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21 pages, 1146 KiB

Open AccessArticle

Ferromagnet-Type System: Integrable Flows of Curves/Surfaces, Soliton Solutions, and Equivalence

by Gulgassyl Nugmanova, Guldana Bekova, Meruyert Zhassybayeva, Aigul Taishiyeva, Kuralay Yesmakhanova and Zhaidary Myrzakulova

Symmetry 2025, 17(7), 1041; https://doi.org/10.3390/sym17071041 - 2 Jul 2025

Viewed by 212

Abstract

This paper investigates an integrable spin system known as the Myrzakulov-XIII (M-XIII) equation through geometric and gauge-theoretic methods. The M-XIII equation, which describes dispersionless dynamics with curvature-induced interactions, is shown to admit a geometric interpretation via curve flows in three-dimensional space. We establish [...] Read more.

This paper investigates an integrable spin system known as the Myrzakulov-XIII (M-XIII) equation through geometric and gauge-theoretic methods. The M-XIII equation, which describes dispersionless dynamics with curvature-induced interactions, is shown to admit a geometric interpretation via curve flows in three-dimensional space. We establish its gauge equivalence with the complex coupled dispersionless (CCD) system and construct the corresponding Lax pair. Using the Sym–Tafel formula, we derive exact soliton surfaces associated with the integrable evolution of curves and surfaces. A key focus is placed on the role of geometric and gauge symmetry in the integrability structure and solution construction. The main contributions of this work include: (i) a commutative diagram illustrating the connections between the M-XIII, CCD, and surface deformation models; (ii) the derivation of new exact solutions for a fractional extension of the M-XIII equation using the Kudryashov method; and (iii) the classification of these solutions into trigonometric, hyperbolic, and exponential types. These findings deepen the interplay between symmetry, geometry, and soliton theory in nonlinear spin systems. Full article

(This article belongs to the Section Physics)

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17 pages, 7847 KiB

Open AccessArticle

Electrochemical Analysis of Corrosion Resistance of Manganese-Coated Annealed Steel: Chronoamperometric and Voltammetric Study

by Francisco Augusto Nuñez Pérez

AppliedChem 2024, 4(4), 367-383; https://doi.org/10.3390/appliedchem4040023 - 19 Nov 2024

Cited by 1 | Viewed by 2333

Abstract

Metal corrosion poses a significant challenge for industries by decreasing the lifespan of materials and escalating maintenance and replacement costs. This study is critically important, as it assesses the corrosion resistance properties of annealed steel wire electrodes coated with manganese, employing chronoamperometry and [...] Read more.

Metal corrosion poses a significant challenge for industries by decreasing the lifespan of materials and escalating maintenance and replacement costs. This study is critically important, as it assesses the corrosion resistance properties of annealed steel wire electrodes coated with manganese, employing chronoamperometry and linear voltammetry techniques. The electrodes were immersed in an electrolyte solution and subjected to chronoamperometry at various voltages (−0.55 V, −0.60 V, and −0.70 V) and durations (60 s and 1800 s). Subsequently, linear voltammetry was performed over a potential range from −0.8 V to 0.8 V to generate Tafel plots. The Butler–Volmer equation was applied to the data obtained to determine the corrosion current density. The results indicate that the optimal conditions for forming a highly effective protective manganese layer occur at a potential of −0.70 V for 1800 s. Under these conditions, the electrodes exhibited superior corrosion resistance. This study also revealed that shorter durations and less negative potentials led to less-effective manganese coatings, with higher corrosion rates and reduced stability. These findings are significant for developing efficient corrosion protection methods in industrial and research applications, providing clear parameters for optimizing the manganese electrodeposition process on annealed steel. Full article

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16 pages, 5993 KiB

Open AccessArticle

Investigating the Applicability of the Tafel Equation in Polymer Electrolyte Membrane Electrolyzers via Statistical Analysis

by Fabian Scheepers and Werner Lehnert

Energies 2024, 17(13), 3298; https://doi.org/10.3390/en17133298 - 5 Jul 2024

Cited by 1 | Viewed by 2161

Abstract

Analyzing PEM electrolyzer polarization curves via voltage breakdown analysis involves decomposing contributions from underlying processes, typically based on the assumption of reaction kinetics that may be expressed by means of the Tafel equation. When extrapolating the corresponding straight line to high current densities, [...] Read more.

