Ohmic Drop Effects Research Articles

Differential pulse techniques in weakly supported media: Changes in the kinetics and thermodynamics of electrode processes resulting from the supporting electrolyte concentration

Square wave voltammetry (SWV) and differential multipulse voltammetry (DMPV) in weakly supported media are investigated. The numerical simulation procedures reported in literature (Streeter et al., J. Phys. Chem. C 112 (2008) 13716–13728; Limon-Petersen et al., J. Phys. Chem. C 114 (2010) 2227–2236) for electrochemical experiments in low conductivity solutions is applied with success. From this theory, the influence of the concentration of supporting electrolyte on the voltammograms is discussed for different redox couples and at electrodes of different size. The variation of the peak current and peak potential due to migration and ohmic drop effects are reported. The theory is applied to the experimental study of the one-electron reduction processes of cobaltocenium and cobalt (III) sepulchrate at mercury hemispherical electrodes of 25μm radius. The kinetic parameters and formal potential are obtained in a wide range of support ratio from the SWV and DMPV voltammograms. Possible changes of the kinetic and thermodynamic properties of the electrode reactions are analyzed as a function of the level of support.

Combined effects of Tafel kinetics and Ohmic potential drop on the nonlinear responses of electrochemical systems to low-frequency sinusoidal perturbation of electrode potential – New approach using the Lambert W-function

Nonlinearity effects of electrochemical systems kinetics on impedance measurements are re-examined in the low-frequency (LF) domain through symbolic manipulation and numerical computation performed with Mathematica. It is a new approach to some problems not yet completely resolved in electrochemical impedance spectroscopy despite a number of publications on this subject in the specialized literature. This article is focused on electrochemical systems governed by Tafel kinetics under steady-state conditions, so-called Tafelian systems below, and perturbed by a sinusoidal variation of electrode potential vs. time, at low frequency. First, harmonic analysis of the system response to sinusoidal perturbation of potential with negligible Ohmic drop effects is dealt with. Next, the combined effects of Tafel kinetics and Ohmic drop are thoroughly examined. The current–potential response at low frequency is modelled using the Lambert W-function. New formulations are derived for the nonlinear polarization resistance of Tafelian systems in the presence of Ohmic drop. Closed-form or infinite-series formulations are derived for the amplitudes of fundamental and harmonic components of periodic current. Finally, the validity condition for impedance measurements carried out in the LF domain is derived for Tafelian systems.

In situ mapping of electrode potential in a PEM fuel cell

Here we describe an innovative fuel cell reference electrode array using a through-plate configuration, which makes possible for the first time accurate mapping of the variation in electrode potential across the active area of an operating polymer electrolyte membrane fuel cell (PEMFC). This configuration overcomes the major limitations of conventional fuel cell reference electrodes in that ohmic drop, potential distribution and electrode edge effects in the membrane are negated. The utility of the technique is neatly demonstrated in the study of catalyst support corrosion during fuel cell start-up, which is associated with movement of the air/fuel boundary through the anode flowfield.

Desenvolvimento e uso do compósito de Nb2O5|Cu como revestimento aplicado por aspersão térmica sobre o aço AISI 1020 para proteção contra a corrosão pelo solo em estruturas enterradas

An Nb2O|Cu corrosion-resistant coating was developed and applied onto AISI 1020 steel substrate by Powder Flame Spray. A galvanostatic electrochemical technique was employed, with and without ohmic drop, in four different soils (two corrosively aggressive and two less aggressive). Behavior of coatings in different soils was compared using a cathodic hydrogen reduction reaction (equilibrium potential, overvoltage and exchange current density) focusing on the effect of ohmic drop. Results allow recommendation of Nb2O5|Cu composite for use in buried structure protection.

Square wave voltammetry at disc microelectrodes for characterization of two electron redox processes

Analytical explicit solutions are presented for the use of square wave voltammetry (SWV) at disc microelectrodes to study two-electron reversible redox processes. This combines the advantages of SWV (minimization of capacitative effects, peak-shaped response and quick experiments) with those of microelectrodes (reduction of capacitative and ohmic drop effects, enhanced mass transport and measurements of small volumes). Further, the analytical expressions are very easy to implement in comparison with the numerical methods usually employed for simulation of electrochemical experiments at microdisc electrodes. From the theory, the effects of the technique parameters (frequency, pulse amplitude) are examined and procedures are given for the characterization of the redox system from the values of the peak current, peak potential and half-peak width. Finally, the theory is applied to the experimental study of the two-electron reduction of anthraquinone-2-sulfonate in aqueous media. For this system, the formal potentials of the redox centres in aqueous solutions can be tuned by means of the electrolyte cation.

