Levich Equation Research Articles

Silver triangular nanoplates as electrocatalyst for oxygen reduction reaction

Triangular Ag nanoplates with large and small sizes were successfully synthesized for oxygen electroreduction. From the results of the x-ray diffraction analysis, it was concluded that Ag nanoplates of small size are the crystals that are essentially composed of (111) planes. The data provided by electrochemical measurement and the Koutecky–Levich equation showed that the electron numbers involved in the oxygen reduction reaction of small and large Ag nanoplates are 3.27 and 3.16, respectively. Small Ag nanoplates exhibit maximum activity towards the oxygen reduction reaction.

On application of lubrication approximations to nonunidirectional coating flows with clean and surfactant interfaces

In this work, the characteristic properties of the lubrication approximation are studied and its weak ellipticity is established, in contradistinction to the commonly accepted parabolic character of the lubrication equations resulting from the underlying unidirectional flow assumption. The weak ellipticity property allows the lubrication analysis to capture flow topologies around stagnation points, contact lines, and flows over edges, all of which normally require elliptic operators to be accounted for. This is used to explain the empirically observed overperformance of the lubrication approximation from the perspective of characteristic analysis. While the analysis is developed in the context of the classical Landau–Levich problem of dip-coating, which is known to possess an interfacial stagnation point both in the clean and surfactant interface cases, the analysis is general since the Landau–Levich equation is common to many other lubrication problems. The analytical approach presented here when applied to the surfactant interface case, also allows one to establish a new physical result: a variation of the bulk surfactant concentration is the necessary condition for the film thickening phenomenon in the Landau–Levich problem to occur due to surfactant-induced Marangoni effects.

Codeposition of copper and tin from acid sulphate solutions containing gluconic acid

RDE voltammetry, XPS and XRD techniques were applied to investigate the codeposition of copper and tin from acid gluconate solutions. Voltammograms contain two plateaus of limiting current of diffusive nature which obeys Levich equation. Underpotential deposition of tin occurs at potentials 0.3 V higher than the equilibrium potential of Sn|Sn(II) electrode. Cu–Sn deposits contain carbon and oxygen that prevail at the surface and are found in the deeper layers of coatings. Chemosorption of gluconic acid with its partial destruction is supposed to take place. Bright Cu–Sn coatings are obtained when the quantity of inclusions is sufficiently high. Cu–Sn coatings obtained in the UPD area consist of α phase or solid solution of tin in copper and a small amount of pure copper. The β-CuSn and δ-CuSn phases as well as a small amount of η phase were detected at −0.31 V. At a more negative potential (−0.4 V) Cu–Sn coatings contain the pure Sn phase, η phase and a small amount of β-CuSn.

Alumina Solubility and Diffusion Coefficient of the Dissolved Alumina Species in Low-Temperature Fluoride Electrolytes

The solubility of alumina was measured by rotating an alumina cylinder (~500 rpm) in a high-purity melt for ~3 to 6 hours, crushing and sampling the frozen melt, and determining the oxygen content in a Leco analyzer. The alumina solubilities determined were as follows: (1) 3.2 ± 0.3 wt pct in NaF-AlF3 eutectic at 1023 K (750 °C); (2) 3.0 ± 0.3 wt pct in NaF-AlF3-CaF2 (5 wt pct) at 1023 K (750 °C); and (3) 5.2 ± 0.5 wt pct in a KF-AlF3 eutectic at 1003 K (730 °C). The alumina solubility in the KF-AlF3 eutectic was 2 wt pct more than in the sodium analogue, offering the possibility of operating a low-temperature aluminum smelting cell without the need for an alumina slurry. The diffusion coefficient of the dissolved alumina species was determined in the NaF-AlF3 eutectic at 1023 K (750 °C) using the rotating disc method and applying the Levich equation. Through a limited range of rotation rates, the system seemed to be mass-transfer controlled, and the diffusion coefficient was estimated to be in the range 1.8 to 2.2 × 10−6 cm2 s−1. This value is about five times lower than the values encountered at traditional aluminum smelting temperatures (~1233 K (960 °C)) and would result in relatively low mass transfer coefficients.