Analyzing PEM electrolyzer polarization curves via voltage breakdown analysis involves decomposing contributions from underlying processes, typically based on the assumption of reaction kinetics that may be expressed by means of the Tafel equation. When extrapolating the corresponding straight line to high current densities, there is a discrepancy between the measurement and model, which is often attributed to mass transport resistance. In addition to the qualitative description of this mass transport resistance, a consistent quantification is difficult to obtain from the measurement results. Accordingly, the approach to the breakdown analysis of the polarization curves is strongly based on assumptions that evade experimental verification. In this study, an alternative statistical method is introduced that permits the falsifiability of the standard approach. By means of experiments at different hydrogen partial pressures and a subsequent data fit, it is possible to extract the kinetic behavior without prior specification. The results indicate that behavior corresponding to the Tafel equation cannot be proven wrong. In addition, transport coefficients can be evaluated that fall between those of membranes and porous transport layers, indicating that the catalyst layer predominantly contributes to the mass transport resistance. Full article

(This article belongs to the Collection Energy-Efficient Chemistry)

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11 pages, 5781 KiB

Open AccessArticle

Classic Evans’s Drop Corrosion Experiment Investigated in Terms of a Tertiary Current and Potential Distribution

by Abraham Sainz-Rosales, Xóchitl Ocampo-Lazcarro, Azalia Hernández-Pérez, Ana Gabriela González-Gutiérrez, Erika Roxana Larios-Durán, Carlos Ponce de León, Frank C. Walsh, Maximiliano Bárcena-Soto and Norberto Casillas

Corros. Mater. Degrad. 2022, 3(2), 270-280; https://doi.org/10.3390/cmd3020016 - 10 Jun 2022

Cited by 7 | Viewed by 5068

Abstract

Background: Evans’s drop is a classic corrosion experiment that is nearly 100 years old, and it is analogous to other corrosion systems promoted by O₂ gradients. The availability of more robust finite element software packages opens the possibility to reach a deeper [...] Read more.

Background: Evans’s drop is a classic corrosion experiment that is nearly 100 years old, and it is analogous to other corrosion systems promoted by O₂ gradients. The availability of more robust finite element software packages opens the possibility to reach a deeper understanding of these kind of corrosion systems. Methodology: In order to solve the problem, the model includes the governing mass transport diffusion and migration equation and the material balance in a nonsteady state by the finite element method. This is performed using COMSOL Multiphysics to predict the tertiary current and potential distribution considering the geometry, reaction kinetics, and mass transport for each ionic species. Significant Findings: A simulation of the tertiary current and potential distribution of the Evans’s drop corrosion experiment on an iron surface is presented. An oxygen concentration difference of 0.18 mol m⁻³ between the center and the drop periphery sets up a potential difference of 60 mV which acts as a corrosion driving force. Reaction kinetics are described by Tafel equations. Results include the evolution of concentration profiles for OH⁻, Fe²⁺, Fe³⁺, Fe(OH)₂, and Fe(OH)₃. Full article

(This article belongs to the Special Issue Atmospheric Corrosion of Materials)

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15 pages, 3774 KiB

Open AccessArticle

Phytochemical-Assisted Green Synthesis of Nickel Oxide Nanoparticles for Application as Electrocatalysts in Oxygen Evolution Reaction

by Vidhya Selvanathan, M. Shahinuzzaman, Shankary Selvanathan, Dilip Kumar Sarkar, Norah Algethami, Hend I. Alkhammash, Farah Hannan Anuar, Zalita Zainuddin, Mohammod Aminuzzaman, Huda Abdullah and Md. Akhtaruzzaman

Catalysts 2021, 11(12), 1523; https://doi.org/10.3390/catal11121523 - 15 Dec 2021

Cited by 44 | Viewed by 7054

Abstract

Electrocatalytic water splitting is a promising solution to resolve the global energy crisis. Tuning the morphology and particle size is a crucial aspect in designing a highly efficient nanomaterials-based electrocatalyst for water splitting. Herein, green synthesis of nickel oxide nanoparticles using phytochemicals from [...] Read more.

