Butler-Volmer Expression Research Articles

Clearing the Smoke: Revisiting the Liquid Phase Potential in Newman’s Battery Model

Abstract Lithium ion battery cell-level and sub-cell modelling has become almost synonymous with Newman’s Model. This paper sheds light on a specific part of the model, the liquid phase potential, clarifying its difference from the liquid phase potential found in the Butler-Volmer expression. Critically, we show that these two potentials should not be used interchangeably. In fact, the concentration potential gradient differs by a factor of six in standard LiPF6 electrolytes. Consequently, the Butler-Volmer current densities could be affected strongly if the definitions of electrostatic liquid phase potential are inadvertently interchanged.

Physics-Based Model to Represent Membrane-Electrode Assemblies of Solid-Oxide Fuel Cells Based on Gadolinium-Doped Ceria

This paper reports a physics-based model that predicts membrane-electrode assembly (MEA) performance of solid-oxide fuel cells (SOFCs) with Ce0.9Gd0.1O2−δ (GDC10) electrolyte membranes. The paper derives self-consistent thermodynamic and transport properties for GDC1o mobile charged defects (oxide vacancies and reduced-ceria small polarons) by fitting published measurements of oxygen non-stoichiometry and conductivity over ranges of temperature and O2 partial pressures. The button-cell model is applied to evaluate how mixed ionic-electronic conductivity influences the performance of an SOFC MEA with a GDC10 electrolyte sandwiched between a porous, composite Ni-GDC10 anode and a porous, composite cathode of Sm0.5Sr0.5CoO3−δ (i.e., SSC) and GDC10. SSC properties are also derived by fitting published conductivity and oxygen non-stoichiometry measurements. Mixed conductivity of GDC10 and competing charge transfer reactions at both electrodes reduce open circuit voltages due to leakage current and buildup of defect concentrations at electrode-electrolyte interfaces. To fit polarization data, the button-cell model includes heterogeneous reaction rates for defect incorporation on the GDC10 surface along with Butler–Volmer expressions derived for competing charge transfer reaction rates from rigorous analyses assuming rate-limiting, elementary charge transfer reactions for each electrode. The calibrated MEA model can support rigorous SOFC modeling with GDC10 electrolytes over the range of conditions within a fully operating cell.

Multiphysics Modeling for Solid Oxide Electrolyzer Cell with Heterogenous Synthetic Microstructure

Solid oxide fuel cell (SOFC) and electrolyzer cell (SOEC) are the main focus for researchers in recent times to diminish greenhouse gas emissions and meet cleaner energy demand, as these devices have highest energy conversion rates and efficiencies [1]. The major hinderance in commercializing SOEC is due to its faster cell degradation under higher current density, compared against its SOFC counterpart. The delamination of oxygen electrode (OE) from the electrolyte (EL) is one of the major causes for the cell degradation [2].We employed a multi-physics numerical model to understand the electrochemical performance of a SOEC half-cell more precisely at a microscale. In this study, widely used mixed ionic and electronic conductor (MIEC) La1-xSrxCo1-yFeyO3-d (LSCF) and Gadolinium-doped Ceria (GDC) composite is used as the oxygen electrode and, pure ionic conductor 8 mol% Y2O3 doped ZrO2 (YSZ) is used as the electrolyte. A GDC buffer layer is tucked in between to prevent undesirable side reactions between OE and EL during long term polarization operation. Until now, a homogenous OE structure has commonly been used with effective physicochemical properties to predict the performance of SOFC/SOEC [3,4]. Only a few researchers have worked on heterogenous microstructure model [5] and simulated the electrochemical performance of the cell.Synthetic microstructure of LSCF-GDC porous electrode as shown in Figure 1 are constructed with an opensource software Dream 3D with particle size ranging from 0.45um - 1.5um. We developed in-house Matlab code for labelling domains, interfaces (2PB and 3PB) and digitally removing the unconnected phases to reduce numerical instabilities while solving the mathematical model in COMSOL Multiphysics 6.0. Mesh in these domains is constructed using Iso2Mesh toolbox [6] and translated as mphtxt file which is later imported into COMSOL. This practice reduces the computational time and memory.We employed Nernst-Planck theory for solving the transport of species like vacancy, hole and electron within LSCF inside OE. Multi-step charge transfer at two phase boundary (2PB) and triple phase boundary (3PB) interfaces for oxygen evolution reaction are formulated by Butler-Volmer expressions [4]. A physics-based impedance model under DC bias is developed to separate the electrochemical contributions from 2PB and 3PB transport pathways. The voltage-current curve during long-term polarization test is coupled with the model for validation and approximation of process parameters. Furthermore, we will simulate the crack propagation at OE-buffer layer interface in various directions and orientations to understand the failure mechanism on the synthetically constructed microstructure.

