The variation of current density and electrode potential with electrode resistance and its role in cell design

The potential drop along parallel electrodes of finite resistance has been calculated (a) assuming a pure resistive representation of the cell and (b) by considering the polarization characteristics of an irreversible electrode reaction. It was found that a much more uniform potential (and also current) distribution was obtained with the current feeders at opposite ends of the electrodes rather than at the same ends. With this configuration it is advantageous to have electrodes of equal resistance. Equations are given that enable the potential and current density distribution to be easily calculated. A factor I_tot/I_max was derived which is a measure of the effective utilization of the electrode area. It may be used for calculating the required electrode area with non-uniform cd distribution.     

A numerical method of calculating secondary current distributions in electrochemical cells

A numerical method is proposed based on the analogy between the potential distribution in an electrolytic solution and the temperature distribution in a heat-conducting medium. Thus the equation of non-steady-state heat conduction which contains a hypothetical temperaturev(x, y, t) is solved numerically with appropriate boundary conditions. In the steady state the distribution ofv(x, y, t) corresponds to the distribution of potentialφ _s (x,y) which satisfies Laplace's equation. The method is useful not only for conventional electrochemical cells but also for complicated systems such as a bipolar electrode for which boundary conditions provide neither the potential nor the current density at the electrode surface.     

In situ measurement of conductivity and active surface area of porous electrodes by the current step method—I. Theory

If the electrical conductivity of a plate-shaped porous electrode immersed in an electrolyte is measured by the four-point d.c. method using a current step, the potential drop, Δφ₁, is a function of the time, t. The course of this function can be derived theoretically by solving two simultaneous partial differential equations describing the potential distribution in both the solid and liquid phases. It is shown that the Δφ₁ − t dependence permits not only to determine the conductivity of the electrode but also to estimate its true surface area and the conductivity of the pore electrolyte.     

Measuring electrochemical noise of a single working electrode for assessing corrosion resistance of polymer coated metals

Electrochemical noise measurement (ENM) of the spontaneous perturbation of current and potential of coated samples immersed in electrolyte determines the resistance of the coating system. ENM offers several advantages: the measurement is relatively simple to make, it is completely non-interfering with the natural process occurring on the surface and the data are simple to interpret. The original standard arrangement for ENM using a pair of samples has limitations for practical applications because two separate and nominally identical working electrodes are needed and this requirement is very hard (if not impossible) to fulfil in on-site application. This paper describes an alternative approach for electrochemical noise measurement to measure the noise resistance (R_n) of protective coatings based on use of just one working electrode. In this so-called “Single Cell” (SC) arrangement the electrochemical noise current and electrochemical noise potential between the working electrode and a non-noisy reference electrode is measured separately and consecutively. This new approach has been tested for a range of coating resistances. Also, the coating's resistance has been measured using DC resistance and EIS (at low frequency) and the results were compared with the R_n obtained from the single cell (SC) set up.     

Spread and recoiling of liquid droplets impacting solid surfaces

The impact of water droplets on solid surfaces is studied experimentally and theoretically. Theoretical equations based on energy conservation are developed. In our theoretical study, the droplet is modeled as a ring‐like shape, which matches the dynamic shape of droplets observed from our experimental tests. In the analysis of energy conservation, the nonuniform distribution of pressure inside the deformed droplet is taken into account by introducing a flow potential energy term in the theoretical equations. To derive viscous dissipation for recoiling, a viscous layer coefficient is introduced. Its values for the tests using smooth surfaces are found to be within a small range. Both theoretical predictions and experimental data show significant influence of surface wettability on maximum spread and recoiling process. With the increase of advancing contact angle, surface energy shows a decreasing trend, whereas flow potential energy shows an increasing trend and becomes significant for hydrophobic surfaces. © 2014 American Institute of Chemical Engineers AIChE J, 60: 2683–2691, 2014     

Ohmic potential drop during alkaline water electrolysis

Advanced alkaline water electrolysis may be an attractive method of producing hydrogen in the future. Large energy losses in water electrolysis are caused by evolution of gas bubbles. The main aim of this investigation is to obtain a dimensionless correlation for the increase of ohmic resistance between working electrode and diaphragm due to the presence of gas bubbles. The ohmic potential drop across the solution layer between diaphragm and working electrode, distance from the rear of the working electrode to the back wall of the compartment of the working electrode, the height in the electrolytic cell, the electrode type, nature of the electrode surface and of the gas evolved. From the experimental results the dimensionless correlation has been deduced as

where ΔR_wm^* denotes the increase in resistance of solution layer between diaphragm and working electrode due to bubbles, divided by the resistance of this layer in absence of bubbles, Re Reynolds number, h^* reduced height in the electrolytic cell, d_wm^* reduced distance between the working electrode and the diaphragm, n empirical experimental constant depending on nature of electrode surface, nature of gas evolved and whether or not the bubbles can enter a chamber behind the working electrode, K empirical constant depending on nature of both electrode surface and gas evolved. A remarkable result is that ΔR_wm^* is independent of current density in the current density range from 1–10 kA m^?2.     