Electrocatalytic water splitting is a promising solution to resolve the global energy crisis. Tuning the morphology and particle size is a crucial aspect in designing a highly efficient nanomaterials-based electrocatalyst for water splitting. Herein, green synthesis of nickel oxide nanoparticles using phytochemicals from three different sources was employed to synthesize nickel oxide nanoparticles (NiO_x NPs). Nickel (II) acetate tetrahydrate was reacted in presence of aloe vera leaves extract, papaya peel extract and dragon fruit peel extract, respectively, and the physicochemical properties of the biosynthesized NPs were compared to sodium hydroxide (NaOH)-mediated NiO_x. Based on the average particle size calculation from Scherrer’s equation, using X-ray diffractograms and field-emission scanning electron microscope analysis revealed that all three biosynthesized NiO_x NPs have smaller particle size than that synthesized using the base. Aloe-vera-mediated NiO_x NPs exhibited the best electrocatalytic performance with an overpotential of 413 mV at 10 mA cm⁻² and a Tafel slope of 95 mV dec⁻¹. Electrochemical surface area (ECSA) measurement and electrochemical impedance spectroscopic analysis verified that the high surface area, efficient charge-transfer kinetics and higher conductivity of aloe-vera-mediated NiO_x NPs contribute to its low overpotential values. Full article

(This article belongs to the Special Issue Heterogeneous Photocatalysis: A Solution for a Greener Earth)

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11 pages, 1445 KiB

Open AccessArticle

Modelling the (Essential) Role of Proton Transport by Electrolyte Bases for Electrochemical Water Oxidation at Near-Neutral pH

by Holger Dau and Chiara Pasquini

Inorganics 2019, 7(2), 20; https://doi.org/10.3390/inorganics7020020 - 13 Feb 2019

Cited by 17 | Viewed by 6094

Abstract

The oxygen-evolution reaction (OER) in the near-neutral pH-regime is of high interest, e.g., for coupling of OER and CO₂-reduction in the production of non-fossil fuels. A simple model is proposed that assumes equal proton activities in the catalyst film and the [...] Read more.

The oxygen-evolution reaction (OER) in the near-neutral pH-regime is of high interest, e.g., for coupling of OER and CO₂-reduction in the production of non-fossil fuels. A simple model is proposed that assumes equal proton activities in the catalyst film and the near-surface electrolyte. Equations are derived that describe the limitations relating to proton transport mediated by fluxes of molecular “buffer bases” in the electrolyte. The model explains (1) the need for buffer bases in near-neutral OER and (2) the pH dependence of the catalytic current at high overpotentials. The latter is determined by the concentration of unprotonated buffer bases times an effective diffusion constant, which can be estimated for simple cell geometries from tabulated diffusion coefficients. The model predicts (3) a macroscopic region of increased pH close to the OER electrode and at intermediate overpotentials, (4) a Tafel slope that depends on the reciprocal buffer capacity; both predictions are awaiting experimental verification. The suggested first-order model captures and predicts major trends of OER in the near-neutral pH, without accounting for proton-transport limitations at the catalyst–electrolyte interface and within the catalyst material, but the full quantitative agreement may require refinements. The suggested model also may be applicable to further electrocatalytic processes. Full article

(This article belongs to the Special Issue Recent Advances in Water Oxidation Catalysis)

