Search Results (21)

The Zeta-Minimizer Theorem provides a fully deductive variational foundation for the hydrogen oxidation reaction (HOR) and oxygen reduction reaction (ORR) in proton exchange membrane fuel cells. Starting from three primitive thermodynamic axioms and the helical geometry of the phase functional, a multi-extent dynamical system is constructed that simultaneously treats the electrochemical reaction coordinates and the adsorption extents of the participating species at the solid–electrolyte interface. The combined Hessian of the phase functional yields a complete spectrum of relaxation rates whose eigenvalues and eigenvectors emerge directly from the solid blackbox constants $C_k$ and the helical partition functions of the reactive species. Adiabatic elimination of the fast surface modes produces an effective single-extent description in which voltage (or overpotential) appears as the conjugate variable, exactly analogous to the role of pressure in the corresponding gas-phase ammonia synthesis framework. The resulting nonlinear rate law is thermodynamically consistent at all conditions, recovers the Butler–Volmer and Tafel forms as well-defined limiting cases, and incorporates the effects of temperature, dilution, and catalyst-specific interface constants without empirical activation energies or adjustable reaction orders. The framework therefore unifies equilibrium, kinetics, and modal dynamics of HOR and ORR within a single variational structure, offering a parameter-light, first-principles alternative to classical empirical electrocatalytic rate expressions while preserving transparent contact with established limiting laws. Full article

3D electrodeposition printing is an emerging process for fabricating metallic parts with controllable geometry, yet the coupled influences of electrochemical kinetics, ion transport, and tool motion on layer height remain difficult to interpret. This work presents a physics-based process model that links key process inputs, current density, electrolyte concentration, the inter-electrode gap, and tool scanning speed, to the resulting layer height in 3D electrodeposition printing of nickel-based structures. The model combines species transport in the inter-electrode gap with Butler–Volmer kinetics, under carefully stated assumptions regarding current efficiency, overpotential, and lateral spreading. Model predictions are validated against experimentally reported layer heights over a range of process conditions, yielding average errors (9–15%) and root-mean-square errors (0.13–0.28 µm) that demonstrate good agreement and highlight the impact of simplifying assumptions. Systematic parametric studies reveal how each process input monotonically influences layer height in ways consistent with Faraday’s law and diffusion-controlled growth, while also quantifying the relative sensitivity to different parameters. Building on these results, we introduce a dimensionless 3D Electrodeposition Printing Index that consolidates the key process and material parameters into a single scalar describing the geometric growth regime. The index enables construction of process maps that capture how combinations of current density, scan speed, concentration, and gap affect achievable layer height within the validated operating window. The scope and limitations of the proposed modeling framework and the index, particularly regarding other materials, more complex geometries, and pulsed or strongly convective regimes, are explicitly discussed, providing a basis for future model extensions and experimental validation. Full article

This study concerns the simulation of copper electrodeposition and related phenomenological and technological aspects as influenced by electrode geometry and electrolyte flow velocity. A multiphysics simulation approach was employed, integrating mathematical models accounting for electrochemical deposition and hydrodynamic behavior. Ionic transport is described by the Nernst-Planck equations, electrode kinetics by Butler–Volmer expressions, and fluid flow by the Navier–Stokes equations. Simplified 2D and 3D models were developed to investigate industrial frame plating electrodeposition processes. The results indicate that the fluid direction of the solution in relation to the position of the substrate within the electrodeposition cell enables the distribution of the thickness of the coating to be optimized. Numerical simulation can be used to guide the choice of the orientation of cathodes to be electroplated inside the electroplating tank, to take into consideration agitation direction, and to achieve the best deposit uniformity. Full article

Metal electrodeposition on additively manufactured lattice structures enables the creation of functionally graded hybrid components with enhanced mechanical properties. However, predicting coating thickness distribution remains challenging due to complex current density fields in intricate geometries. This study develops and validates a finite element electrochemical simulation model for predicting coating thickness distribution in lattice structures using COMSOL Multiphysics 6.1. The model incorporates Butler–Volmer electrode kinetics, mass transport limitations, and the Laplace equation for current distribution. Experimental validation was performed using FCCZ lattice structures electrochemically coated with nickel for 24 h at 200 A/m². CT scanning analysis revealed mean absolute errors of 5.25% between simulation and experiment after model calibration. The validated model successfully captures the exponential coating gradient from exposed edges to internal regions and provides a robust predictive tool for coating thickness distribution, which is essential for the effective design and optimization of electrochemically metallized lattice structures. Full article

Reported rate constants of charge transfer reactions (CTs) have ranged widely, depending on techniques and timescales. This fact can be attributed to the time-dependent double-layer capacitance (DLC), caused by solvent interactions such as hydrogen bonds. The time variation of the DLC necessarily affects the heterogeneous electrode kinetics. The delay by the solvation, being frequency dispersion, is incorporated into the CT kinetics in this report on the basis of the conventional reaction rate equations. It is different from the absolute rate theory. This report insists on a half value of the transfer coefficient owing to the segregation of the electrostatic energy from the chemical one. The rate equation here is akin to the Butler–Volmer one, except for the power law of the time caused by the delay of the DLC. The dipoles orient successively other dipoles in a group associated with the delay, which resembles that in the DLC. The delay suppresses the observed currents in the form of a negative capacitance. The above behavior was examined with a ferrocenyl derivative by ac impedance methods. The delay from diffusion control was attributed to the negative capacitance rather than the CT, even if the conventional DLC effect was corrected. Full article