Output voltage control of double chambers microbial fuel cell using intelligence-based optimized adaptive neuro fuzzy inference controller

Microbial fuel cell (MFC) has become a very important biotechnological tool to produce clean energy in recent years. It is very important to adjust the output voltage and power density in order to obtain the desired energy quickly and smoothly at the output of the MFC. In this study, an optimization-based neuro-fuzzy inference controller is proposed for improving voltage tracking performance of the MFC. A double-chambers MFC model including biochemical reactions, Butler-Volmer expressions and mass/charge balances was studied and Particle Swarm Optimization (PSO) and Improved Grey Wolf Optimization (IGWO) algorithms are used to adjust the parameters of the neuro-fuzzy controller. The results show that PSO and IGWO based controllers have efficient performances to follow the reference voltage pattern quickly and robustly against external load changes, distributions and parameter uncertainties. Moreover, it was observed that IGWO was a more stable and robust controller than PSO according to rise time, overshoot and peak time.

Nonlinear Phase-Field Modeling of Lithium Dendritic Growth during Electrodeposition

Lithium batteries have been widely used, but the growth of lithium dendrites does lead to some hazards, such as internal short circuit, thermal runaway and even explosion. In paper, a nonlinear phase field model combined with Butler-Volmer expression was developed to study dendrite growth during electrodeposition. Two types of initial electrode-electrolyte interface are applied in numerical simulations. Results show that the cation concentration enrichment occurs near the dendritic tip due to the electromigration, and the curve of the growth velocity versus time follows a simple power law relation, indicating that the stability of the dendritic array originating from initial electrode-electrolyte interface can be broken with the applied electrical potential increasing. Moreover, we found that applied electric potential gradient can strongly influence the dendritic growth velocity and the dendritic growth during electrodeposition is less relative to the surface tension anisotropy.

Modeling of the solid oxide fuel cell anode based on a new analytical model using nonlinear Butler-Volmer expression

Modeling of the solid oxide fuel cell anode based on a new analytical model using nonlinear Butler-Volmer expression

Experimental and Theoretical Investigation of Lib-Active Materials Properties

Li-ion batteries (LIB) are currently used for energy storage in several applications. The design of LIB system must ensure the holding of performance for a given application during its entire life. Nowadays, Newman based models [1] are among the electrochemical models developed to compute the physical phenomena at the electrode scale, while predicting the behaviour of the entire cell. However, they require electrode’s components physical parameters. Finding out these physical parameters and their evolution during their lifetime is thus critical to simulate and predict with a high reliability the electrochemical response of the LIB via these models. Among the physical parameters, the equilibrium potential Eq , the solid diffusion Ds , and the exchange current density i0 of positive and negative active materials are affecting significantly this electrochemical response. Determining their expressions according to stoichiometry and their consistency based on thermodynamic approach [2] is an improvement for modelling Li-ion batteries. In this work, Ni0.6Mn0.2Co0.2O2 (NMC 622) is considered as the active material of the positive electrode and graphite for the negative one.In this paper, a methodology to extract these parameters from experimental data as function of the stoichiometry is presented. Then, an analytical model of their stoichiometry dependence is derived based on thermodynamic considerations. Eq and Ds have been measured using the Galvanostatic Intermittent Titration Technique (GITT) [3] on both half cells and a pouch cell with a lithium reference electrode. Results on the first design (half-cell) allow to quantify the active materials available at the positive and negative electrodes of the second design (pouch cell) and determine active materials stoichiometry as function of cell’s state of charge (SOC). i0 is determined from electrochemical impedance spectroscopy measurements (EIS) [4] performed at different cell’s state of charge on a specific experimental design with two references electrodes (Figure 1a). A lithium iron phosphate (LFP) reference electrode has been used to measure simultaneously the impedance spectra of both positive and negative electrodes. Lithium has been implemented as a second reference electrode to follow the LFP reference electrode potential, and the negative electrode potential at the different SOC of the EIS measurements. The exchange current densities are extracted using a Transmission Line Model (TLM) [5] and obtained results are presented (Figure 1b) for the two materials as function of the stoichiometry. A comparison of these results with the classical Butler-Volmer expression (classical BV) used in porous electrode theory shows a gap between them. This difference was highlighted by Bazant [6] where he presented an intercalation kinetics model dedicated to lithium iron phosphate intercalation, going beyond the elementary reaction considered in classical BV. With the classical BV, the molecular intercalations (repulsive or attractive forces) are neglected.The measured stoichiometry dependence of these three active material’ parameters is further analyzed, based on thermodynamic considerations. For the positive material, a model is proposed for this observed stoichiometry dependence, highlighting the non-ideal molecular behavior of lithium inside the host material.Finally, to validate the methodology and assess the predictability of Newman based LIB model, a comparative numerical simulation of the impedance spectra for the positive and negative electrodes with Newman electrochemical model with Eq , Ds , and i0 has been performed. Results at 20 and 80% SOC are presented Figure 1c for the negative electrode.