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14 pages, 1693 KiB

Open AccessArticle

Experimental and One-Dimensional Mathematical Modeling of Different Operating Parameters in Direct Formic Acid Fuel Cells

by Shingjiang Jessie Lue, Nai-Yuan Liu, Selvaraj Rajesh Kumar, Kevin Chi-Yang Tseng, Bo-Yan Wang and Chieh-Hsin Leung

Energies 2017, 10(12), 1972; https://doi.org/10.3390/en10121972 - 27 Nov 2017

Cited by 8 | Viewed by 4424

Abstract

The purpose of this work is to develop a one-dimensional mathematical model for predicting the cell performance of a direct formic acid fuel cell and compare this with experimental results. The predicted model can be applied to direct formic acid fuel cells operated [...] Read more.

The purpose of this work is to develop a one-dimensional mathematical model for predicting the cell performance of a direct formic acid fuel cell and compare this with experimental results. The predicted model can be applied to direct formic acid fuel cells operated with different formic acid concentrations, temperatures, and with various electrolytes. Tafel kinetics at the electrodes, thermodynamic equations for formic acid solutions, and the mass-transport parameters of the reactants are used to predict the effective diffusion coefficients of the reactants (oxygen and formic acid) in the porous gas diffusion layers and the associated limiting current densities to ensure the accuracy of the model. This model allows us to estimate fuel cell polarization curves for a wide range of operating conditions. Furthermore, the model is validated with experimental results from operating at 1–5 M of formic acid feed at 30–80 °C, and with Nafion-117 and silane-crosslinked sulfonated poly(styrene-ethylene/butylene-styrene) (sSEBS) membrane electrolytes reinforced in porous polytetrafluoroethylene (PTFE). The cell potential and power densities of experimental outcomes in direct formic acid fuel cells can be adequately predicted using the developed model. Full article

(This article belongs to the Section L: Energy Sources)

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11 pages, 4589 KiB

Open AccessArticle

The Electrochemical Investigation of the Corrosion Rates of Welded Pipe ASTM A106 Grade B

by Trinet Yingsamphancharoen, Nakarin Srisuwan and Aphichart Rodchanarowan

Metals 2016, 6(9), 207; https://doi.org/10.3390/met6090207 - 31 Aug 2016

Cited by 15 | Viewed by 8384

Abstract

The aim of this work was to investigate the corrosion rate of welded carbon steel pipe (ASTM (American Society for Testing and Materials) A106 Grade B) by GTAW under the currents of 60, 70, and 80 A. All welded pipes satisfied weld procedure [...] Read more.

The aim of this work was to investigate the corrosion rate of welded carbon steel pipe (ASTM (American Society for Testing and Materials) A106 Grade B) by GTAW under the currents of 60, 70, and 80 A. All welded pipes satisfied weld procedure specifications and were verified by a procedure qualification record. The property of used materials was in agreement with the ASME standard: section IX. The welded pipe was used for schematic model corrosion measurements applied in 3.5 wt % NaCl at various flow rates and analyzed by using the electrochemical technique with Tafel’s equation. The results showed the correlation between the flow rate and the corrosion rate of the pipe; the greater the flow rate, the higher corrosion rate. Moreover, the welded pipe from the welding current of 70 A exhibited higher tensile strength and corrosion resistance than those from currents of 60 and 80 A. It indicated that the welding current of 70 A produced optimum heat for the welding of A106 pipe grade B. In addition, the microstructure of the welded pipe was observed by SEM. The phase transformation and crystallite size were analyzed by XRD and Sherrer’s equation. The results suggested that the welding current could change the microstructure and phase of the welded pipe causing change in the corrosion rate. Full article

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14 pages, 287 KiB

Open AccessArticle

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

by Kuo-Chuan Ho, Wen-Tung Hung and Jin-Cherng Yang

Sensors 2003, 3(8), 290-303; https://doi.org/10.3390/s30800290 - 22 Aug 2003

Cited by 16 | Viewed by 11346

Abstract

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 [...] Read more.

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. Full article

(This article belongs to the Special Issue Nitric Oxide Sensors and Their Applications in Biomedical Research)

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