The demand for green hydrogen is increasing, as it is estimated to reduce ten percent of total global green-house-gas emissions from fossil fuel. The solid oxide electrolysis cell (SOEC) is an electrochemical energy-conversion device (EECD) that produces green hydrogen via steam electrolysis. It is preferred to other EECDs for clean hydrogen production owing to its high efficiency, robust kinetics, and lack of precious-metal requirements for cell construction. Herein, we report a Multiphysics model describing the transport phenomena in the SOEC. The governing equations used in the model include a thorough description of the electrode kinetics and of the behavior of the three electrode–electrolyte interfaces in the cell. For the first time, the effect of the scandium-doped zirconia (SCGZ), yttrium-stabilized zirconia (YSZ), and gadolinium-doped ceria (GDC) electrolytes was modeled at different temperatures and pressures. By linking the convection and diffusion equations with the Butler–Volmer at shorter scales, a true representation of the cell operation was simulated. Our models show a R² value of over 0.996 in predicting the cell-polarization curves and electrochemical properties at the given operating conditions. The impedance of the SCGZ was 0.0240 Ohm.cm². This value was two- and four-fold lower than the values of the YSZ and GDC, respectively. Furthermore, our theoretical findings of both the polarization data and the impedance were in good agreement with the experimental data. Full article

Chronoamperometric curves for the oxidation of a ferrocenyl derivative via a potential step, calculated using the Cottrell equation, showed less diffusion-controlled currents on a platinum wire electrode. This lower deviation cannot be explained via Butler–Volmer heterogeneous kinetics, but was ascribed to the negatively capacitive current associated with a redox reaction. The deviation in fully oxidized electrical potential corresponds to the non-zero concentration at the electrode surface, which cannot be predicted using the Nernst equation. This equation expresses the relationship between the electrical potential and activity at the electrode surface rather than the concentration. The diffusion equation determines the relationship between the current and surface concentration rather than activity. Negative capacitance or a non-zero concentration may arise from structure formation on the electrode owing to dipole–dipole interactions, which are similar to the generation of double-layer capacitance, including frequency dispersion. Following this concept, we derive expressions for a lowered diffusion-controlled current and time-dependent surface concentration. The negatively capacitive current shows the time dependence of t^−0.9, which is similar to the decay of double-layer capacitive currents. The surface concentration decays with t^−0.4-dependence. Full article

Ethanol is considered an alternative fuel to power fuel cells, especially due to its ease of transport and storage and renewable production on a large scale. However, its use in direct ethanol fuel cells (DEFC) is still limited by incomplete electro-oxidation and slow reaction kinetics. Modeling approaches have focused on investigating different reaction mechanisms, but so far, no formal analysis of model parameter sensitivity has been conducted. This work modeled and identified sensitive parameters for different types of Pt–Sn catalysts previously prepared by our research group that displayed good performance in the 5–15 mW/cm² range (relative to a performance of 12 mW/cm² achieved by a commercial ETEK catalyst). Analyses to study the effect of these parameters on coverage fraction distribution, reaction rates and possible correlations were also performed. The model was developed based on Butler–Volmer kinetics and on a reaction mechanism previously reported in the literature. Statistical developments were considered to compute parameter uncertainties for a non-linear system with non-linear restrictions. The model achieved very good fits to experimental data, with low RMSE values between 0.22 × 10⁻⁴ and 4.2 × 10⁻⁴ A/cm², while also showing surface coverage fraction distributions in agreement with other experiment-based works from the literature. All catalysts taken into account, the most sensitive parameters were the reaction rate constants associated with the formation of adsorbed CH₃CO, and the direct and reverse water dissociative adsorption reactions, respectively. Additional analyses suggested that there is not much correlation between the parameters. The results from this work could contribute to the state-of-the-art DEFC models by providing insights into which variables may be assumed constant or which ones have the greatest impact on the model output, thus helping to reduce the model size and computational time for future broader DEFC models. Full article

Electrochemical behaviors of individual carbon fibers coming from carbon felts were investigated using two different redox couples, 1,1′-dimethanolferrocene and potassium ferrocyanide. Electrochemical responses were examined after different oxidation treatments, then simulated and interpreted using the Kissa 1D software and existing models. Our experiments indicate that a crude carbon fiber behaves as an assembly of sites with different electrochemical reactivities. In such case, the Butler–Volmer law is not appropriate to describe the electron transfer kinetics because of the large created overpotential. Oxidation of the fiber erases the effect by increasing the kinetics of the electron transfer probably by a homogenization and increase of the reactivity on all the fiber. Additionally, analysis of the signal shows the large influence of the convection that affects the electrochemical response even at moderate scan rates (typically below 0.1–0.2 V s⁻¹). Full article

