Tafel Kinetics Research Articles

Modeling of the anode side of a direct methanol fuel cell with analytical solutions

In this work, analytical solutions were derived (for any methanol oxidation reaction order) for the profiles of methanol concentration and proton current density, by assuming diffusion mass transport mechanism, Tafel kinetics, and fast proton transport in the anodic catalyst layer of a direct methanol fuel cell. An expression for the Thiele modulus that allows to express the anodic overpotential as a function of the cell current and kinetic and mass transfer parameters was obtained. For high cell current densities, it was found that the Thiele modulus ( ϕ 2 ) varies quadratically with cell current density; yielding a simple correlation between anodic overpotential and cell current density. Analytical solutions were derived for the profiles of both local methanol concentration in the catalyst layer and local anodic current density in the catalyst layer. Under the assumptions of the model presented here, in general, the local methanol concentration in the catalyst layer cannot be expressed as an explicit function of the position in the layer. In spite of this, the equations presented here for the anodic overpotential allow the derivation of new semi-empirical equations.

Corrosion of Ferritic Steels in High Temperature Molten Salt Coolants for Nuclear Applications

ABSTRACTCorrosion of ferritic steels, including oxide dispersion strengthened (ODS) variants, in high temperature molten fluoride salts may limit the life of advanced reactors, including some hybrid systems that are now under consideration. In some cases, the steel may be protected through galvanic coupling with other less noble materials with special neutronic properties such as beryllium. This paper reports the development of a model for predicting corrosion rates for various ferritic steels, with and without oxide dispersion strengthening, in FLiBe (Li2BeF4) and FLiNaK (Li-Na-K-F) coolants at temperatures up to 800 °C. Mixed potential theory is used to account for the protection of steel by beryllium, Tafel kinetics are used to predict rates of dissolution as a function of temperature and potential, and the thinning of the mass-transfer boundary layer with increasing Reynolds number is accounted for with dimensionless correlations. The model also accounts for the deceleration of corrosion as the coolants become saturated with dissolved chromium and iron. Electrochemical impedance spectroscopy has been used for the initial in situ study of an ODS ferritic steel in high-temperature molten fluoride salt environments, with the complex impedance spectra obtained at its open circuit corrosion potential (OCP) interpreted in terms of the basic components of the equivalent circuit, which include the electrolyte conductivity, the interfacial charge transfer resistance, and the interfacial capacitance. Such in situ measurement techniques may provide valuable insight into the degradation of materials under realistic conditions.

Simulation of Pulse Discharge of the Li – CFx System

A zero-dimensional model is developed for the system to account for Butler–Volmer kinetics, internal cell resistance, and double-layer (or capacitive) charging. At the low rates involved, other transport processes can be neglected. Furthermore, for this system, Tafel kinetics is appropriate. This model is used to compare with discharge data for periodic pulses superposed on an otherwise low rate of discharge. The internal resistance and high double-layer capacity account for some aspects of the pulses, such as a long time relaxation when the load is changed, but do not account for other time constants of less than . For a long constant-load discharge without pulses, the model can be simplified further, with the capacitance being negligible and the internal resistance being important only at low load resistances. Development of a modified open-circuit potential function allows all discharge data for cells of different design and load resistance to be collapsed using a generalized design equation.

Oxygen Reduction Reaction Kinetics in Subfreezing PEM Fuel Cells

An experimental procedure was developed to measure oxygen reduction reaction kinetics in subfreezing polymer electrolyte membrane (PEM) fuel cells. The procedure was also used to measure kinetics at temperatures above , and results compared to those collected with a traditional kinetic measurement technique. In general, because of brief time durations in which PEMFCs can be operated below freezing temperatures, short equilibration times were required and thus, enhanced catalyst activity was observed. At progressively lower subfreezing temperatures, suspected mass transport or uncompensated ohmic losses resulted in nonlinear Tafel plots, which at lower decades of current density become linear with a slope close to that predicted by Tafel kinetics, . Consistent with results of other researchers at nonfrozen conditions, low water (or ice) content in the fuel cell results in lower catalyst activity and performance at subfreezing temperatures. Cyclic voltammograms indicate that the rate of oxide formation decreases at subfreezing temperatures and low water contents, indicating proton activity as a likely reason for reduced catalytic activity. Arrhenius plots of current density at a constant overpotential are linear (constant activation energy) over the temperature range from , indicating no fundamental change in reaction mechanism at subfreezing temperatures.

