Butler-Volmer Equation Research Articles

Electrochemical Polarization Part 1: Fundamentals and Corrosion

Polarization measurement is one of the major electrochemical methods used by electrochemists. The changes in current/potential with time at constant potential/current are investigated. The outcomes of these observations can be used to plot a current–potential curve. Therefore, it is important to understand the relationship between the three parameters: electrode potential, current, and time. In this paper, we described the fundamentals of the polarization, especially the current–potential curve (Butler–Volmer equation) and mass-transfer. In addition, the concept of polarization in corrosion reactions is explored.

Impact of Proton Activity in PFSA Membranes on Electrochemical Kinetics Using Microelectrodes

Polymer-electrolyte fuel cells and electrolyzers (PEFC&Es) have the potential to play a prominent role in green energy technologies including transportation, chemical manufacturing, and grid-scale energy storage. PEFC&Es have made significant advancements in recent years, largely due to improvements in the catalyst layers, and especially at the ionomer/catalyst interface. However, it is not yet definitively known how this solid-state environment impacts electrochemical kinetics, especially under various operating conditions (e.g., temperature, humidity, etc.). Additionally, it is challenging to probe local conditions at the catalyst/ionomer interface using traditional analytical techniques. In this study, we explore the influence and nature of proton activity in Nafion and 3M ionomers using a specialized microelectrode setup containing a 50 μm platinum microelectrode in a solid-state three-electrode cell for hydrogen oxidation and evolution (HOR&HER) reactions. Proton activity was calculated through open circuit voltage measurements, and was found to increase with increasing water content, mirroring trends in reaction performance. The effect of proton activity on the reactions' kinetics was investigated using semi-empirical fitting with the Butler-Volmer equation, which gives insight into the reaction rate order and possible mechanism for the reactions. This study demonstrates that microelectrodes can be used to probe solid-state kinetics and can also elucidate complex ion interactions within the ionomer at the catalyst/ionomer interface.

Computational Optimization of Functionally Graded Electrodes for Solid Oxide Fuel Cells

Solid Oxide Fuel Cells (SOFCs) are widely considered to be an ideal power source across a range of industries in the near future due to their high efficiency, high power density, and fuel flexibility. However, for widespread usage of SOFCs to be feasible, certain disadvantages, such as their high operating temperature, electrochemical losses, and high cost of manufacturing, must be solved. In particular, the field of materials research occupies a unique position of being able to quickly and simultaneously solve many of these issues through the development of material compositions and structures that do not currently exist in the industry. Especially relevant to solid oxide fuel cells in particular, is the impact that the electrodes’ geometries and compositions have on the operating performance. The electrodes’ ability to quickly move reactants to the interface of the electrolyte and remove products to the bulk flow comes into play as the fuel cell operates at higher current densities and concentration losses become prominent. Therefore, the microstructures present throughout the electrodes’ depth plays a vital role in improving overall cell performance. However, current fuel cell research has not yet effectively captured and defined the connections of the microstructure parameters and measured their impact on cell behavior. Additionally, homogeneous electrode design and implementation have dominated the research and commercial space thus far. The technique of functional material grading, which has begun to see wide research and commercial usage for such problems as acoustic impedance matching, thermal control, and mechanical design will be leveraged for the enhancement of SOFC electrodes. Functionally graded electrodes have been used in solid oxide fuel cell research in recent years in an effort to improve the cell performance by altering the microstructure including porosity, particle size, and composition of electronic and ionic conductors near the triple phase boundary region. Normally the functional grading process adds additional fabrication steps making it less desirable as an optimization process and easy manufacturing method. However, by using an additive manufacturing process it eliminates the need for multiple discrete graded layers to be deposited to obtain a graded electrode functional layer. This study seeks to explore the correlations of geometry and structure parameters from the meso-scale through to the micro-scale level, together with mass transfer, ionic and electronic transport, and gas-surface electrochemical reactions inside the electrodes to guide future additive manufacturing of SOFCs. Outlined is the development of an effective medium model for simulating the performance of fuel cell microstructures as a function of specific operating ranges in temperature, pressure, and in fuels used. Smooth and continuous linear and nonlinear functional gradation profiles of porosity and material composition are studied within the framework of an effective medium boundary value problem where the electrochemical relations, such as the Butler-Volmer equation, percolating conduction paths, and gas diffusion are solved using the finite difference method. The form of these relations for homogeneous electrodes was analyzed by Costamagna, et. al [1], who also defined outstanding problems with regards to optimizing SOFC electrodes [2]. Globally optimal linear and nonlinear gradation profiles and cell parameters are derived as a function of particle sizes, ratio of conductivities, and desired operating conditions and scored based on their reduction of cell overpotentials.[1] Costamagna, P., P. Costa, and V. Antonucci, Micro-modelling of solid oxide fuel cell electrodes. Electrochimica Acta, 1998. 43(3-4), pp.375-394.[2] Costamagna, P., P. Costa, and E. Arato, Some more considerations on the optimization of cermet solid oxide fuel cell electrodes. Electrochimica Acta, 1998. 43(8), pp.967-972. Figure 1