Fabrication of Versatile Channel Flow Cells for Quantitative Electroanalysis Using Prototyping

Here we demonstrate the use of microstereolithography (MSL), a 3D direct manufacturing technique, as a viable method to produce small-scale microfluidic components for electrochemical flow detection. The flow cell is assembled simply by resting the microfabricated component on the electrode of interest and securing with thread! This configuration allows the use of a wide range of electrode materials. Furthermore, our approach eliminates the need for additional sealing methods, such as adhesives, waxes, and screws, which have previously been deployed. In addition, it removes any issues associated with compression of the cell chamber. MSL allows a reduction of the dimensions of the channel geometry (and the resultant component) and, compared to most previously produced devices, it offers a high degree of flexibility in the design, reduced manufacture time, and high reliability. Importantly, the polymer utilized does not distort so that the cell maintains well-defined geometrical dimensions after assembly. For the studies herein the channel dimensions were 3 mm wide, 3.5 mm long, and 192 or 250 mum high. The channel flow cell dimensions were chosen to ensure that the substrate electrodes experienced laminar flow conditions, even with volume flow rates of up to 64 mL min(-1) (the limit of our pumping system). The steady-state transport-limited current response, for the oxidation of ferrocenylmethyl trimethylammonium hexaflorophosphate (FcTMA(+)), at gold and polycrystalline boron doped diamond (pBDD) band electrodes was in agreement with the Levich equation and/or finite element simulations of mass transport. We believe that this method of creating and using channel flow electrodes offers a wide range of new applications from electroanalysis to electrocatalysis.

A cyclo olefin polymer microfluidic chip with integrated gold microelectrodes for aqueous and non-aqueous electrochemistry

This paper presents an entirely polymeric microfluidic system, made of cyclo olefin polymer (COP), with integrated gold microband electrodes for electrochemical applications in organic media. In the present work, we take advantage of the COP's high chemical stability to polar organic solvents in two different ways: (i) to fabricate gold microelectrodes using COP as a substrate by standard lithographic and lift-off techniques; and (ii) to perform electrochemical experiments in organic media. In particular, fourteen parallel gold microelectrodes with a width of 14 microm and separated from their closest neighbour by 16 microm were fabricated by lithographic and lift-off techniques on a 188 microm thick COP sheet. A closed channel configuration was obtained by pressure-assisted thermal bonding between the COP sheet containing the microelectrodes and a microstructured COP sheet, where a 3 cm long, 50 microm wide and 24 microm deep channel was fabricated via hot embossing. Cyclic voltammetric measurements were carried out in aqueous and organic media, using a solution consisting of 5 mM ferrocyanide/ferricyanide in 0.5 M KNO(3) and 5 mM ferrocene in 0.1 M TBAP/acetonitrile, respectively. Experimental currents obtained for different flow rates ranging from 1 to 10 microL min(-1) were compared to the theoretical steady state currents calculated by the Levich equation for a band electrode (R. G. Compton, A. C. Fisher, R. G. Wellington, P. J. Dobson and P. A. Leigh, J. Phys. Chem., 1993, 97, 10410-10415). In both cases, the difference between the experimental and the predicted data is less than 5%, thus validating the behaviour of the fabricated device. This result opens the possibility to use a microfluidic system made entirely from COP with integrated microband electrodes in organic electroanalysis and in electrosynthesis.

Biphasic Numerical Simulation of a Rotating Disc Electrochemical Cell

On electrochemical studies involving forced convection, the cell with rotating disc is the most widely used. Traditionally, Levich equation is used to interpret the information obtained from physical experiments. However, electrochemical results can be accurately interpreted through this equation only if the velocity field near the electrode active face is in accordance with the ideal behavior described by Cochran. In this work, the Computational Fluid Dynamics (CFD) technique was employed to determine the effect of the distance between the electrode active surface and the cell bottom on the cell inner hydrodynamic behavior. Biphasic 3D numerical simulations were performed using the commercial software Fluent. Numerical results were validated with experimental data. A simple rule for the optimal distance between the electrode active surface and the cell bottom is presented in this work.