An Algorithm for the Extraction of Tafel Slopes

The Tafel equation, which serves as a linearized representation of the Butler–Volmer expression, permits the extraction of fundamental parameters of electrochemical systems, such as exchange curren...

Simulation of corrosion of a dual phase alloy steel based on its constituent phase polarization properties

In this study, the corrosion of dual phase alloy steel namely super duplex stainless steel (SDSS) is simulated by taking into consideration the presence of two distinct phases that are austenite and ferrite. A simulation algorithm is developed by the authors for simulating micro galvanic corrosion by random assignment of anode and cathode zones assuming non-linear polarization curves. The governing equation for electric potential in the electrolyte is Laplace equation owing to charge neutrality implying diffusion limited corrosion rate. The metal-electrolyte interface is allowed to dissolve as a moving boundary problem approach in a computer simulation by assigning ferrite property to anode and austenite property to cathode randomly. To validate this proposition, the true non-linear polarization data and its fluctuations in the form of fitted Butler–Volmer expressions of individual phases of the SDSS alloy are used as the boundary condition on anode and cathode zones corresponding to ferrite and austenite phases. This modeling approach is applied to pure austenite as SS304 and pure ferrite as SS430 and 50–50 austenite-ferrite as SDSS. The obtained simulation results of corrosion rate of the SDSS and its constituent pure phases compared well with the direct polarization prediction of corrosion rate for various concentrations of NaCl in water. The simulation prediction is found to be a good fit than by weighted average method.

(Norman Hackerman Young Author Award) Multiphase Porous Electrode Theory

As batteries become increasingly common and important in products we use in our daily lives, it becomes similarly important to be able to model their behavior at full cell length and time scales. This capability facilitates both their design and use. The diverse applications in which batteries are applied each require careful design optimization in order to provide the most cost-effective solution satisfying the product needs, and experimentally exploring the full design space in order to find the optimum is impractical. Cell models help drastically narrow the space, enabling cost-effective product development. With existing cells, the models can help provide estimates of difficult-to-measurable internal variables, which may inform usage constraints. In order for the models to provide the most value and ability to extrapolate beyond their training data, their underlying physics must be as representative as possible of the real electrochemical system. Porous electrode theory has been developed, validated, and extended for many battery chemistries for decades and serves as the basis for most physical models at full cell length scales. In this work, we continue in that tradition by exploring the incorporation of new models for both the active particles and the interfacial electron transfer reaction kinetics. In the active particles, we employ non-equilibrium thermodynamics, enabling us to consistently describe particles with internal phase separation within a Cahn-Hilliard-type phase field framework. Many practically relevant electrode materials exhibit phase separation during lithium insertion, and various approaches have been used to model these systems, many of which either neglect the details of the resulting concentration profiles or describe the phase interfaces using numerically inconvenient phase boundaries with no interfacial tension. In the phase field approach, phase boundaries appear and disappear spontaneously according to the governing free energy functional without specialized numerical methods for interface tracking, and they naturally structure themselves in energy-minimizing configurations according to their interfacial tension, system stresses, etc. Rather than being a fit input, the equilibrium voltage emerges as a result of the free energy functional and the highly non-uniform concentration profiles as the average system concentration varies. The lithium in the active materials is consistently coupled to the electrolyte phase by variationally defined reaction kinetics, represented either by a generalized Butler-Volmer expression or quantum-mechanical electron transfer theories such as Marcus-Hush-Chidsey kinetics extended for concentrated solutions. This generalization of porous electrode models reduces directly to the more familiar “Newman” model with concentrated solution theory in the electrolyte in the case of solid solution active materials. Here, we will explore the theoretical developments in the model and present relevant examples, with a focus on comparisons with previous models and some experimental evidence in support of the approach.