Cyclic Voltammetry is an analysis method for characterizing the behaviors of electrochemically active materials by measuring current through defined potential sweeps. The current–potential relationship depends on key variables such concentration of electrolyte, electron-transfer rate, and the distance and time of species in relation to the electroactive surface of the material. A MATLAB^® simulation was developed on a diffusion and kinetics basis, simulating the equations of Fick’s second law and Butler–Volmer, respectively, towards understanding the energy-storage mechanisms of cobalt hydroxide electrodes. The simulation was compared to a real cobalt hydroxide system, showing an accurate approximation to the experimentally obtained response and deviations possibly related to other physical/chemical processes influencing the involved species. Full article

A transient three-dimensional comprehensive numerical model was established to study ion transport caused by diffusion, convection, and electro-migration in the electro-refining process for scrap-metal recycling. The Poisson–Nernst–Planck equations were used to define ion transport within the electrolyte, while the Naiver–Stokes equations and the energy equation were employed to describe fluid flow and heat transfer. In addition, the Butler-Volmer formulation was used to represent the kinetics of the electrochemical reaction. The comparison between the measured and simulated data indicates the reliability of the model. Under the action of diffusion and electro-migration, the positive copper ion moves from the anode to the cathode, while the negative sulfate ion migrates in the opposite direction. The distribution of the ion concentration, however, greatly changes if the fluid flow is taken into account. The ion concentration around the anode and the rate of the electrochemical reaction that occurs at the anode surface are reduced by the fluid flow. The proposed computational framework offers a valuable basis for future research and development in the field of scrap-metal recycling technology. Full article

Bioelectrochemical systems have been the focus of extensive research due to their unique advantages of converting the chemical energy stored in waste to electricity. To acquire a better understanding and optimize these systems, modelling has been employed. A 2D microbial fuel cell (MFC) model was developed using the finite element software Comsol Multiphysics^® (version 5.2), simulating a two-chamber MFC operating in batch mode. By solving mass and charge balance equations along with Monod–Butler–Volmer kinetics, the operation of the MFC was simulated. The model accurately describes voltage output and substrate consumption in the MFC. The computational results were compared with experimental data, thus validating the model. The voltage output and substrate consumption originating from the model were in agreement with the experimental data for two different cases (100 Ω, 1000 Ω external resistances). A polarization curve was extracted from the model by shifting the external resistance gradually, calculating a similar maximum power (47 mW/m²) to the observed experimental one (49 mW/m²). The validated model was used to predict the MFC response to varying initial substrate concentrations (0.125–4 g COD/L) and electrolyte conductivity (0.04–100 S/m) in order to determine the optimum operating conditions. Full article

The charging safety of electric vehicles is an area of focus in the electric automobile industry. For the purpose of ensuring safety, charging electric vehicles as soon as possible is a goal pursued by the public. In order to ensure the safety of electric vehicles during fast charging and to reduce the cycle life decay of the battery, a simplified multi-particle lithium-ion battery model is proposed, based on the pseudo two-dimensional (P2D) model. The model was developed by considering heterogeneous electrochemical reactions in the negative electrode area. The Butler–Volmer (BV) kinetic equation and the distribution of the pore wall flux in the negative electrode is approximated by the quasi-linear approximation method. Furthermore, this paper also analyzes the conditions of lithium precipitation from the negative electrode of a lithium-ion battery in the case of high charging rates, which has a certain reference significance for fast-charging control applications. The experimental and simulation results show that the model has a high simulation accuracy and can reflect the heterogeneity of electrochemical reactions in the negative electrode of the battery. The model can be adapted to fast-charging control applications. Full article

Li-rich and catalytically active $\gamma$-$L{i}_x{V}_2{O}_5$ (x = 1.48) was investigated as a cathode for its heterogeneous charge transfer kinetics. Using a specially designed two-electrode system lithium half cell, Butler–Volmer analysis was performed, and Raman spectra were acquired in 18 mV intervals. A direct correlation was observed between the Raman shift of the active modes $A_g$,$B_g$, $A_u$, and $B_u$, and the development of the Faraday current at the working electrode. The Raman intensity and the Raman shift were implemented to replace the current in a Tafel plot used for the analysis of Butler–Volmer kinetics. Striking similarities in the charge transfer proportionality constants $\alpha$ were found for current and Raman-based analysis. The potential of this new method of Raman-aided electrochemical detection at the diffraction limit is discussed. Full article

In this paper, a comprehensive model for LiFePO₄ batteries is proposed to ensure high efficiency and safe operation. The proposed model has a direct correlation between its parameters and the electrochemical principles to estimate the state of charge (SoC) and the remaining capacity of the LiFePO₄ battery. This model was based on a modified Thévenin circuit, Butler–Volmer kinetics, the Arrhenius equation, Peukert’s law, and a back propagation neural network (BPNN), which can be divided into two parts. The first part can be represented by the dual exponential terms, responsive to the Coulomb efficiency; the second part can be described by the BPNN, estimating the remaining capacity. The model successfully estimates the SoC of the batteries that were tested with an error of 1.55%. The results suggest that the model is able to accurately estimate the SoC and the remaining capacity in various environments (discharging C rates and temperatures). Full article