Evaluation of the Zn 2+ transport properties through a cation-exchange membrane by chronopotentiometry

In this work the effect of zinc concentration, pH, and boric acid concentration on the zinc transport properties through an IONICS 67-HMR-412 cation-exchange membrane was evaluated. The limiting current density and the transport numbers were determined by means of chronopotentiometry. A model between the limiting current density and the bulk zinc concentration was established, assuming a potential relationship between the zinc transport number through the membrane and the bulk zinc concentration together with the Levich equation for the DBL thickness. A decrease in the initial pH value of the solutions causes considerable modifications both in the plateau region and in the overlimiting current density region of the current–membrane potential curves. The results show that the presence of boric acid produces the precipitation of zinc metaborate on the anodic layer of the cation-exchange membrane.

Electrochemical reduction of dioxygen on Alizarin modified glassy carbon electrode in acidic medium

The catalytic behaviour of glassy carbon electrode modified by 1,2-dihydroxy antraquinone (Alizarin) was investigated. The electrocatalytic ability of modified electrode for the reduction of dioxygen was examined by cyclic voltammetry and rotating disk electrode (RDE) voltammetry techniques. The Alizarin modified glassy carbon electrode possesses excellent electrocatalytic abilities for dioxygen reduction over potential 400 mV lower than at the bare glassy carbon electrode. Hydrodynamic studies were performed to determine the heterogeneous rate constant for the reduction of O2 at the surface of modified electrode. It was determined by Koutecky-Levich plot. The apparent diffusion coefficient of O2 in O2 saturated acidic solutions was estimated by using Levich equation. Studies show the involvement of four electrons in dioxygen reduction at the surface of this modified electrode.

Electrochemical Investigation of Zinc(II)-Furdap Amide Complex in DMSO Medium

The electrochemical behavior of Zinc(II)-furdap amide complex has been investigated by the use of several electrochemical methods in DMSO on platinum electrode. Both the ligand and the complex gave one electron transfer re- duction. Although there was no oxidation peak observed corresponding to the reduction of ligand, there was a correspond- ing oxidation peak appeared for the complex. The number of electrons transferred was calculated as 1 by the use of bulk electrolysis, rotating disc electrodes employing Kouteck� -Levich equation. The reversibility tests revealed that the reac- tion followed a quasi reversible mechanism. The mechanism was also confirmed by simulation studies. ks and  values were found to be 1.0 10 -7 cm s -1 and 0.4, respectively. The diffusion coefficient (D) was found as 6.93  10 -5 cm 2 s -1 by the use of Cottrell slope obtained from chronoamperometry experiments and ultra micro disc steady state current (iss).

Cathodic reaction kinetics and its implication on flow-assisted corrosion of aluminum alloy in aqueous ethylene glycol solution

The cathodic reaction kinetics and anodic behavior of Al alloy 3003 in aerated ethylene glycol–water solution, under well-controlled hydrodynamic conditions, were investigated by various measurements using a rotating disk electrode (RDE). The transport and electrochemical parameters for cathodic oxygen reduction were fitted and determined. The results demonstrate that the cathodic reaction is a purely diffusion-controlled process within a certain potential region. The experimentally fitted value of diffusion coefficient of oxygen is 3.0 × 10−8 cm2 s−1. The dependence of cathodic current on rotation speed was in quantitative agreement with Levich equation. At potentials more positive than the diffusion controlled region, the cathodic process was controlled by both diffusion and electrochemical kinetics. The electrochemical reaction rate constant, k 0, was determined to be 1.1 × 10−9 cm s−1. There is little effect of electrode rotation on anodic behavior of Al alloy during stable pitting. However, fluid hydrodynamics play a significant role in formation of the oxide film and the Al alloy passivity. An enhanced electrode rotation would increase the mass-transfer rate of solution, and thus the oxygen diffusion towards the electrode surface for reduction reaction. The generated hydroxide ions are favorable to the formation of Al oxide film on electrode surface.