Finite-Element Simulation for Ion Co-Intercalation Chemistry on Si Anode at Lithium-Ion Half-Cell

The increasing demand for higher capacity energy storage technologies is rapidly becoming an important consideration in the development of EV and related energy storage devices. Silicon is one promising solution as an earth-abundant element with a higher capacity than the more commonly used graphite anode of a lithium-ion battery. However, silicon anodes face unique challenges with volume expansion, notable during lithium ion intercalation and the stability of the SEI layer. To solve this problem, some recent research efforts discovered introducing a co-intercalation ion in the traditional lithium electrolyte Gen2 increases the coulombic efficiency, capacity, and stability of the silicon anode, but its mechanism of action remains unclear.In this work, in combination with experimental measurements we demonstrate the use of Newman's P2D Lithium Model in COMSOL together with the Butler-Volmer equation and concentrated solution theory to describe cation co-intercalation into the porous silicon anode material. Experimental data indicates that phase formation and transformation coincide with ion insertion, as reflected in the current response signal. Both the original ion intercalation and the foreign ion intercalation are reflected by CV generated by our model under the influence of model parameters, such as the variable speed of potential changed per second. As designed, our model can be extended towards general application in the cointercalation system and understanding of the foreign ion effect.

(Digital Presentation) Micro-Scale Simulation of PEFC Catalyst Layer with Dynamic Structure Change

