Magnetochemistry

19 pages, 1022 KB

Open AccessArticle

Imputation of Thermal and Magnetic Variables in Shape-Memory Alloys (Ni–Mn–Ga) Using Machine Learning Techniques with Cross-Validation and Multi Seed

by Juan C. Buitrago Diaz, Edwin G. Castro Rodas, Carolina Ortega-Portilla, Juan E. Bedoya-Rodriguez, Daniel Salazar, Manuel G. Forero and Jeferson Fernando Piamba

Magnetochemistry 2026, 12(8), 93; https://doi.org/10.3390/magnetochemistry12080093 - 19 Aug 2026

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Abstract

Magnetic shape memory alloys based on the Ni–Mn–Ga system are of strategic interest for aerospace and robotics applications due to their ability to respond to both thermal and magnetic stimuli. However, the NASA Shape Memory Materials Database a key resource for the community [...] Read more.

Magnetic shape memory alloys based on the Ni–Mn–Ga system are of strategic interest for aerospace and robotics applications due to their ability to respond to both thermal and magnetic stimuli. However, the NASA Shape Memory Materials Database a key resource for the community exhibits significant gaps in functional parameters, with up to 93.7% of records missing critical properties such as the Curie temperature, and over 88% lacking complete magnetic data. To address this limitation, this study proposes a data imputation strategy based on a stacking ensemble comprising twelve machine learning models (LGBM, XGBoost, CatBoost, GradientBoosting, RandomForest, MLP, BayesianRidge, KNN, SVR, GPR, MICE, and AutoEncoder), optimized via Optuna and evaluated using ten random seeds with 10 repetitions each. The approach was applied to reconstruct missing entries in NASA’s database. For heat treatment 1, the method achieved coefficients of determination (

R^{2}

) of 0.95 for duration (h) and 0.88 for temperature (°C), respectively. For the phase transformation temperatures (Mf, Ms, As, and Af), the method yielded

R^{2}

values of 0.83, 0.82, 0.79, and 0.80, respectively. Magnetic properties saturation magnetization and maximum magnetic field were imputed with an

R^{2}

of 0.92. In contrast, the Curie temperature exhibited limited predictive performance (

R^{2}

= 0.15–0.35), primarily due to insufficient data availability. Overall, the proposed methodology integrates machine learning based imputation with physically supported constraints, providing a viable alternative to enhance the completeness and utility of materials databases. Full article

(This article belongs to the Special Issue Magnetic Materials and Composites: Synthesis, Properties, and Applications)

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25 pages, 2581 KB

Open AccessArticle

The Analysis of NMR Magnetic Shieldings of Transition Metal (M)-Containing Molecules, M Belonging to Groups IIB, VIB and VIIIB, by Applying the LRESC-Loc Model

by Andy D. Zapata-Escobar, Alejandro F. Maldonado and Gustavo A. Aucar

Magnetochemistry 2026, 12(8), 92; https://doi.org/10.3390/magnetochemistry12080092 - 19 Aug 2026

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Abstract

We studied the electronic origin of the NMR nuclear magnetic shieldings (

σ

) of compounds containing the following transition metal atoms:

M =

Zn, Cd, Hg, Co, Rh, Cr, Mo, W. The electronic mechanisms that underlie the relativistic effects on those shieldings [...] Read more.

We studied the electronic origin of the NMR nuclear magnetic shieldings (

σ

) of compounds containing the following transition metal atoms:

M =

Zn, Cd, Hg, Co, Rh, Cr, Mo, W. The electronic mechanisms that underlie the relativistic effects on those shieldings were assessed with the LRESC–Loc model, which permits one to quantify the set of leading relativistic electronic mechanisms responsible for such effects in terms of well-known non-relativistic operators, and also allows for the determination of which molecular orbitals (MOs) are involved in each of those mechanisms. These MOs are such that the chemist’s intuition associated with core, lone-pair (LP), and bonding MOs is satisfied. The LRESC model is a reliable semi-relativistic methodology that has been shown to reproduce, in a semiquantitative manner, the magnetic shieldings and experimental chemical shifts of transition metals in a large set of molecules. Several new features appear in the shieldings analyzed. Trends in the total shieldings within a given family of compounds depend on relativistic effects—the spin-orbit mechanism is one of the most involved—though, within it, one must consider the Fermi contact (FC) and the spin-dipolar (SD) mechanisms. We found that the contributions that are due to partially filled d atomic orbitals (AOs) become too large when the electron correlation is not properly included. This is overcome in our case using density functional theory. A large influence of lone-pairs of

π

-type on

σ

(M) is also seen in some of the molecules studied. Full article

(This article belongs to the Special Issue 10th Anniversary of Magnetochemistry: Past, Present and Future)

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18 pages, 9200 KB

Open AccessArticle

Synergistic Electrical–Magnetic–Thermal Response of Fe Soft Magnetic Composites Enabled by Thiol-Functionalised Silicon Nitride Nanosheet Interfacial Engineering

by Shuang Chen, Zhongqiu Fu, Kang Wang, Gongyu Ji and Cheng Liu

Magnetochemistry 2026, 12(8), 91; https://doi.org/10.3390/magnetochemistry12080091 - 18 Aug 2026

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Abstract

Pure Fe soft magnetic composites (SMCs) hold a prominent position in cost-sensitive 10–100 kHz medium-to-low-frequency power devices owing to their low raw-material expenditure and high saturation magnetisation. Nevertheless, the inherently poor interparticle electrical resistivity permits the formation of contiguous conduction paths under alternating [...] Read more.

Pure Fe soft magnetic composites (SMCs) hold a prominent position in cost-sensitive 10–100 kHz medium-to-low-frequency power devices owing to their low raw-material expenditure and high saturation magnetisation. Nevertheless, the inherently poor interparticle electrical resistivity permits the formation of contiguous conduction paths under alternating magnetic fields, giving rise to marked eddy-current dissipation and localised thermal accumulation. To surmount this limitation, the present work introduces γ-mercaptopropyltriethoxysilane (KH580)-functionalised silicon nitride (Si₃N₄) nanosheets as a multifunctional interfacial regulating layer that simultaneously establishes an electrically insulating barrier and a thermally conductive network on the surface of Fe particles. The structural integrity, surface chemical speciation and deposition behaviour of Si₃N₄-s nanosheets on Fe particles were systematically examined, and correlations among lamellar coverage completeness, interfacial bonding robustness and the coupled electrical–magnetic–thermal response were elucidated. The findings reveal that KH580 silanisation introduces a surface functional layer while preserving the parent α-Si₃N₄ crystal structure, and XPS analysis suggests possible local N–Fe and Fe–S interfacial interactions between Si₃N₄-s and the Fe surface. At a loading of 4 wt.% Si₃N₄-s, a comparatively continuous and uniform lamellar coating develops on the Fe particle surfaces. The corresponding Fe/Si₃N₄ SMCs exhibit the highest volume resistivity and a peak thermal conductivity of approximately 12.1 W·m⁻¹·K⁻¹, while maintaining a core loss of approximately 600.2 kW·m⁻³ at 50 mT and 100 kHz. These results indicate that the 4 wt.% specimen provides the most favourable overall balance among electrical insulation, magnetic response, core-loss suppression and thermal transport within the investigated composition range, furnishing a functionalised lamellar interfacial engineering strategy for performance advancement of low-cost Fe-based SMCs. Full article

(This article belongs to the Special Issue Advances in Soft Magnetic Materials—2nd Edition)

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15 pages, 1801 KB

Open AccessArticle

Diastereoisomerism and SIM Behavior in Mononuclear Co(II) Systems Based on Mepirizole

by Emilio Escrivà and José Martínez-Lillo

Magnetochemistry 2026, 12(8), 90; https://doi.org/10.3390/magnetochemistry12080090 - 18 Aug 2026

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Abstract

Two diastereoisomers of bis(mepirizole)bis(isothiocyanato-κ,N)cobalt(II) (1 and 2) are isolated from the reaction of cobalt(II) thiocyanate and mepirizole, depending on the crystallization solvent (ethanol, 1; acetonitrile, 2). In both crystal structures, the Co(II) ions exhibit distorted octahedral [CoN [...] Read more.