Carbon-supported Co1.67Te2 nanoparticles as electrocatalysts for oxygen reduction reaction in alkaline electrolyte

Well-dispersed Co1.67Te2 nanoparticles supported on carbon black have been synthesized via a solid-state reaction using Co and Te precursors in an autoclave at elevated temperatures. Their oxygen reduction reaction (ORR) activity and selectivity as a function of heating temperatures in catalyst synthesis were evaluated by rotating disk (RDE) and ring-disk electrodes (RRDE). It was found that the best performing catalyst (CoTe/C-900) was synthesized at a temperature of 900 °C, with regard to the most positive RDE onset (−0.18 V vs Ag/AgCl) and half-wave potentials (−0.35 V vs Ag/AgCl) as well as the lowest peroxide yield (ca. 5%) in alkaline solution (0.1 M KOH, pH = 13). Meanwhile, well-defined limiting currents were reached in the mass transfer-controlled potential range at various rotating speeds, attesting to the high density and uniform distribution of ORR active sites on the catalyst. The average electron transfer number of ORR was determined to be 3.5 for the CoTe/C-900 catalyst by using a modified Koutecky–Levich equation, nearly providing a four-electron pathway for the ORR. A transition of the Tafel slope from ca. −60 mV/dec to ca. −120 mV/dec with overpotential is directly associated with oxide formation and their coverage variation onto catalysts, suggesting a change of the rate-determining step in the ORR mechanism from intermediate-migration to charge-transfer. Extensive physical characterizations including X-ray diffraction (XRD), high-resolution transmission electron microscopy (HR-TEM), and X-ray photoelectron spectroscopy (XPS) were conducted for each CoTe/C sample prepared at various heating temperatures to provide insights into the origins of active sites, and Co1.67Te2 chalcogenide nanoparticles supported on carbon were found to be highly active toward ORR in alkaline electrolytes.

Electrochemical Characterization of Nitrate Reduction on Recently Deposited Cooper Nuclei

This work shows that nitrate ion reduction occurs on electrochemically deposited copper nuclei over a glassy carbon electrode in aqueous acid media. It was found that plots of J vs v1/2 at constant [NO3-] and J vs [NO3-], with constant sweep speed (v) the Randles-Sevick equation gives a congruent diffusion limiting rate that involves NO(g) formation, through transfer of 3 electrons. Under hydrodynamic conditions imposed on the electrode, it was possible to observe the simultaneous reduction of protons and nitrates with a deviation of the Levich equation at high rotation speeds

Flow-injection amperometry at microfabricated silicon-based μ-liquid–liquid interface arrays

Geometrically regular silicon membrane-based micropore arrays were employed for defined arrays of micrometer-sized interfaces between two immiscible electrolyte solutions (μITIES). These were incorporated into a poly(tetrafluoroethylene) (PTFE) hydrodynamic cell. Electrochemistry at the μITIES array was undertaken following gellification of the organic phase using polyvinyl chloride (PVC) and flowing an aqueous phase over the array surface. Cyclic voltammetric characterization of asymmetric diffusion profiles on either side of the μITIES was accomplished under flowing conditions using positively and negatively charged (TEA + and 4-OBSA −, respectively) model analyte species. Incorporation of an ionophore (dibenzo-18-crown-6 ether) into the organogel allowed the ion-transfer detection of two oligopeptides (phenylalanine dipeptide and lysine dipeptide) within the available potential window under stationary and flowing conditions. Flow rate studies with TEA + indicated that the amperometric peak currents do not obey the Levich equation, due to diffusion dominating the mass transport, as opposed to convection. The influence of the applied potential ( Δ O W ϕ ) on the amperometric response of the oligopeptides was studied and hydrodynamic voltammograms (HDVs) for the individual oligopeptides were subsequently constructed. The data presented provide a basis for the use of silicon membrane-based μITIES arrays in flow analytical methods.