In order to develop high performance Polymer Electrolyte Fuel Cells (PEFCs), the innovative electrode materials are needed and utilized in optimal catalyst structure from the viewpoint of high output density, low amount of Pt and durability. In present PEFC, the resistance of the oxygen reduction reaction (ORR) at the cathode are dominant factors, and a key requirement is the smooth, rapid, and uniform supply of protons, electrons, and oxygen to the Pt surface. Moreover, an improved mass transport flux in the catalyst layer offers the possibility of increasing current densities, which in turn allows the reduction of cell areas, enabling further cost reductions. In our past studies, we focused on the actual heterogeneous porous structure of catalyst layer. From these results, it was found that mass transport performance of oxygen and proton in heterogeneous porous catalyst layer, which consists of carbon support, ionomer and void space, is much lower than that of theoretical prediction in homogeneous porous media [1-5]. In addition, it depends on the structure of carbon black, the coating structure of ionomer and the local distribution of these materials. Accordingly, optimization of porous structure of catalyst layer is needed, and the mechanism of mass transport resistance and reaction distribution have to be understood in detail. The numerical simulation is effective to understand it because the difficulty of experimental measurement directly. In this study, to understand the relationship between heterogeneous porous structure and cell performance, a three-dimensional heterogeneous CL structure consisting of a simulated CB aggregate and an ionomer coating model was developed using numerical analysis. Moreover, this simulation was applied to actual experimental cell test condition.Firstly, we simulated CB aggregate structure. Previously, our research group examined a numerical model for actual CB aggregate structures (Vulcan and Ketjen black) [6, 7]. These structures were reconstructed with a probability density distribution that was a function of the distance between particles. And various structural properties, such as aggregate size, anisotropy, surface volume and surface weight were evaluated with experimental data. With this model, actual CB aggregate structure was simulated which was same as that in experimental cell test. The structure of catalyst layer was simulated by random packing these CB structure and ionomer coating model [8]. Pt particles were placed on the CB surface and in CB pore. In the calculation of cathode electrochemical reaction, the kinetic activity (exchange current density) of exterior and interior Pt surface were set different value by considering effect of ionomer coating [9]. The electrode reaction was calculated using the Butler–Volmer equation for the formation of Pt oxide on the Pt surface. This oxide layer inhibits the absorption of oxygen, and the coverage depends on the local potential. The resistance of oxygen diffusion and dissolution in ionomer was included. The mass balance equations for oxygen, vapor, protons, and electrons in catalyst layer was coupled with local reaction [10]. The current density distribution was found to depend on the carbon black structure and ionomer adhesion shape. From the viewpoint of increasing both Pt utilization and mass transport performance, an adequate heterogeneous pore structure is necessary in the catalyst layer. Furthermore, this simulation was applied the evaluation of structure change of catalyst layer after long-time durability test. The information of the diameter of CB primary particle and Pt particle of BOL and EOL that obtained by 3D TEM was used. The effect of this dynamic structure change on cell output performance will be reported in this presentation.Acknowledgements This research was supported by the New Energy and Industrial Technology Development Organization (NEDO), Japan, grant number P20003-20001327-0.

Comparison of Serpentine and Interdigitated Monopolar Plates on the Performance of an Anion Exchange Membrane Fuel Cell By CFD

The continuous energy demand and the growing population have focussed the scientific research on developing alternative energy sources or green fuels.The anion exchange membrane fuel cell (AEMFC) arises as an excellent alternative because of its low-cost electrocatalyst used at the cathode, energy production, and no pollutants emissions to the environment. Nowadays, several studies have been conducted to improve the performance of the AEMFC modifying membrane materials, types of gas diffusion layers (GDL), and catalysts, among other cell components.However, the design of the flow channels by changing plate topologies and materials is still under development. About flow channels topologies, conventional geometries array (pin, straight, parallel, and serpentine) flow fields lead the flow in the direction parallel to the electrode surface, and the reactive gas flow towards the catalyst layer (CL) mainly by molecular diffusion. On the other hand, interdigitated flow fields provide convection velocity normal to the CL and forced convection flow in GDL for better mass transfer. The interdigitated flow fields could prevent water flooding and improve high current density operations performance.These flow fields have been tested in proton exchange membrane fuel cells (PEMFC) with excellent results at low current densities. Nonetheless, there is an essential balance and management of water in an AEMFC. It presents simultaneous production and consumption of water in anode and cathode, respectively, where the production is twice the consumption.Poor water management could provoke anode flooding or membrane drying. These scenarios are undesirable due to mass transport limitations, membrane polymer degradation, and cathodic channels flow can be flooded. Therefore, an appropriate design of flow field that allows the correct water balance on AEMFC is needed for optimal performance. This research deals with the computational fluid dynamic (CFD) comparison of serpentine and interdigitated flow fields on the performance of an AEMFC. For the development of this model, the Navier-Stokes and Brinkmann equations were implemented for momentum transfer. In addition, the average mixture model represents the transport of chemical species, and the Butler-Volmer equation denotes the electrochemical reaction at the CL; water balance is analyzed at low and high current densities to evaluate the scenarios above mention.Preliminary results indicate that a serpentine design is functional at the anode due to the water management is favored. An interdigitated flow field is implemented at the cathode to improve the distribution of the reactants from channels until the CL.