Electrochemical Modeling of HTPEM Fuel Cells Using Elementary Step Kinetics

High temperature polymer electrolyte fuel cells (HT-PEM) offer certain advantages over the low temperature polymer electrolyte membrane fuel cells (LT-PEM). Numerical modeling is a powerful tool to understand the thermo-chemical and physico-chemical processes that takes place within the gas diffusion layer (GDL) and the catalyst layer (CL) during the cell operation. The models reported in the literature varies from simple analytical expressions to 3D models. Most of these models are based on a general Butler-Volmer equation, without giving any importance to the underlying charge transfer mechanism, and therefore the exchange current densities are fitted to some arbitrary order with respect to hydrogen and oxygen concentrations. Furthermore, most of these models are validated by reproducing the IV curve often by a one dimensional model by resolving the electrode thickness. Whenever such as validation is done, the fuel and oxidant depletion along the cell length and hence the fuel utilization is not accounted for. To the best of our knowledge no attempt has been done to date to validate the experimentally measured axial current density profile. A predictive model should be capable of predicting the measured axial current density profile and the IV curves. The objective of the current work is to develop an electrochemical model based on elementary step charge transfer that occur at the anode and cathode of the HT-PEM fuel cell. In order to develop the mechanistic steps, dissociative adsorption of H2 and O2 is considered. In addition, to account for performance drop in presence of CO, adsorption of CO is also considered in the elementary step reactions. Assuming the protonation reaction to be rate limiting at the anode three phase interface and OH formation to be rate limiting at the cathode three phase interface, Butler-Volmer expressions are derived for the charge transfer reactions at the respective electrodes.The exchange current density at the anode follows i=ioa [exp (βafηa) - exp (-βcfη)], and at the cathode follows i=ioc [exp (-βcfηc) - exp ((1+βa)fηc)].Here, the exchange current densities at the anode and cathode are respectively given by i0a =i*x [(KH2pH2)1/4]/[1+(KCOpCO)+(KH2pH2)1/2)]andioc = i*x [(pH2/p0)1/4 (KO2pO2)3/8]/[1+(KO2pO2)1/2+(pH2/p0) exp (- ΔG*/RT)]. The equilibrium constants appearing the expression for the exchange current densities are evaluated from the adsorption desorption equilibrium of the reactant species (H2, O2, and CO). The adsorption rates are calculated from the sticking coefficients. The activation energy for the desorption reactions is calculated using Unity Bond Index Quadratic Exponential Potential method (UBI-QEP) and the frequency factor for the desorption reactions is calculated from transition state theory. The electrochemical model is incorporated into a quasi-two dimensional numerical transport model of the cell.The transport model accounts for the species transport in the flow channels and diffusive transport across the thickness of the electrode (GDL + CL). The diffusive transport in the porous electrode is modeled using Dusty Gas Model (DGM). The resulting governing equations for the species transport are solved using the ODE solver CVode. The electrochemical model, i.e., the Butler-Volmer equations and the cell voltage equation, forms a set of algebraic equations, which are solved using a damped Newton iteration for every call made by the CVode solver.The whole model is implemented in C++. The model developed can predict the current density and species profiles along the cell length and the thickness of the catalyst layer required to achieve best cell performance. The current density profile predicted by the model along the length is validated by comparing against the experimental measurements reported in the literature. For demonstrating the capability of the model, a comparison between the simulated IV curves and the experimental measurements (Li et. al, 2003 ECS) is given in the Figure. Figure 1

Insight on Tafel slopes from a microkinetic analysis of aqueous electrocatalysis for energy conversion.