AC impedance modelling study on porous electrodes of proton exchange membrane fuel cells using an agglomerate model

A one-dimensional model of the PEM fuel cell cathode is developed to analyse ac impedance spectra and polarisation curves. The porous gas diffusion electrode is assumed to consist of a network of dispersed catalyst (Pt/C) forming spherically shaped agglomerated zones that are filled with electrolyte. The coupled differential equation system describes: ternary gas diffusion in the backing ( O 2 , N 2 , water vapour), Fickian diffusion and Tafel kinetics for the oxygen reduction reaction (ORR) inside the agglomerates, proton migration with ohmic losses and double-layer charging in the electrode. Measurements are made of a temperature-controlled fuel cell with a geometric area of 1.4 cm × 1.4 cm. Lateral homogeneity is ensured by using a high stoichiometry of λ min . The model predicts the behaviour of measured polarisation curves and impedance spectra. It is found that a better humidification of the electrode leads to a higher volumetric double-layer capacity. The catalyst layer resistance shows the same behaviour depending on the humidification as the membrane resistance. Model parameters, e.g. Tafel slope, ionic resistance and agglomerate radius are varied. A sensitivity analysis of the model parameters is conducted.

Simulation of the Li – CFx System

The system has been successfully used in implantable batteries to power medical devices for humans. Amassed data is analyzed to show that the behavior is dominated by the open-circuit potential and Tafel kinetics. Data from several discharge load resistances can be collapsed onto a single curve on this basis. At the low rates of interest, transport limitations can be neglected. Data for open-circuit relaxation show that the potential is a straight line when plotted against the logarithm of time. This is in harmony with the dominance of Tafel kinetics.

Cathode Catalyst Utilization for the ORR in a PEMFC: Analytical Model and Experimental Validation

The following model/experiment comparisons aid in predicting the maximum performance of a proton exchange membrane fuel cell (PEMFC) for a cathode catalyst with known oxygen reduction reaction (ORR) kinetics in the absence of gas transport resistances. Specific focus was on modeling the voltage loss within the cathode catalyst layer, which results from a balance between slow ORR kinetics and resistance to proton transport. A unique plot of proton resistance correction vs the ratio of ohmic (expressed by the proton conduction sheet resistance, ) to charge transfer resistance (expressed by the ratio of the Tafel slope of the ORR over the current density, ) in a PEMFC cathode was developed, based on an analytical solution to effective proton resistance in the porous cathode electrode of a proton exchange membrane fuel cell. Additionally, a plot of catalyst utilization vs was developed to serve as a guideline of experimental design parameters such that catalyst utilization is kept above 90%, which is a prerequisite for measuring the ORR kinetics. The model is applicable as long as the ORR follow simple Tafel kinetics.

Modeling techniques applied to the study of gas diffusion electrodes and proton exchange membrane biochemical fuel cells

Mathematical modeling has been extensively applied to the study and development of fuel cells. In this laboratory, modeling studies of gas diffusion electrodes and proton exchange membrane biochemical fuel cells are being developed. Regarding the modeling of usual physical systems, the available knowledge makes it possible to develop mechanistic models. For biochemical fuel cells, on the other hand, semi-empirical and empirical models can be used. In this work, there are three objectives: characterize a phenomenological model for a Pt–air cathode and perform appropriate simulations; characterize a semi-empirical model to predict the performance of a Pt–H 2/H 2O 2-peroxidase fuel cell; investigate the effectiveness of ( empirical) neural networks to predict the performance of a Pt–H 2/O 2-peroxidase fuel cell. The mechanistic model of a Pt–air cathode developed here is based on proper material balances, on Fick's law of diffusion and on Tafel kinetics. It can provide details of the physical system (such as the limit of the one-phase regime). A semi-empirical model based on Michaelis–Menten kinetics, in turn, can predict the performance of a Pt–H 2/H 2O 2-peroxidase biochemical fuel cell. Artificial neural networks were capable of fitting the potential/current relationship of a Pt–H 2/O 2-peroxidase biochemical fuel cell.