Simulation of dynamic response of mixed-potential hydrogen sensors

Knowledge about factors affecting the dynamic response process is crucial for development of mixed-potential gas sensor for various applications such as hydrogen detection. Based on a double layer capacitor model and the Butler-Volmer equation, the present work studied the dynamic hydrogen sensing process by numerical simulation in combination with experimental assessment. Simulation shows that both response and recovery times are jointly determined by the decrease rate of the net reaction current and the magnitude of response. Increase of standard reaction rate constants, transfer coefficients, standard equilibrium potential, or gas concentrations accelerates both the response and recovery processes, while double layer capacitance has a reverse effect. A power-law concentration dependence of the response/recovery time is obtained under Tafel kinetics. The simulated response curves and behavior agree quite well with the experimental results. These findings shed lights on the sensing kinetics of the mixed-potential hydrogen sensor, and may help guide the sensor design.

Advanced impedance modeling for micropatterned polymer electrolyte membrane fuel cells

Cathode patterning is an effective means of improving the oxygen reduction reaction in polymer electrolyte membrane fuel cells. Because the conventional one-dimensional transmission line model cannot be applied to micropatterned electrodes, impedance modeling for micropatterned electrodes is conducted using a two-dimensional transmission line matrix model. In this study, the charge transfer resistance is considered a function of proton potential in the equivalent circuit based on the Butler–Volmer equation. Micropatterned membrane electrode assemblies (MEAs) with three different pattern depths are fabricated, and electrochemical measurements are performed on them. The measured and simulated impedances are evaluated using the distribution of relaxation times analysis results. This study validates the proposed model by comparing the simulated and measured impedances of the MEAs. The experimental and matrix model simulation results confirm that cathode patterning reduces both the charge transfer and proton conduction resistances. For each MEA, the charge transfer resistances obtained by fitting the matrix model to the measured impedances are plotted on a straight line; thus, the Tafel slope is obtained. The matrix model demonstrated in this study leads to the design of patterned electrodes through the impedance analysis of various patterned electrodes.

Determination of kinetic parameters from a new quadratic approximation of the Butler-Volmer equation

The determination of the parameters of the Butler-Volmer equation is a typical nonlinear parameter fitting task. Linear approximations are feasible at high and very low polarizations. However, in both cases the intermediate (transition) potential range, carrying probably the most valuable information on the exchange or corrosion current of an electrochemical system, remains out of scope. The linearization of the Butler-Volmer equation in this intermediate potential range, enabling the determination of both the polarization resistance and the Tafel slopes, can provide a powerful evaluation tool in electrochemical kinetic studies. A simple, robust and accurate method to meet this challenge is proposed, linear in the Tafel slopes and quadratic in the polarization, providing all practical advantages of the linearized systems. The performance of the new model is tested on simulated and experimental data.

Exploration of the dislocation-electrochemistry relation in LiFePO4 cathode materials

Defects, such as dislocations, in electrode materials play a significant role in the performance of lithium-ion batteries. The dislocation-electrochemistry relation has only been observed experimentally and not been fully clarified. Computational studies on this mechanism were also very limited, especially the altered cyclic voltammetry behaviors and associated effective diffusivity. This work focuses on the influences of few characteristics of dislocations on the electrochemical performance of an anisotropic cathode material, lithium iron phosphate (LiFePO4). Utilizing linear elastic mechanics and the superposition principle, we study stress and displacement fields of a LiFePO4 particle containing different densities and orientations of dislocations. With the mechanical-electrochemical coupling effects expressed by the modified Butler-Volmer equation and using the finite different method, the cyclic voltammetry curves for different dislocation configurations in the particle are investigated. Our results show that introducing dislocations can shift and distort the cyclic voltammetry curves, especially at one specific dislocation orientation. It is also found that the Li-ion molar fraction-dependent partial molar volume is an important prerequisite of the distortion in cyclic voltammetry curves. Moreover, the altered cyclic voltammetry curves at different scanning rates indicate the improvements of electrical power, stored electrical energy, and the effective diffusivity of lithium. Our discrete dislocation model indicates that the capacity loss of LiFePO4 nanoparticles can be alleviated by introducing tailored dislocations. This study assists the understanding of electrode materials with pre-existing dislocations and provides strategies of using defect engineering to improve the kinetic performance in lithium-ion batteries.