Two diastereoisomers of bis(mepirizole)bis(isothiocyanato-κ,N)cobalt(II) (1 and 2) are isolated from the reaction of cobalt(II) thiocyanate and mepirizole, depending on the crystallization solvent (ethanol, 1; acetonitrile, 2). In both crystal structures, the Co(II) ions exhibit distorted octahedral [CoN₄N′₂] environment. The analysis of the packing frameworks shows a cooperative relationship between non-classical H-bonds C(sp³)-H···X (X = N, O, S, π) and π-hole bonds, which control the arrangement of the supramolecular 3D networks. The values of the shortest intermolecular metal–metal separation are 8.584(2) Å in 1 and 8.249(1) Å in 2. Both diastereoisomers exhibit magnetic behavior typical of mononuclear Co(II) systems with significant zero-field splitting (ZFS) values, with D being 75.8(1) and 52.9(2) cm⁻¹ for 1 and 2, respectively. Q-band EPR studies confirm the positive value for the D parameters for both compounds. Alternating current dynamic susceptibility measurements show that 1 and 2 exhibit field-induced slow relaxation of the magnetization, which is reminiscent of single-ion magnet (SIM) behavior. Full article

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21 pages, 4694 KB

Open AccessArticle

Study of Helix Angle Parameters of Helical-Channel Magnetohydrodynamic Thrusters

by Tianyang Cao, Yiyue Cheng, Ziwu Wang, Chao Zhou and Chun Zhang

Magnetochemistry 2026, 12(8), 89; https://doi.org/10.3390/magnetochemistry12080089 - 15 Aug 2026

Viewed by 253

Abstract

The helical-channel magnetohydrodynamic (MHD) thruster is a silent underwater propulsion device free of rotating mechanical components, which fundamentally eliminates the inherent mechanical noise induced by blades and shaft systems in conventional propeller-driven thrusters. Taking a 10 T-class superconducting helical-channel MHD thruster as the [...] Read more.

The helical-channel magnetohydrodynamic (MHD) thruster is a silent underwater propulsion device free of rotating mechanical components, which fundamentally eliminates the inherent mechanical noise induced by blades and shaft systems in conventional propeller-driven thrusters. Taking a 10 T-class superconducting helical-channel MHD thruster as the research object, this work establishes a three-dimensional numerical simulation model with bidirectional electromagnetic-fluid coupling via Maxwell–Fluent, filling the research gap of systematic optimization of helical pitch angles in existing low-magnetic-field numerical investigations. A composite magnetic circuit configuration consisting of main coils and compensation coils is adopted, achieving a magnetic field uniformity of 90.13% within the effective working section and markedly alleviating magnetic field attenuation at both ends of the flow channel. Three schemes with helical pitch angles of 23.00°, 17.66°, and 14.29° are quantitatively compared to analyze the effects of helical pitch angle on current density, static pressure, total pressure, radial/axial flow velocities and three-dimensional helical streamlines. Under the rated design mass flow rate of 15.5 kg/s, the scheme with the small pitch angle of 14.29° delivers a thrust of 262.56 N and an electromagnetic efficiency of 7.23%; compared with the large pitch angle scheme of 23.00°, its thrust is improved by 28% and electromagnetic efficiency rises by 53%. Reducing the helical pitch angle extends the effective coupling distance between seawater and the electromagnetic field, optimizes the uniformity of radial current distribution, suppresses eddy currents and Joule heat loss, converts more electromagnetic energy into fluid pressure energy, and thus greatly improves the energy utilization efficiency of the propulsion system. This study provides quantitative design references for the structural optimization and engineering prototype development of low-noise superconducting underwater propulsion equipment, and supports the engineering application of helical-channel magnetohydrodynamic thrusters. Full article