An investigation of the dip-Ion Layer Gas Reaction process to produce ZnO films with increased deposition rates

Intrinsic ZnO thin film layers have previously been deposited using the dip-ILGAR ‘Ion Layer Gas Reaction’ method. This deposition method and material has been effectively employed to deposit the buffer layers in chalcopyrite solar cells [M. Bär, H.-J. Muffler, Ch.-H. Fischer, S. Zweigart, F. Karg, M.C. Lux-Steiner Prog. Photovolt: Res. Appl. 10 (2002) 173]. The original parameters for the ZnO dip ILGAR deposition process were optimised for film quality. These parameters, however, were not suitable for an up-scaled technology transfer to tape deposition as the dip speed and growth rate meant impractically long deposition times. The results presented here are from an investigation, using the laboratory scale ILGAR apparatus with 2.5 × 5 cm 2 substrates, into parameters e.g. solvent, salt and apparatus parameters, which could allow an increased deposition rate and dip speed yet retains film quality. Simple dip mechanics and the Landau–Levich equation, which describes film thickness as a function of dip withdrawal speed, gravitational acceleration and the properties of the solution, are considered. The recently optimised deposition parameters given here will allow a dip speed of more than 7 m/min and deposition rate of 7.5 nm/cycle.

Rotating disk electrode analysis of oxygen reduction at platinum particles under limiting diffusion conditions

An analysis is carried out of oxygen reduction under limiting diffusion conditions on a rotating disk electrode partially covered with platinum particles (‘particulate electrode’). First a model is developed for the current response at a rotating particulate electrode, because Levich equation, used for the classical continuous disk electrodes, is not applicable in this case. The model allows for the calculation of the limiting diffusion current by an iterative algorithm, as a function of the density and size of the particles, and the constants for the adsorption/desorption and diffusion of reactants over non-covered areas of the substrate. The model is valid when there is no overlapping of surface diffusion areas around the particles. In a second part, the oxygen reduction on platinum particles electrodeposited on a glassy carbon disk is studied. Platinum particulate electrodes with a variable density and size of particles are prepared by single pulse electrodeposition technique. Limiting diffusion currents for oxygen reduction are analysed on the light of the proposed model. Values for the oxygen surface diffusivity and the equilibrium adsorption/desorption constant on the glassy carbon substrate are obtained from the analysis.

Electrochemistry of tin deposition from mixed sulphate and methanesulphonate electrolyte

The electrodeposition of tin, at a copper surface, from a tin sulphate (0˙014 mol dm–3) electrolyte containing methanesulphonic acid (12 ˙5 vol.-%) at 295 K has been studied. Cyclic voltammetry, using potential sweep rates of 8–128 mV s–1, at a stationary copper electrode provided information on the potential ranges for tin deposition and stripping. Linear sweep voltammetry, at a copper rotating disc electrode was used to evaluate the mass transport characteristics of the system under controlled, laminar flow conditions. The changes in the limiting current density with a Sn2+ concentration of 0˙006–0˙078 mol dm–3 and an electrode rotation rate of 200–4800 rev min–1 were quantified. Randles-Sevčik and Levich equations were used to give an averaged diffusion coefficient for Sn2+ of 5˙4 × 10–6 cm2 s–1.