Microkinetic analyses of aqueous electrochemistry involving gaseous H2 or O2, i.e., hydrogen evolution reaction (HER), hydrogen oxidation reaction (HOR), oxygen reduction reaction (ORR) and oxygen evolution reaction (OER), are revisited. The Tafel slopes used to evaluate the rate determining steps generally assume extreme coverage of the adsorbed species (θ ≈ 0 or ≈1), although, in practice, the slopes are coverage-dependent. We conducted detailed kinetic analyses describing the coverage-dependent Tafel slopes for the aforementioned reactions. Our careful analyses provide a general benchmark for experimentally observed Tafel slopes that can be assigned to specific rate determining steps. The Tafel analysis is a powerful tool for discussing the rate determining steps involved in electrocatalysis, but our study also demonstrated that overly simplified assumptions led to an inaccurate description of the surface electrocatalysis. Additionally, in many studies, Tafel analyses have been performed in conjunction with the Butler-Volmer equation, where its applicability regarding only electron transfer kinetics is often overlooked. Based on the derived kinetic description of the HER/HOR as an example, the limitation of Butler-Volmer expression in electrocatalysis is also discussed in this report.

Energy Payback Time Modeling of Integrated Photoelectrochemical Devices Using Concentrated Solar Irradiation

The photoelectrochemical (PEC) production of hydrogen offers a direct pathway for the conversion of solar energy into an energy dense and transportable fuel. In an integrated PEC device, solar radiation is absorbed by photoactive components which provide the necessary potential for water electrolysis to take place in the integrated proton exchange membrane electrolysis cell (PEMEC). The produced current density in the photovoltaic component (PV) increases with increasing solar irradiation, i.e. concentration. This results in higher hydrogen production rates for a PEMEC with small overpotentials, i.e. good ohmic conductors and efficient catalysts, compared to non-concentrating systems. We also expect further reduction in energy and material requirements of a concentrated PEC (CPEC) device and its fabrication and, consequently, its energy payback time (EPBT). We compared the EPBT of PEC and CPEC devices for water electrolysis. For the latter, we compared existing concentrating technologies - lenses, mirrors, and Cassegrain reflectors - and a novel integrated CPEC device using a self-tracking wave-guide concentrator.We developed a model that assesses the energy requirements of the different component (concentrator, electrolysis cell, photovoltaic cell, external components) by coupling the energy and material inventory of devices to a detailed performance model under different concentrations. The model uses the Shockley-Queisser limit to assess the performance of the multijunction photovoltaic cell, and an equivalent circuit model was used to assess the performance of the electrolysis cell, including kinetic overpotentials via Butler-Volmer expressions, ohmic resistances via Ohm’s law, and mass transport overpotentials [1].The results show that the EPBT of all concentrating technologies are in the same order of magnitude (5-10 years). However, the integrated self-tracking concentrator design shows a lower EPBT than Fresnel lenses-based concentrating systems due to a lower primary energy demand of the former (1600 MJ/m² for integrated, self-tracking concentrator, and 2800 MJ/m² for external Fresnel concentrator coupled to PV-electrolyzer). A sensitivity analysis showed that the most influential parameters for the reduction of the EPBT are the yearly solar irradiation, the primary and operating energy demand of the concentrator, the performance of the concentrator, the exchange current density of the catalysts, and the fill factor of the photovoltaic cell. The EPBT could be reduced by at least 6% with a variation of 10% of one of these parameters for all the technologies studied. This developed model provides a useful tool for device design to compare and optimize the energy requirements of integrated PEC and CPEC devices[1] P. K. Das, X. Li, and Z.-S. Liu, “Analytical approach to polymer electrolyte membrane fuel cell performance and optimization,” J. Electroanal. Chem., vol. 604, no. 2, pp. 72–90, Jun. 2007.