(Invited, Digital Presentation) Tafel Analysis Algorithm: Objective Identification of the Linear Region

Electrocatalysts for hydrogen evolution and oxidation (HER and HOR) reactions, oxygen reduction and evolution (ORR and OER) reactions, and carbon dioxide reduction reactions (CO2RR) are evaluated by Tafel analysis. The Tafel equation specifies the log-linear relationship between current and overpotential \U0001d6c8. Heterogenous electron transfer parameters of exchange current density j o and transfer coefficient \U0001d6c2 are found. Standard heterogenous electron transfer rate k 0 can be found from j o.Conventionally, Tafel analysis is an extension of the Butler-Volmer equation applied at high overpotentials but where mass transport is not significant and the reverse reaction rate is negligible. Applicable at high \U0001d6c8 when electron transfer rates are slow, kinetic parameters are extracted by linear regression. The conventional method is, however, subject to inaccuracies because the linear region is often determined subjectively, without attention to the constraints on overpotential range, no mass transport limitations, and low j o.An algorithm is developed to automate Tafel analysis with the objective to increase measurement accuracy and decrease subjective identification of the linear region. From linear sweep voltammograms (LSVs), j o and α are determined from Tafel slopes in the best fit, linear range.Comparisons of kinetic parameters between conventional and algorithmic Tafel analyses are made for the hydrogen evolution reaction (HER, 2H+ + 2e- ⇌ H2) on various unmodified electrodes and electrodes modified with Nafion® composites. The algorithmic Tafel analysis parameters correlate well with conventional Tafel analyses that respect constraints on mass transport, \U0001d6c8, and j o. Similar agreement is observed between literature and algorithmically fitted kinetic parameters for different electrochemical systems. The algorithm allows for straightforward, rapid Tafel analysis for improved measurement of rate parameters that is independent of user bias in selection of the linear region. Acknowledgments This work was supported by the Army Research Office.

Experimental and Numerical Analysis of Low Temperature Proton Exchange Membrane Fuel Cell (PEMFC) with Different Fuel Flow Rate in Improving Fuel Cell Performance

The PEM fuel cell was examined using numerical simulation in varied circumstances. To restore the fuel cell performance, a 3D-based PEMFC model was designed employing COMSOL Multiphysics 5.1. The analysis validity was confirmed using the V-I curves derived from data analysis in varied operational circumstances. The continuity, momentum, species transport and charge equations were used to represent the cell transport phenomenon. The flow of permeable medium in the gas diffusion layer was defined by employing Brinkman equations. V-I curves were obtained using the Butler-Volmer equations. According to findings, the current supply in the cathode catalyst layer achieves an optimum one, functioning as mass transport, ionic and charge transport resistances. It indicates optimum current supply in the cell holds a feature of highest oxygen deprivation on the channel's output side.

A Numerical Study of Bubble Blockage in Microfluidic Fuel Cells

Based on fuel crossover behavior and bubble nucleation in the microfluidic fuel cell’s channel, this research numerically presents the performance of air-breathing direct formic acid microfluidic fuel cells. In the simulation, a three-dimensional microfluidic fuel cell model was used. The continuity, momentum, species transport, and charge equations were used to develop the model transport behavior, whereas the Brinkman equation represented the porous medium flow in the gas diffusion layer. The I–V and power density curves are generated using the Butler–Volmer equation. The simulation and current experimental data were compared under identical operating conditions to validate the I–V curve of the microfluidic fuel cell model. The model was used to investigate the current density distribution in the microchannel due to bubble obstruction and the reactant concentration on both electrodes. Fuel crossover resulted in a large decrease in open-circuit voltage and a reduction in fuel concentration above the anode electrode. The findings also showed that a low-flow rate air-breathing direct formic acid microfluidic fuel cell is more prone to CO2 bubble formation.