Performance analysis of the ordered and the conventional catalyst layers in proton exchange membrane fuel cells

Two steady-state, one-dimensional models of the cathode active layer for the proton exchange membrane fuel cell, a conventional active layer model with the agglomerate structure and an ordered active layer model, have been compared. The model equations account for the Tafel kinetics of oxygen reduction reaction, proton migration and oxygen diffusion in the polymer electrolyte and gas pores. The polarization curves simulated by the ordered active layer predict a superior performance than the conventional active layer model even with lower platinum loadings. Analysis of the overpotential contributions indicates that the better performance of the ordered catalyst layer can be attributed to the reduction of concentration polarization. Simulation results also reveal that the ordered active layer gives more uniform oxygen concentration and overpotential distributions while the conventional catalyst layer shows more evenly distributed local current source. The present results will be helpful for practical fuel cell designs.

Numerical simulation of the ordered catalyst layer in cathode of proton exchange membrane fuel cells

A steady-state, one-dimensional numerical model based on cylindrical electrode structure is presented to analyze the performance of the ordered cathode catalyst layer in Proton Exchange Membrane Fuel Cells. The model equations account for the Tafel kinetics of oxygen reduction reaction, proton migration, oxygen diffusion in the cylindrical electrolyte and the gas pores, oxygen distribution at the gas/electrolyte interface. The simulation results reveal that ordered catalyst layers have better performance than conventional catalyst layers due to the improvements of mass transport and the uniformity of the electrochemical reaction rate across the whole width of the catalyst layer. The influences of oxygen diffusivity in gas phase and electrolyte, and the proton conductivity have been shown. The limitation by oxygen diffusion in gas phase drives the active region of the catalyst layer to the catalyst layer/gas diffuser interface. The limitation by proton migration confines the active region of the catalyst layer to the membrane/catalyst layer interface. The limitation due to oxygen diffusion in electrolyte film maintains the uniform distribution of the active region throughout the ordered catalyst layer.

Transient Techniques for Investigating Mass-Transport Limitations in Gas Diffusion Electrodes : I. Modeling the Cathode

The use of electrochemical impedance spectroscopy and current-interruption techniques with the scope of determining mass-transport limitations in PEFC gas-diffusion electrodes is investigated. The porous electrode is assumed to be composed of spherical agglomerates consisting of a homogeneous mixture of the electrolyte and the electronic phase. The model is applied to the reduction reaction in the cathode and includes Tafel kinetics for the reduction, Ohm’s law for proton migration, Fick’s law for diffusion, and capacitive current due to the contribution of the double layer. A novel impedance is defined, enabling the results to be presented in a simpler manner than with the usual one. It is shown how these transient techniques can be employed to qualitatively separate diffusion from migration effects. The parameter groups that can be quantitatively determined from the processing of experimental data are presented. The effect of pressure and electrode thickness on the predicted electrode response is also investigated. © 2003 The Electrochemical Society. All rights reserved.

On the Electrooxidation and Amperometric Detection of NO Gas at the Pt/Nafion® Electrode

The electrochemical oxidation of nitric oxide (NO) gas at the Pt/Nafion® electrode has been studied at a concentration of 500 ppm. The electrooxidation of NO taking place over a wide potential range can be described by a transcendental equation, from which the half-wave potential of the reaction can be determined. For NO oxidation with appreciable overpotentials but negligible mass-transfer effects, the Tafel kinetics applies. The obtained charge transfer coefficient (a) and the exchange current density (io) are 0.77 and 14 mA/cm2, respectively. An amperometric NO gas sensor based on the Pt/Nafion® electrode has been fabricated and tested over the NO concentration range from 0 to 500 ppm. The Pt/Nafion® electrode was used as an anode at a fixed potential, preferably 1.15 V (vs. Ag/AgCl/sat. KCl), which assures current limitation by diffusion only. The sensitivity of the electrochemical sensor was found to be 1.86 mA/ppm/cm2. The potential interference by other gases, such as nitrogen dioxide (NO2) and carbon monoxide (CO), was also studied in the range 0-500 ppm. Both sensitivity for NO and selectivity of NO over NO2/CO show significant enhancement upon using a cyclic voltammetric (CV) activation, or cleaning procedure.