LSV/CV modelling of electrochemical reactions with interfacial CPE behaviour, using the generalised Mittag–Leffler function

This article deals with the influence of interfacial CPE (constant phase element) behaviour on linear scan voltammograms (LSV) and cyclic voltammograms (CV). Theoretical investigation is carried out using the generalised Mittag–Leffler function which arises naturally in the solution of fractional order integral or differential equations. First, ohmic drop and CPE effects are analysed in the absence of electrochemical reaction through the closed-form expression of current vs. time. Next, the combined effects of ohmic drop, CPE and faradaic processes are modelled using the integral equation approach. Finally, the example of one-step electrochemical reaction, investigated under semi-infinite linear diffusion conditions, is dealt with for illustration of the calculation procedure.

Peak heights and peak widths at half-height in square wave voltammetry without and with ohmic potential drop for reversible and irreversible systems

The behavior of voltammograms in square wave voltammetry in the presence of a significant ohmic potential drop for reversible and irreversible simple electrode reactions has been investigated. It is shown that the effects of ohmic potential drop can be drastically reduced by choosing adequately the square wave amplitude. Zone diagrams are drawn to define the conditions for which peak currents and peak widths at half-height can be expressed by simple formulas without considering the occurrence of ohmic potential drop. It follows that square wave voltammetry can be properly implemented in low-conductive media or in molten salt media where high concentrations of depolarizer are used.

Evaluation of voltammetric redox potential for Fe3+/Fe2+ in silicate liquids

Redox potentials of Fe3+/Fe2+ in silicate liquids measured by voltammetry were evaluated by comparison with those obtained by other analytical methods. Differential pulse voltammetry was carried out for 20Na2O·80SiO2 and 18K2O·82SiO2 (mol%) melts doped with 0.5 or 3 wt% Fe2O3 and 15Na2O·9CaO·76SiO2 and 25CaO·16MgO·9Al2O3·50SiO2 melts doped with 1 wt% Fe2O3. Observed half wave potentials (E1/2) agreed with those of previous voltammetry experiments, however, systematically smaller than E1/2 calculated from redox ratios measured by wet chemistry and Mossbauer spectroscopy and redox potentials estimated from calorimetric data by about 0.1-0.3 V. The Fe3+/Fe2+ ratios calculated from the E1/2 by the voltammetry were always overestimated compared with those by other analytical methods. We could not explain the reason for discrepancy of the E1/2. It is expected that at least the discrepancy can not result from reduction of oxygen in working electrode, ohmic drop effect and difference between diffusivities of Fe2+ and Fe3+ in the liquids.

Theoretical Analysis of Microscopic Ohmic Drop Effects on Steady-State and Transient Voltammetry at the Disk Microelectrode: A Quasi-Conformal Mapping Modeling and Simulation

The effect of uncompensated solution resistance on steady-state and transient voltammograms at the disk microelectrode was for the first time treated theoretically and numerically at the microscopic level using specific quasi-conformal mapping for the case of absence of electric migration. It has been shown that microscopic distributions of electric potential and current density at a disk microelectrode affect the voltammetric waves at different degrees across the electrode surface due to the variation of elementary resistances and elementary current fluxes over the electrode surface which leads to nonlinear effects that have not been discussed in existing theoretical treatments of ohmic drop at microelectrodes. The analysis of steady state voltammetry in strongly resistive media under Nernstian conditions has allowed justification by appropriate analytical derivations of the widely used potential-shift correction of steady state voltammograms by plotting i vs ( E - iR e).

Electrochemical characterisation and anodic stripping voltammetry at mesoporous platinum rotating disc electrodes

Using the technique of liquid crystal templating a rotating disc electrode (RDE) was modified with a high surface area mesoporous platinum film. The surface area of the electrode was characterised by acid voltammetry, and found to be very high (ca. 86 cm(2)). Acid characterisation of the electrode produced distorted voltammograms was interpreted as being due to the extremely large surface area which produced a combination of effects such as localised pH change within the pore environment and also ohmic drop effects. Acid voltammetry in the presence of two different types of surfactant, namely Tween 20 and Triton X-100, suggested antifouling properties associated with the mesoporous deposit. Further analysis of the modified electrode using a redox couple in solution showed typical RDE behaviour although extra capacitive currents were observed due to the large surface area of the electrode. The phenomenon of underpotential deposition was exploited for the purpose of anodic stripping voltammetry and results were compared with data collected for microelectrodes. Underpotential deposition of metal ions at the mesoporous RDE was found to be similar to that at conventional platinum electrodes and mesoporous microelectrodes although the rate of surface coverage was found to be slower at a mesoporous RDE. It was found that a mesoporous RDE forms a suitable system for quantification of silver ions in solution.