Modelling and Simulation of A Direct Ethanol Fuel Cell: Electrochemical Reactions and Mass Transport Consideration

Mathematical modelling was developed for direct ethanol fuel cell (DEFC) by considering electrochemical reactions and mass transport. The model was validated against experimental data from previous research and showed good agreement with the data. The developed mathematical modelling for this research was based on the Butler-Volmer equation, Tafel equation and Fick’s law. The model was used to investigate parameters such as ethanol concentration and cell operating temperature. The developed mathematical model simulated the data from previous research. Ethanol concentration played a vital role to achieve high-performance DEFC. The higher the ethanol concentration, the higher current could be generated in DEFC. Nonetheless, the higher the usage of the ethanol concentration, the higher the ethanol crossover might occur. The highest current density produced from the fuel cell was at 21.48 mA cm-2, for 2M of ethanol concentration. Operating temperature also affected cell performance. The higher the operating temperature, the higher power density could be generated—the peak power density of 5.7 mWcm-2 at 75 oC with 2M of ethanol. As for ethanol crossover, the highest ethanol crossover was at 12.4 mol m-3 for 3M concentration of ethanol. It proved that higher ethanol concentration led to higher ethanol crossover.

Mixed potential model for passivity characters of hyper-duplex stainless steel 2707 in ammonium carbonate solution containing chloride

A mixed potential model (MPM) comprising the Point Defect Model (PDM) and the Generalized Butler Volmer Equation (GBVE) was successfully developed to study the passivity of HDSS 2707. The results show that the dominant point defect within the passive film is the Min+, thereby rendering n-type semiconductor behavior of the barrier layer. The anodic current is independent of the film formation potential whereas it increases with increasing temperature and follows the Arrhenius law. The partial cathodic current of hydrogen reaction is affected by the applied voltage. The anodizing constant of the passive film is calculated to be 2.91 nm/V.

A Finite-Element Model for Underpotential Deposition of Ce(III) on an Active Aluminum Electrode in LiCl–KCl Melts

Underpotential deposition on an active Al cathode plays an increasingly important role in pyroprocessing of used nuclear fuel, but most of the developed models are applied to simulate underpotential deposition at atomic level without considering electron transfer process which is a critical step in electrochemical reactions. In this work, a novel finite-element model for the underpotential deposition of Ce(III) in LiCl–KCl melts is developed with the consideration of Ce(III) activity in the Al electrode and the electron transfer process which is described by Butler-Volmer equation. This model was applied to investigate cyclic voltammetry(CV), square wave voltammetry(SWV) and electrodeposition behaviors of Ce(III) on an Al/Mo electrode. Additionally, the effect of temperature and electrode surface area on the electrodeposition thickness was investigated. Simulated CV and SWV curves are obtained and compared with our pervious experimental data. The results also provide the distribution diagrams of current density, electrostatic potential, Ce(III) concentration and electrodeposition thickness. Furthermore, the electrodeposition thickness is found to be linearly proportional to temperature and the inverse of cathode’s area, respectively. This work proposes a new pathway for the further study of underpotential deposition process.