Investigation of Mass-Transport Limitations in the Solid Polymer Fuel Cell Cathode : I. Mathematical Model

In this paper, a one-dimensional, steady-state agglomerate model was used to describe the functioning and the mass transport limitations of the cathode in the solid polymer fuel cell (SPFC). This mathematical model is then compared to experimental results obtained on cathodes in an SPFC. The following processes were considered: Tafel kinetics of the oxygen reduction reaction, proton migration, oxygen diffusion in the agglomerates, and diffusion of a ternary gas mixture vapor in the pores of the active layer and of the gas backing. The model shows that limitation by proton migration in the active layer or by oxygen diffusion in the agglomerates leads to a doubling of the Tafel slope at higher current densities. For those two types of transport limitations, the dependence of the reaction rate on the active-layer thickness, oxygen partial pressure, and relative humidity of the gas were simulated. When additional limitation due to slow gas phase diffusion appears, the double Tafel slope is distorted. A mathematical expression for the limiting current density due to this process is presented. By using this expression, it is possible to correct the polarization curves for slow gas phase diffusion. © 2002 The Electrochemical Society. All rights reserved.

Performance of catalyst layers of polymer electrolyte fuel cells: exact solutions

Performance of a catalyst layer of polymer electrolyte fuel cell under the assumptions of ideal transport of reactants and Tafel kinetics of electrochemical reaction is considered. Explicit expressions for the profiles of basic parameters (proton current density, overpotential and reaction rate) across the catalyst layer are obtained and a new conservation law is found. Exact expression for voltage–current curve of the catalyst layer is derived and simplified in the limiting cases of small and large current densities. The physics of transition from small to large currents is discussed.

An electrochemical and microstructural assessment of erosion-corrosion of austenitic cast iron for marine applications

In this paper the corrosion and erosion-corrosion characteristics of an austenitic cast iron (BS 3468 S2W) are examined under an impinging flow free from solid particles. Under static and erosion-corrosion conditions the corrosion process is controlled by activation effects and conforms to Tafel kinetics. The corrosion rate is increased under impingement conditions compared with under static conditions but the trend is complex. Although corrosion plays a part in the degradation of BS 3468 S2W under an impinging jet, it is clear that there is a significant role played by mechanical processes and the effect that corrosion has on the mechanical erosion processes. The pure electrochemical corrosion component of the material loss is reduced as a percentage of the overall weight loss on increasing the impinging jet velocity. Corrosion has been seen to initiate at the boundary between the nodules of graphite and the surrounding Fe-rich matrix and hence a physical interpretation of the effect of corrosion on erosion is identified. Elektrochemische und Gefügebeurteilung von Erosionskorrosion an austenitischem Gusseisen für Meeresanwendungen In dieser Arbeit werden Korrosions- und Erosionskorrosionsmerkmale eines austenitischen Gusseisens (BS 3468 S2W) unter einer aufprallenden Strömung ohne Feststoffpartikel untersucht. Unter statischen und Erosionskorrosionsbedingungen wird der Korrosionsprozess durch Aktivierungseffekte kontrolliert und entspricht der Tafel-Kinetik. Die Korrosionsgeschwindigkeit wird unter Aufprallbedingungen erhöht verglichen mit statischen Bedingungen; der Trend ist allerdings komplex. Auch wenn die Korrosion bei der Schädigung von BS 3468 S2W unter Strahlaufprall eine Rolle spielt, gibt es aber einen signifikanten Anteil durch mechanische Prozesse und durch den Einfluss, den die Korrosion auf die mechanischen Erosionsprozesse ausübt. Mit steigender Strahlaufprallgeschwindigkeit wird die rein elektrochemische Korrosionskomponente des Materialverlustes als Prozentanteil des Gesamtgewichtsverlustes geringer. Die Korrosion beginnt an der Grenzfläche zwischen den Graphitkugeln und der umgebenden Fe-reichen Matrix; dadurch kann eine physikalische Interpretation des Effektes der Korrosion auf die Erosion identifiziert werden.