Thermodynamic derivation of a Butler–Volmer model for intercalation in Li-ion batteries

We present an exclusively thermodynamics based derivation of a Butler–Volmer expression for the intercalation exchange current in Li ion insertion batteries. In this first paper we restrict our investigations to the actual intercalation step without taking into account the desolvation of the Li ions in the electrolyte. The derivation is based on a generalized form of the law of mass action for non ideal systems (electrolyte and active particles). To obtain the Butler–Volmer expression in terms of overpotentials, it is necessary to approximate the activity coefficient of an assumed transition state as function of the activity coefficients of electrolyte and active particles. Specific considerations of surface states are not necessary, since intercalation is considered as a transition between two different chemical environments without surface reactions. Differences to other forms of the Butler–Volmer used in the literature [1,2] are discussed. It is especially shown, that our derivation leads to an amplitude of the exchange current which is free of singular terms which may lead to quantitative and qualitative problems in the simulation of overpotentials. This is demonstrated for the overpotential between electrolyte and active particles for a half cell configuration.

Modelling and simulation of two-chamber microbial fuel cell

Microbial fuel cells (MFCs) offer great promise for simultaneous treatment of wastewater and energy recovery. While past research has been based extensively on experimental studies, modelling and simulation remains scarce. A typical MFC shares many similarities with chemical fuel cells such as direct ascorbic acid fuel cells and direct methanol fuel cells. Therefore, an attempt is made to develop a MFC model similar to that for chemical fuel cells. By integrating biochemical reactions, Butler–Volmer expressions and mass/charge balances, a MFC model based on a two-chamber configuration is developed that simulates both steady and dynamic behaviour of a MFC, including voltage, power density, fuel concentration, and the influence of various parameters on power generation. Results show that the cathodic reaction is the most significant limiting factor of MFC performance. Periodic changes in the flow rate of fuel result in a boost of power output; this offers further insight into MFC behaviour. In addition to a MFC fuelled by acetate, the present method is also successfully extended to using artificial wastewater (solution of glucose and glutamic acid) as fuel. Since the proposed modelling method is easy to implement, it can serve as a framework for modelling other types of MFC and thereby will facilitate the development and scale-up of more efficient MFCs.

Modulation of electroosmotic flows in electron-conducting microchannels by coupled quasi-reversible faradaic and adsorption-mediated depolarization

A theoretical model is proposed for the description of steady electroosmotic flows within a cylindrical electron-conducting microchannel that is depolarized by faradaic and adsorption-mediated processes. The bipolar electron-transfer (e.t.) reactions are examined in the general situation where the electrolyte contains a quasi-reversible redox couple. The rate of the e.t. reactions is governed by transversal convective diffusion of the electroactive species to/from the surface and a position-dependent degree of reversibility. The nonuniform distribution of the electric field in solution, that is intimately coupled to that of the local faradaic current density, alters the double layer composition along the conducting surface via the occurrence of simultaneous electronic and ionic double layer charging processes. This in turn generates a nonlinear distribution of the zeta potential, which affects the electroosmotic flow. The highly coupled spatial profiles for the concentrations of the electroactive species, the faradaic current density, the electrokinetic potential, the electric field and the electroosmotic velocity in/along the metallic channel are solved by consistent numerical analysis of (i) the convective-diffusion equation, (ii) the generalized Butler–Volmer expression that includes mass transport and electron-transfer kinetic contributions, (iii) the continuity and Navier–Stokes equations, and (iv) the Poisson equation for finite currents. The results reported as a function of the surface properties of the channel and the kinetic characteristics of the e.t. reaction illustrate the deviations of the electroosmotic flow profiles as compared to the typical pluglike distribution predicted by Smoluchowski's equation and encountered for homogeneous and dielectric channels. Manipulation of the flow patterns by bipolar electrochemical means is a promising way to control and optimize the local detection and separation of electroactive molecules or molecules dyed with electroactive elements.