Effective Representation of Active Material and Carbon Binder in Porous Electrodes

Active cathode material and graphite anode material are routinely mixed with conductor and binder to improve the electric conductivity and mechanical stability of electrodes. Despite its benefits, this carbon binder domain (CBD) impedes ionic transport and reduces the active surface area, thus impacting the battery performance. We consider a composite spherical particle, whose active-material core is coated with CBD, and its homogeneous counterpart, for which we derived equivalent electrical conductivity, ionic diffusivity, and reaction parameters in the Butler-Volmer equation. These equivalent characteristics are defined to ensure that the same mass and charge enter the composite and homogenized spheres. They are expressed in terms of the volume fraction of the active material and transport properties of the active material and CBD. In general, the equivalent effective diffusion coefficient and reaction parameters are time-dependent and exhibit two-stage behavior characterized by the reaction delay time. At later times, these characteristics are time-independent and given explicitly by closed-form formulae. The simplicity of these expressions facilitates their use in single- and multi-particle representations of Li-ion and Li-metal batteries.

Numerical simulation of steel corrosion in chloride environment based on random aggregate concrete microstructure model

The corrosion of steel bar in concrete structure under chloride environment is simulated considering the influence of concrete coarse aggregate. Firstly, the random polygonal coarse aggregate is generated, and the meso numerical cross-section of reinforced concrete is obtained. Then, based on Butler-Volmer equation, considering the coupling effect of diffusion and electrochemical corrosion, an electrochemical corrosion model of steel bar is established. Next, the accuracy of the model is verified by existing experimental data. Finally, the relationships between the volume fraction of coarse aggregate and corrosion morphology, steel corrosion quantity and corrosion process are gotten. The results show that the coarse aggregate causes irregular corroded section shape of the steel bar, and there are convexities and concavities on the corroded surface. The coarse aggregate can suppress the steel corrosion. As the volume fraction of coarse aggregate increases, the durations of the non-corrosive stage and the corrosion expansion stage extend.

YSZ-Based Mixed Potential Type Sensors Utilizing Pd-doped SrFeO3 Perovskite Sensing Electrode to Monitor Sulfur Dioxide Emission

Sulfur dioxide (SO2) is one of the key pollutants in the atmosphere that should be monitored in many combustion facilities. In this paper, YSZ-based mixed potential SO2 sensors were developed utilizing the perovskite-type SrFeO3 sensing electrode, and Pd doping was applied to enhance the sensing performance. It was found that the sensor utilizing the Pd0.05-SrFeO3 sensing electrode showed the highest sensitivity toward 1–30 ppm SO2 at 575 and exhibited a piecewise linear relationship between and the logarithm of SO2 concentrations in this concentration range. The significant enhancement of sensing performances by 5 at% Pd doping was mainly attributed to the increasing of electrochemical catalytic activity of the anodic reaction. After the sensing performance test in the temperature range between 525 –625 575 was selected as the optimum operating temperature. The sensing performances of the developed Pd0.05-SrFeO3 sensor were further evaluated at 575 exhibiting good selectivity to CO, CO2, NO, and NO2 interference and good long-term stability. In addition, the fluctuation of oxygen concentration can be corrected by the Butler-Volmer equation following the mixed potential theory.

Deformed Butler–Volmer Models for Convex Semilogarithmic Current-Overpotential Profiles of Li-ion Batteries

The Butler-Volmer (BV) equation links the current flux crossing an electrochemical interface to the electric potential drop across it with the assumption of Arrhenius kinetics and the Boltzmann factor. Applying the semilogarithmic Tafel analysis in which the logarithm of current is plotted vs. the overpotential one expects straight lines from which the fundamental reaction rate of the kinetic process can be computed. However, some Li-ion battery data, which is the focus here, show nonlinear convex profiles that cannot be adequately fitted with the standard BV model. We propose instead two deformed BV models for the analysis of such types of behaviors constructed from the superposition of cells exhibiting only local equilibrium and thus giving rise to the power-law $q$-exponential and $\kappa$-exponential functions. Non-Boltzmann distributions have been successfully employed for the modeling of a wide spectrum of physical systems in nonequilibrium situations, but not yet for batteries. We verify the validity of the deformed BV models on experimental data obtained from \ce{LiFePO4} and \ce{Li}-\ce{O2} batteries.