Passive behaviour of niobium

The passive behaviour of niobium at electrode potentials from −1 to 4 V (sce) in aqueous solutions of pH 0–13 at 25°C has been studied by quasi-steady (20 h) and transient polarization measurements, dc capacitance determinations and some AES depth profile investigations. Niobium exhibits a quasi-steady passive current varying little with the electrode potential and pH. After potential (or current) steps, transient superpolarization occurs. The transient data accord with the Cabrera-Mott equation and fit reasonably with λ = 1.5 Å and z = 5 for metal ion transfer at the metal—oxide interface. The capacitance data satisfy a simple insulator model, reveal the main charge distribution in the passive electrode, and combine with film thickness data to give ε = 46 for the static dielectric constant of the passive film. The anodization ratio is 37 Å V⁻¹ under quasi-steady conditions. The passive niobium electrode seems mostly to carry a net negative charge. Anodic oxygen evolution does not occur.     

Computerized design and evaluation of improved electrodes for lead-acid batteries

A mathematical model of a positive-negative electrode pair in a lead-acid battery has been developed, and can be solved to determine the potential and current density distribution over the electrode surfaces. With the aid of a computer the model was used to improve the grid design of the positive electrode. The results were compared with those obtained by discharging full-size electrode pairs in a laboratory cell. Agreement between projections and experimental data was about 70% with the assumptions made for certain input parameters. Further development is needed before the model can be applied to the design of radial grids with curvilinear grid members.     

The electrochemical impedance of metal hydride electrodes

The electrochemical impedance responses for different laboratory type metal hydride electrodes were successfully modeled and fitted to experimental data for AB₅ type hydrogen storage alloys as well as one MgNi type electrode. The models fitted the experimental data remarkably well. Several AC equivalent circuits have been proposed in the literature. The experimental data, however, could not always be satisfactorily approximated. The approximation model presented here exhibits smooth fit to the experimental results for all frequencies in the whole range from 10 kHz to 0.1 mHz. Equivalent circuits, explaining the experimental impedances in a wide frequency range for electrodes of hydride forming materials mixed with copper powder, were obtained. Both charge transfer and spherical diffusion of hydrogen in the particles are important sub processes that govern the total rate of the electrochemical hydrogen absorption/desorption reaction. To approximate the experimental data, equations describing the current distribution in porous electrodes were needed. Indications of one or more parallel reduction/oxidation processes competing with the electrochemical hydrogen absorption/desorption reaction were observed. The impedance analysis was found to be an efficient method for characterizing metal hydride electrodes in situ.     

Temperatur- und konzentrationsabhängigkeit der stromausbeute bei der transpassiven auflösung des eisens unter stationären bedingungen

It is possible, to write an expression for the current efficiency of transpassive metal-dissolution reactions, connected with an oxygen evolution, as a function of reaction cd. It can be shown, which parameter of this function is affected by temperature and the concentration of the reactants. The variation of this parameter allows the calculation of the order of the reactions and the activation energies. This introduces a new method for the estimation of kinetic parameters of electrode reactions at high cd, avoiding potential measurements. With respect to the practical importance of a mathematical expression for the current efficiency as a function of cd, concentration of electrolyte and temperature, for instance for the electrochemical machining, the validity of the deduced equations is demonstrated by experimental investigations concerned with the dissolution of steels in nitrate solutions.     

Role of surface states in electrodeposition of Pb on n-Ge(111)

The influence of surface states on the kinetics of the initial stages of Pb electrodeposition on n-Ge(111) was studied by cyclic voltammetric and current transient measurements. The substrate surface was modified to n-Ge(111)H or n-Ge(111)OH applying appropriate experimental and polarization routines. In transient experiments, the driving force for nucleation, the supersaturation, was varied by both changing the electrode potential U at c_Pb²⁺=const and the concentration c_Pb²⁺ at U=const. The results obtained indicate that, under the experimental conditions used, the nucleation site density N₀ remains constant with the electrode potential and thus, does not influence the initial nucleation kinetics. The nucleation rate, the density of nucleation sites and the number of atoms N_crit in critical nuclei were obtained analyzing current transients on the basis of models for instantaneous and progressive nucleation. Nucleation kinetics were found to be more inhibited on n-Ge(111)OH. The experimental results show that the different nucleation behavior of H- and OH-terminated n-Ge(111) surfaces can be explained by different densities of Ge surface free radicals acting as nucleation sites. Problems connected with an application of electrodeposition for metallization of micro- and nanostructures are discussed.     