Deposition of polyaniline on RVC electrodes: effect of substrate thickness

Polyaniline films, obtained by either chemical or electrochemical deposition on reticulated vitreous carbon (RVC), were investigated as a function of the substrate thickness. The electrochemical properties of these RVC/Pani electrodes were assessed by cyclic voltammetry and electrochemical impedance spectroscopy (EIS), whereas the morphology of the Pani films on RVC was analyzed by scanning electron microscopy (SEM). The cyclic voltammetric results revealed that the oxidation/reduction charges for electrodeposited polyaniline decrease as the RVC thickness is increased. Conversely, the charge densities for the chemically deposited films do not present a significant dependence on the substrate thickness. Two time constants, appearing in all the EIS spectra, indicate that an ohmic drop effect within the RVC substrate affects the polymer electrodeposition and the electrochemical behavior of the obtained electrodes. Therefore, an electric equivalent circuit considering the different electrochemical environments at the outer and inner RVC surfaces was proposed to analyze the EIS data.

Apparent diffusion coefficient of intercalated species measured with PITT: A simple formulation

Apparent values ( D ap) of chemical diffusion coefficients ( D) of intercalated species are measured with the potentiostatic intermittent titration technique (PITT) due to the usual approximations of infinitely fast charge-transfer kinetics at the electroactive interface and negligible Ohmic drop effects. A simple expression is derived in this work that enables one to predict the parametric dependence of the diffusion coefficient ratio ( D ap/ D) on the ‘key-factor’ ( Λ) for insertion/extraction processes. The parameter Λ can be either experimentally determined from electrochemical impedance spectra, or predicted from theoretical expressions of insertion/extraction reaction rate. The measurement error of diffusion coefficient is predicted theoretically due to slow charge-transfer kinetics at the interface, Ohmic drop effects and bulk interactions in the host material. The influence of electrode or particle geometry is also analyzed. In most cases, but not in all cases, a minimum value of apparent diffusion coefficient is observed near the standard potential of insertion material. The measurement error of D becomes very important in the presence of attractive interactions in host materials, together with slow charge-transfer kinetics at the electroactive interface. Finally, the superposition between spurious behavior of the chemical diffusion coefficient and its dependence on the guest ions interactions is investigated within the framework of Frumkin insertion isotherm.

Simulation and experimental determination of the macro-scale layer thickness distribution of electrodeposited Cu-line patterns on a wafer substrate

The impact of adjacent patterned zones with different active area densities on the current density and electrodeposited layer thickness distribution over a wafer substrate is examined, both by experiment and numerical simulation. The experiments consist in running an acid copper plating process on the patterned wafer, and layer thickness measurements by means of X-ray fluorescence (XRF) and atomic force microscopy (AFM). The simulations are based on a potential model approach taking into account electrolyte ohmic drop and electrode polarization effects, combined to a boundary element method (BEM) approach to compute the current density distribution over the electrodes. Experimental and computed layer thickness distributions are in very good agreement.

Discussion of three models used for the investigation of insertion/extraction processes by the potential step chronoamperometry technique

Three models used in electrochemical literature to fit experimental data for insertion/extraction processes investigated by the potential step chronoamperometry (PSCA) technique are examined and compared in this article. The first model (M I) gives a theoretical expression of Faradaic current transient taking reaction kinetics at the electrode surface, diffusion process in the host material and Ohmic drop effects into consideration. The ‘cell-impedance controlled diffusion’ constraint is used in the second model (M II) together with the diffusion equations and boundary conditions. Finally, the third model (M III) applies when the diffusion flux of injected/extracted species at the electrode surface is limited by interfacial charge transfer kinetics represented by the Butler–Volmer equation. The use of a finite-difference method is required to numerically solve models M II and M III. First, the theoretical predictions from models M I, M II and M III are compared when a small potential step is applied on the electrode. It is stated that the theoretical expression of current transient derived from model M I is the analytical solution of both models M II and M III under small-signal (linearization) conditions. Next, the three models are numerically compared under Langmuir isotherm conditions, assuming a constant diffusion coefficient of guest species in the host material. It is shown that the ‘cell-impedance controlled diffusion’ constraint used in model M II does not work very well when a large potential step is applied on the electrode. Finally, an alternative formulation of the boundary condition at the host material|electrolyte interface (model M III) is used to study the influence of Ohmic drop, together with the use of large potential steps.