Application of chronopotentiometry to determine the thickness of diffusion layer adjacent to an ion-exchange membrane under natural convection

A brief review of the evolution of the diffusion boundary layer (DBL) conception inspired by the works of Nernst, Levich and Amatore is presented. Experimental methods for studying the DBL in electrode and membrane systems are considered. The electrochemical behaviour of a CM2 cation-exchange membrane in NaCl and KCl solutions is studied by chronopotentiometry at constant under-limiting current. Chronopotentiometric curves are described theoretically by applying the Kedem–Katchalsky equations in differential form to a three-layer system including the membrane and two adjoining DBLs. The conductance coefficients entering the equations are found by treating the results of membrane characterisation: the electrical conductivity, transport numbers of ions and water, electrolyte uptake, as functions of the equilibrium electrolyte solution. The two-phase microheterogeneous model is used for this treatment resulting in presentation of the conductance coefficients as functions of (virtual) electrolyte solution concentration in the membrane. The steady-state DBL thickness ( δ) is found by fitting experimental potential drop at sufficiently high times. It is found that δ is proportional to (Δ c) − 0.2 , where Δ c is the difference between the electrolyte concentration in the solution bulk and at the interface. This result differs from the Levich equation, which gives the power equal to − 0.25 for Δ c. This deviation is explained by the fact that the theory of Levich does not take into account microscopic chaotic convection motion recently described by Amatore et al. It is shown that the treatment of experimental chronopotentiometric curves with the model developed allows one to observe the role of streaming potential in the membrane. Different mechanisms of streaming potential and their effect on the shape of chronopotentiograms are discussed. A simple analytical solution of Navier–Stokes equations applied to natural convection near an infinite vertical ion-exchange membrane is found. It is shown that the formation of DBL induced by electric current is quasi-stationary. This fact allows the empirical expression found earlier and linking δ with Δ c under steady-state conditions to be used in transient regimes. The numerical solution of the non-stationary Kedem–Katchalsky equations together with this empirical expression results in quantitative description of the potential difference (pd) and δ as functions of time in chronopotentiometric experiments. The comparison of theoretical and experimental chronopotentiometric curves shows an excellent agreement, especially for the part after switching off the current. The reasons of a small deviation observed just before the curves attain steady state under a constant current applied are discussed.

The limiting current for reduction of ferricyanide ion at nickel: The importance of experimental conditions

AbstractSteady state, hydrodynamic voltammetry is a well‐established technique to measure the rate of mass transport of an electroactive species to, or from, a solid surface electrode in an aqueous electrolyte. Limiting current measurements during the reduction of ferricyanide (hexacyanoferrateIII) ion at a nickel rotating disc electrode (RDE) are critically considered, and the accuracy of the technique is quantitatively assessed. The importance of surface pretreatment, type of indifferent electrolyte, and the effect of sunlight are considered. Limiting current values can show large deviations from the values predicted by the Levich equation for laminar flow to a polished RDE when unsuitable conditions are employed, despite the appearance of well‐defined limiting current plateaux. Using appropriate pretreatment and experimental procedures, the averaged mass transport coefficients or limiting currents values can be obtained, which are close to the values predicted by the Levich equation for laminar flow to a hydrodynamic smooth RDE. © 2008 American Institute of Chemical Engineers AIChE J, 2008

Extensions of the Koutecky–Levich Equation to Channel Electrodes

An analytical solution is herein presented for the current at a channel-type electrode associated with a simple first-order (in the reactant) heterogeneous electron transfer process involving a solution phase species. Assuming a fixed cell geometry, electrolyte composition, and temperature, a series expansion of this solution revealed that in the limit of small values of k3/v o , where k is the first-order kinetic rate constant and v o is the fluid velocity in the center of the channel, the reciprocal of the measured current, 1/i = 1/i k ; + β/i lim . where i k and i lim are the kinetic and diffusion limited currents, respectively, and β = 27/[8Γ(2/3)Γ(1/3)] = 0.93036. This equation bears striking resemblance to that reported by Koutecky and Levich for a rotating disk electrode, except that βin the latter case is unity. Rather surprisingly, and in agreement with recent findings [Electrochim. Acta, 52, 4124 (2007)], a plot of 1 1/ivs k/v 0 1/3 was found to be close to linear, with a slope reaching values slightly higher than β as the magnitude of k/v 0 1/3 increased.