Numerical simulation of salt water electrolysis in parallel-plate electrode channel under forced convection

A steady-state numerical model for multi-ion parallel-plate electrode (PPE) system is developed to investigate the concentration and electric distribution in the process of salt water electrolysis under forced convection. The finite-element method is used to solve this multi-ion transport model coupled with ionic diffusion, convection and ionic migration. The flow field and the electrode current's effect on the concentration distribution are investigated. The comparison between the diffusion-transported current and the migration-transported current demonstrates that the current is almost fully transported by the ionic migration, with the result that the diffusion-transported current can be neglected and the control equation of potential is simplified. For comparison, a hypothetical model with uncoupled situation of concentration and electric field is taken into consideration. The variation of electric field strength near the cathode can reach 25% of the value of the uncoupled model in the condition of u₀ = 0.01 m/s. Compared with this, the variation of ionic electro-conductivity shows a reverse tendency.     

Electrochemical behaviour of aluminium in sodiumpolysulphide melts at 330°C

An experimental set-up was developed which allows the investigation of electrodes in pure sodiumpolysulphide melts. It could be shown that aluminium forms a passivating layer of aluminiumsulphide at an anodic potential of about 1 V vs a sodium reference electrode. Below this value, aluminium is active. With a copper containing aluminium alloy the passivating potential is increased to about 1.2 V. Pitting corrosion was observed after operating the aluminium electrode at current densities of several hundred mA cm^?2. Reaction mechanisms which could explain the active, passive and transpassive regions observed, are discussed.     

The relationship between the impedance of corroding electrode and its polarization resistance determined by a linear voltage sweep technique

The polarization resistance of metallic materials in contact with an electrolyte is largely used for the evaluation of its corrosion rate. The experimental value of polarization resistance is very often determined by plotting the polarization curves at the vicinity of the rest potential by a triangular voltage sweep technique. It is found that, for materials having high resistivity against corrosion, the value of polarization resistance is largely dependent on the sweep rate or the period of sweep cycle. If an equivalent circuit of a corroding electrode is to be presented by a parallel connexion of a resistance and a capacitance, such dependence of the polarization resistance cannot be explained at all. In fact, though the impedance of corroding electrode measured within a large frequency range shows one capacitive arc in the complex plane in accordance with parallel R—C circuit, the values of R and C both depend on frequency. The current response to a triangular voltage sweep signal is calculated numerically by Heaviside operational calculus using experimentally determined electrode impedance. A fairly good agreement was found between the experimental and calculated current—voltage cycles for different periods of a triangular voltage sweep signal.     

Electrocatalysis and the chlorine evolution reaction

The chlorine evolution reaction has been investigated on D.S.A. type electrodes in 5.13 M NaCl solution. A large amount of potentiostatic current—potential and impedance—potential data has been collected over a wide potential and frequency range. The current—potential and impedance—potential data has been reduced by curve fitting to a series of a parameter curves. The impedance—potential data were analysed by two methods: an equivalent circuit and the parameter curves C_dlE, R_ctE, R_ωE reported, and a reaction mechanism and the parameter curves C_dlE, kSHE, R_ωE reported. The two ways of analysing the impedance data are equivalent. However the analysis into a reaction parameter has the advantage that all the data, current—potential and impedance—potential, can be tested using a single set of parameters (kSH, R_ω, a, b, D_A, D_B, δ).In this work the data is compared to that expected for a redox reaction. Any deviation from the expected behaviour of a perfect redox reaction is ascribed to Cl₂ bubble formation and to electrode structure effects. It is suggested that the parameter curves are related also to bubble formation characteristics and the ‘real’ area of the electrode.     

Spurious potential dependence of diffusion coefficients in Li insertion electrodes measured with PITT

Diffusion coefficients of Li⁺ in insertion electrodes determined by the potentiostatic intermittent titration technique (PITT) have been reported in the literature as being potential-dependent (and thus dependent on the degree of insertion). With this PITT method the diffusion coefficients D^PITT are determined from the current response of potential-step experiments using an approach based on the Cottrell equation. This equation assumes as boundary conditions infinitely fast kinetics and a linear system with semi-infinite thickness. Using the example of a spinel-type Li_δMn₂O₄ electrode it will be demonstrated that this potential dependence of D^PITT is not real but occurs, because the inadmissible boundary condition of infinitely fast kinetics which is not fulfilled has been adopted. This will be demonstrated with the help of numerically simulated PITT data calculated with a constant diffusion coefficient D. Diffusion coefficients D^PITT calculated from these simulated PITT data are potential dependent, even though the PITT experiments were simulated with a constant diffusion coefficient D. The inadmissible boundary condition of a linear system with semi-infinite thickness applied to a bed of spherical active particles with finite radii as represented by a Li_δMn₂O₄ electrode leads to further deviations of D^PITT which will be investigated.     