Analytical Pore Scale Modeling of the Reactive Regions of Polymer Electrolyte Fuel Cells

This paper analyzes the effects of the catalyst layer porous structure on the performances of polymer electrolyte membrane fuel cells. Comparing the characteristic lengths of the porous structure with the characteristic lengths of the diffusion phenomena shows that the oxygen and hydrogen concentrations in the electrolyte phase change significantly at the pore scale level; therefore, the related diffusion phenomena need a nonhomogeneous description. These rapidly varying concentrations are coupled to the cell potentials through the reaction rate expression, i.e., the Butler-Volmer equation. Thus, to employ a macrohomogeneous description of the fuel cell without loss of accuracy, it is necessary to find an effective expression for the reaction rate which does not depend explicitly on the rapidly varying concentrations. This is done here through an analytical averaging procedure and results in an effective Butler-Volmer expression that includes implicitly the effects of nonhomogeneity of the porous structure. This expression is compared with the ordinary Butler-Volmer expression and with the agglomerate models in the literature. The former turns out to be valid only in the limit of low current densities, and the latter only in the high porosity limit. Finally, the effective Butler-Volmer expression is inserted in the framework of macrohomogeneous models. From the analysis of the model results, one can conclude that the effects of the porous structure on the cell performances are crucial for the correct description of the cell concentration polarization and the estimation of the effective Tafel slope at high current densities. © 2003 The Electrochemical Society. All rights reserved.

Temperature dependent surface electrochemistry on Pt single crystals in alkaline electrolyte

The kinetics of the oxygen reduction reaction (ORR) was studied in alkaline electrolyte at 293–333 K on Pt(hkl) surfaces by means of the rotating ring-disk electrode technique with solution phase peroxide detected at the ring electrode. The ORR on Pt(hkl) was found to be highly structure sensitive with activities increasing in the sequence (111) > (100) > (110)(1 × 2). Very similar apparent activation energies (37–45 ± 5 kJ mol−1, η = 0.35 V) were found on all three surfaces. Furthermore, at elevated temperature, significantly smaller amounts of peroxide are formed in agreement with enhanced peroxide reduction rates by increasing temperature. We found that the Tafel slopes on all three single crystal surfaces decrease with increasing temperature, indicating that the log i–E relationship is not represented by a classical Butler–Volmer expression. Based on the kinetic analysis of the polarization curves and from simulations of log i–E curves, we propose that the rate of the ORR on Pt(hkl) in alkaline solution is mainly determined by the potential/temperature dependent surface coverage by OHad. We propose two modes of action of the OHad: (i) OHad blocks the adsorption of O2 on active platinum sites; and (ii) OHad alters the adsorption energy of intermediates which are formed during the ORR on Pt sites.

Complex Electron Transfer Kinetic Data from Convolution Analysis of Cyclic Voltammograms. Theory and Application to Diamond Electrodes

A new and versatile procedure, based on convolution analysis, for the evaluation of complex electron transfer kinetic data from cyclic voltammetric experiments is proposed. Both the anodic and the cathodic partial reaction are analyzed independently by the use of a linearized form of the Butler-Volmer equation. It is shown that for both branches well-defined Tafel-type plots can be obtained even from quasireversible cyclic voltammograms. Processes inconsistent with Butler-Volmer kinetics can be analyzed. The approximations inherent in Tafel analysis associated with (i) concentration gradients in the solution phase and (ii) mixed anodic and cathodic processes close to the equilibrium potential can be overcome. Additionally, the sum of anodic and cathodic transfer coefficient needs not to be unity and may even change with potential. The analysis therefore provides a general tool for parametrization and for testing the validity of the Butler-Volmer expression for a given electrode process. The application of the new methodology is tested with simulated voltammograms and is demonstrated for the Fe(CN)63–/4– redox system at a metal electrode, platinum, and at a polished highly boron-doped diamond electrode. At the diamond electrode both reduction and oxidation processes give linear Tafel-type plots with α=0.29±0.02 and β=0.42±0.03.

Current losses in a bipolar cell — II: An analysis of the Butler–Volmer regime

The effects of anodic and cathodic overvoltages given by Butler–Volmer expressions on the determination of bypass parasitic currents are studied in detail, as a function of several design parameters like the bypass resistance and the number of plates as well as other electrochemical parameters like the cell current, the anodic/cathodic exchange currents and the transfer coefficients. The failure of Tafel approximation in the middle plates (even when the cell current is large) is illustrated. Exact expressions for an approximate model are compared with our calculations.