Ohmic drop effects in square-wave voltammetry response for an ion transfer process at a liquid–liquid interface

The effect of ohmic drop on square-wave voltammetry experiments (SWV) at a liquid–liquid interface is analyzed. The study is based on the distortion of SW voltammetric profiles of the tetraethyl ammonium transfer process across the water/1,2-dichloroethane interface when an uncompensated resistance, R Ω , is present. Depending on the experimental conditions significant R Ω values arise as a consequence of the low electrical conductivity of the organic solvent characteristic of these systems, and efficient IR compensation is needed. When R Ω is not totally removed, a non-linear dependence of peak current (Δ I p) on the square root of the frequency, an increase of half-peak width (Δ E p/2) and a shift of peak potential ( E p) towards more positive values are observed in the SW profiles. The influence of signal frequency and R Ω values on SWV parameters (Δ I p, E p and Δ E p/2) is evaluated.

Modelling and characterisation of the OCVD response at an arbitrary time and injection level

We show that the OCVD method can be improved by providing the test diode with a third terminal that enables the suppression of the ohmic drop effect on voltage decay measurements. It's demonstrated that in this way the OCVD response can be extended up to the built-in voltage limit of the diode, where the carrier injection in the heavily doped regions and the Auger mechanism are dominating. Moreover, to physically interpret the numerical simulations, an analytical model has been developed which is capable to describe the voltage response as a continuous function of time and injection level.

Modelling the transient current from two rubbing electrode configurations: insulating pin on metal substrate and metal pin on insulating substrate

The current response from a reciprocal motion pin-on-disc experiment was modelled assuming a rate limiting reaction at a film interface. Two different geometries were considered: inert pin on metal substrate (ipms) and metal pin on inert substrate (mpis). For the ipms configuration and an electrolyte with a high conductivity, an analytical solution was found. To illustrate the effects of ohmic drop and other parameters, numerical solutions were introduced for both configurations. They made it possible to estimate the influence of, e.g. ohmic resistance and wear rates. The passive film growth parameters were taken from electrochemical quartz crystal microbalance (EQCM) experiments. A formalism was proposed for calculating growth fractions by comparing rubbing experiments performed at different potentials. The growth fractions compared qualitatively with those obtained during potential sweep experiments in the EQCM.

Wafer-Scale Profile Evolution of Electrochemically Deposited Copper Films

Wafer-scale profile evolution of electrochemically deposited copper films is experimentally studied and compared with theoretical predictions. The effects of ohmic potential drop, electrochemical current-voltage behavior at the metal/electrolyte interface, and local concentration variations are considered. Results show good agreement with experimental data over a wide range of total currents and times. © 2003 The Electrochemical Society. All rights reserved.

Modeling impedance diagrams of active layers in gas diffusion electrodes: diffusion, ohmic drop effects and multistep reactions

The dc and ac responses of an active layer in a gas diffusion electrode (GDE) have been predicted from theory, considering both diffusion and ionic ohmic drop inside the active layer and a multistep mechanism. This complete approach required numerical resolution. One-step, two-step (Volmer–Heyrovsky) and three-step mechanisms have been investigated. Numerical simulations from original models using dimensionless parameters lead to impedance diagrams involving a nearly perfect semicircle at low frequency and a 45° angle straight line at high frequency, so proving, respectively, the influence of mass and charge transport processes. Finally, a three-step oxygen reduction mechanism gives rise to theoretical impedance diagrams similar to the experimental ones.

Discussion of the potential step method for the determination of the diffusion coefficients of guest species in host materials: Part I. Influence of charge transfer kinetics and ohmic potential drop

Theoretical expressions are given for the output response of ion-insertion electrodes to a potential step assuming linear diffusion, restricted (blocking) diffusion conditions and possible limitations by insertion reaction kinetics. The effects of ohmic potential drop are also investigated. It is shown that slow interfacial charge transfer cannot be distinguished from ohmic drop effects, in contrast to impedance diagrams where ohmic drop and charge transfer effects can be separated. The influence of potential step amplitude is discussed. Chronocoulometric analysis is dealt with considering diffusion controlled processes as well as mixed control conditions. The error in the determination of the chemical diffusion coefficient of a guest species from chronoamperometric data, when using the limiting Cottrell equation in the short-time range or the exponential decay of current in the long-time domain, is evaluated in relation to insertion reaction kinetics and ohmic potential drop. Determination of the diffusion coefficients by curve fitting is also envisaged using the current versus time and charge versus time relationships. Finally, previous results in the electrochemical literature are discussed in the light of the theoretical derivations proposed in this paper.