Mass Transport in Gas‐Diffusion Electrodes: A Diagnostic Tool for Fuel‐Cell Cathodes

Two mathematical models of gas‐diffusion electrodes, one for liquid electrolytes and one for ion‐exchange polymer electrolytes, are presented to investigate the effects of mass‐transport limitations on the polarization characteristics of a reaction obeying Tafel kinetics. The focus is on low‐temperature fuel‐cell cathodes, and in particular, contrasting two limiting cases that may be encountered at high current densities: control by kinetics and dissolved oxygen mass transport vs. control by kinetics and ionic mass transport. It is shown that two distinct double Tafel slopes may arise from these two limiting cases. The former is first order, and the latter is half‐order with respect to oxygen concentration. How the modeling results may be applied to diagnose the performance of fuel‐cell cathodes is also presented. Since the ionic‐mass‐transport‐limited case has generally been neglected in previous gas‐diffusion electrode models, specific examples of fuel‐cell cathode data from the literature which display the behavior predicted by the models in this case are given and briefly discussed.

The interaction between different barrier metals and the copper surface during the chemical-mechanical polishing

The copper polishing rate in a weak acid slurry with H 2O 2 as a oxidizing agent is determined by a two-step process of the formation of copper oxides followed by its mechanical abrasion. The electrochemical potential is a criterion for the driving force of oxidation-reductions reactions that occur during the Cu dissolution process. Using the experiment a corrosion potential ( E corr) was determined. It depends on the potential of the cathodic reaction, the Tafel slopes of each reaction and the control of the reaction by Tafel kinetics or concentration polarisation. Potentiodynamic measurements were performed with different H 2O 2 contents in the slurry. The dissolution current density ( i corr) is correlated to the oxidation-reduction reaction rate. In the presence of a barrier metal, such as WTi, the dissolution rates were influenced by galvanic effects. W and Ti and their compounds were dissolved in the slurry by the complexing ability of H 2O 2. There is an increase in the barrier wet etch rate when copper is present. In the case of polishing both TiW and Cu simultaneously a dramatic increase of the barrier polish rate was observed. The acceleration of the W or Ti polish rate can be explained by the galvanic coupling between Cu and the barrier metal. By the use of TiN as a barrier metal no galvanic interaction has been observed. The removal rates of TiN have not been influenced by the presence of Cu.

Nonuniform Current Distribution and Thickness during Electrodeposition onto Resistive Substrates

The interaction of electrode and electrolyte resistances during plating onto resistive substrates is investigated. Following presentation of an asymptotic treatment for the estimation of current distributions on highly resistive substrates, more general cases are examined by numerical calculation to illustrate the influence of counterelectrode position, Tafel kinetics, and mass‐transfer limitations. The calculations are compared with approximate models presented in the literature or developed in this study in order to determine under which conditions they are applicable. The temporal evolution of the current distribution and conductance during deposit growth is investigated, and an approximate method for the determination of the variation in deposit thickness with time is presented.

New observations on the anodic oxidation of copper in hot acidified copper sulfate solutions

The anodic oxidation of copper in acidified copper sulfate solution has been investigated by potentiostatic and voltammetric techniques. The morphology and composition of the films were determined by X-ray photoelectron spectroscopy (XPS) and scanning electron microscopy (SEM). The passive layer is mainly composed of CuSO4. The presence of a Cu2O phase becomes detectable after multiple sweeps and thorough rinsing of the electrode with water at the end of the experiment. The effects of electrolyte composition and temperature on the phenomenon of passivation are also discussed. The initial steps of the copper dissolution were found to obey Tafel kinetics, and the maximum dissolution current, as well as the limiting transpassive current, was controlled by the rate of diffusion of cupric ions. The phenomenon of current oscillations occurs at potentials near the peak current upon scan reversal, suggesting that oscillations only occur with the formation of a sufficiently thick film. Oscillatory behavior disappears when conditions favor salt film stability.

Internal Ohmic Drop Limits on Effectiveness of Packed Bed Electrodes Obeying Tafel Kinetics

An analytical solution for internal ohmic drop in packed bed electrodes with high matrix conductivity and facile mass transfer is applied to data interpretation and design. Deduction of polarization parameters for simple Tafel behavior from experimental observations is illustrated. An effectiveness factor, Thiele‐type modulus relationship is derived to describe electrode utilization under these conditions.