Numerical simulation of probing the electric double layer by scanning electrochemical potential microscopy

Computational modeling of probing the electric double layer (EDL) by scanning electrochemical potential microscopy (SECPM) was carried out in order to evaluate the applicability of this method. The modeling is based on a continuum approach for the electric double layer in dilute solution using the modified Poisson-Boltzmann equation. This model takes into account the finite ion size and prevents steric effects near the charged surface. The approach of the SECPM probe towards a charged electrode, immersed in electrolyte solution, is simulated obtaining the potential profile in the direction normal to the electrode. The effects of the shape and the size of the metallic protrusion at the apex of the probe were studied. A clear dependence of the probe potential on the apex geometry was observed, and correlated to the apex surface charge density distribution. The overlap of the EDLs located at the probe and the electrode is studied by setting different initial open circuit potentials, i.e., different charging, to the probe. We have found that the obtained potential profiles are consequences of the EDL overlap, characterized by an ionic distribution in the gap separating the probe and electrode. Depending on the strength of both EDLs and their polarity, the Debye screening effect severely influences the probe potential.     

On the theory of the potential and voltage step relaxation techniques for the investigation of fast electrode reactions

The errors of electrode kinetic measurements carried out with the potential and voltage step techniques (for single and double pulses) are calculated for several graphical and numerical data analysis methods. The following errors are examined: the random, experimental errors caused by the uncertainties of the potential, current, time, electrode area, and ir compensation; and the systematic errors caused by the inadequacies of the mathematical treatments and by the neglect of the slow rise time of a real potentiostatic system. The errors are presented as a function of the reaction resistance and of the rate constant parameter. The latter, which is defined as

is equal to 632 k₀ under simplified conditions. For a maximum tolerable error of ±20 per cent in the determination of the exchange current density, the limitation of the techniques can be summarized as follows. The classical potentiostatic technique with exact ir compensation can be used to a rate constant parameter of about 200 (k₀ ≈ 0.3 cm s^?1). The useful range can be extended to about 1000 (k₀ ≈ 1.5 cm s^?1) by using a numerical data evaluation method which takes into consideration the rise time of the potential. For the voltage step technique and the potentiostatic technique with uncompensated resistance, the limits of applicability can be significantly lower than the above values, depending on the ratio of reaction resistance to total cell resistance.     

Fast electrochromic response of ultraporous polyaniline nanofibers

Polyaniline (PAni) nanofibers were prepared by a one-step electrosynthetic method. A gold sputtered electrode was used as the substrate for the nanofiber growth at a constant current density value of 100 μA cm⁻². Substrate morphology induces fiber growing and allows having a remarkable quantity of fibers in a short period of time. Tandem chronoabsorptometric and chronocoulometric data of the electro-synthesis process were collected and analyzed. Several electrochromic parameters were characterized and a short response time (T₉₀) of 20 ms was obtained for a contrast (ΔT %) of 10%. The main reason for this fast response is the ultraporous nature of the prepared nanofibers. This approach represents a straightforward, easy and low cost method to obtain a fast color switching film with potential application in the deployment of an electrochromic device.     

Transient analysis of a flow-through porous electrode at the limiting current

The equations governing the transients in the concentration, current and potential response of a porous flow-through electrode at the limiting current for a single reactant in a well-supported electrolyte have been solved. It was assumed that a potentiostatic step was applied to an electrode with a uniform feed concentration. The dispersive flux of reactant was assumed to be negligible but double-layer charging effects were taken into consideration. If the double-layer time constant is much less than the fluid residence time (νC/?? ? 1), it is quantitatively shown that the capacitive current may be neglected in interpreting the current-time response of the electrode when examined in the fluid residence time frame. If the entire electrode is to operate at the limiting current, it is quantitatively shown that the solution phase ohmic drop can become significant early in the transient such that secondary reactions may become important. The ability to interpretI versust data in terms of the limiting current species mass transfer coefficient is removed under these conditions. The results support the qualitative arguments made by Newman and Tiedemann in their comprehensive review article on porous flow-through electrodes. Finally, it is shown that ln(Faradaic current) versust can be approximately linear in a limited time span, although no useful information can be obtained from such a plot.