polymer blend films

The crystallization of polymeric and metallic materials normally occurs under conditions far from equilibrium, leading to patterns that grow as propagating waves into the surrounding unstable fluid medium. The Mullins-Sekerka instability causes these wave fronts to break up into dendritic arms, and we anticipate that the normal modes of the dendrite tips have a significant influence on pattern growth. To check this possibility, we focus on the dendritic growth of polyethylene oxide in a thin-film geometry. This crystalline polymer is mixed with an amorphous polymer (polymethyl-methacrylate) to "tune" the morphology and clay was added to nucleate the crystallization. The tips of the main dendrite trunks pulsate during growth and the sidebranches, which grow orthogonally to the trunk, pulsate out of phase so that the tip dynamics is governed by a limit cycle. The pulsation period P increases sharply with decreasing film thickness L and then vanishes below a critical value L(c) approximately 80 nm. A change of dendrite morphology accompanies this transition.

Nonequilibrium pattern formation in the crystallization of polymer blend films

We show that the morphology of polyethylene oxide crystallization in thin films can be tuned to obtain circular spherulites, seaweed and symmetric dendrites, and fractal aggregation forms through the addition of clay particles and the amorphous polymer, polymethyl methacrylate. The thin-film polymer crystallization patterns are compared to a two-dimensional phase field model of dendritic growth in Ni/Cu alloys with a variable surface tension anisotropy epsilon. Some aspects of polymer crystallization patterns can be understood from the phase field calculations, but a more general model is required to describe the full range of observed patterns.

Nanostructured copper filaments in electrochemical deposition

In this Letter we report a novel self-organized copper electrodeposition in an ultrathin layer of CuSO4 electrolyte. The macroscopic fingering branches of the deposit consist of long copper filaments covered with periodic corrugated nanostructures. The mechanism of the nanostructure formation is explored and the origin of the significant descent of the branching rate in electrodeposition is discussed. We suggest that this growth phenomenon provides deeper insights into the role of diffusion and migration on pattern formation in electrodeposition.

Electro-osmotically induced convection at a permselective membrane

The paper is concerned with convection at an ion exchange electrodialysis membrane induced by nonequilibrium electro-osmosis in the course of concentration polarization under the passage of electric current through the membrane. Derivation of nonequilibrium electro-osmotic slip condition is recapitulated along with the linear stability analysis of quiescent electrodiffusion through a flat ion exchange membrane. Results of numerical calculation for nonlinear steady state convection, developing from the respective instability, are reported along with those for a slightly wavy membrane. Besides these results, we report those of time dependent calculations for periodic and chaotic oscillations, resulting from instability of the respective steady state flows, and also the results of recent experiments with modified membranes. These latter rule in favor of electro-osmotic versus bulk electroconvective origin of overlimiting conductance through ion exchange membranes.