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19 pages, 2264 KB

Open AccessArticle

Validity of the Quasi-Static Approximation in Low-Field NMR Signal Modeling for Petroleum-Bearing Porous Media

by Rengang Shi, Xinmin Ge, Ju Ge, Yiren Fan, Yiguo Chen, Falong Hu and Cheng Zhai

Magnetochemistry 2026, 12(8), 88; https://doi.org/10.3390/magnetochemistry12080088 - 6 Aug 2026

Viewed by 266

Abstract

Low-field nuclear magnetic resonance (NMR) is widely used for nondestructive characterization of petroleum-related porous media, including pore-structure evaluation, fluid identification, relaxation analysis, wettability assessment, and displacement monitoring. Conventional NMR signal models usually rely on the quasi-static approximation, in which the detected magnetic field [...] Read more.

Low-field nuclear magnetic resonance (NMR) is widely used for nondestructive characterization of petroleum-related porous media, including pore-structure evaluation, fluid identification, relaxation analysis, wettability assessment, and displacement monitoring. Conventional NMR signal models usually rely on the quasi-static approximation, in which the detected magnetic field is assumed to respond instantaneously to Bloch-governed nuclear magnetization. However, classical electrodynamics requires electromagnetic fields generated by time-dependent magnetization sources to depend on the source state at a retarded time. In this study, a retarded magnetic-dipole formulation is developed to evaluate finite-propagation-time effects in low-field NMR signal modeling. The analysis shows that the correction appears mainly as a phase shift governed by the dimensionless parameter

ϵ = ω_{0} L / v

, where

ω_{0}

is the Larmor angular frequency,

L

is the characteristic source–receiver distance, and

v

is the effective electromagnetic propagation velocity, with

v = c

in free space. Relaxation-induced amplitude corrections are generally smaller. Numerical examples demonstrate that the quasi-static approximation is well justified when

ϵ ≪ 1

, as typically satisfied in laboratory core NMR. For extended-scale configurations, including unilateral, borehole, underground, and surface NMR, larger propagation paths and medium-dependent electromagnetic properties may increase \epsilon and produce systematic phase deviations. This work provides a theoretical criterion for assessing the validity range of the quasi-static approximation in low-field NMR applications for petroleum-related porous media. Full article

(This article belongs to the Special Issue Nuclear Magnetic Resonance (NMR) in the Petroleum Industry and Porous Media)

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13 pages, 3227 KB

Open AccessArticle

Study on the Effect of Particle Size on NMR Pore Characterization of Cuttings

by Mingjing Gui, Xuewen Shi, Maojie Liao, Dongjun Zhang, Yingying Ma and Gong Zhang

Magnetochemistry 2026, 12(8), 87; https://doi.org/10.3390/magnetochemistry12080087 - 4 Aug 2026

Viewed by 300

Abstract

To study the effect of particle size on nuclear magnetic resonance (NMR) pore characterization of sandstone, core samples were gradually crushed into five particle sizes and the transverse relaxation time (T₂) spectrum and NMR response characteristics of the crushed samples [...] Read more.

To study the effect of particle size on nuclear magnetic resonance (NMR) pore characterization of sandstone, core samples were gradually crushed into five particle sizes and the transverse relaxation time (T₂) spectrum and NMR response characteristics of the crushed samples were measured. The experimental results show that within the particle size range of 2.4 mm, the T₂ spectrum position, T₂ mean value, and NMR porosity of sandstone cuttings are basically consistent with the core samples. When the particle size is 1.2 mm, the right peak amplitude of the T₂ spectrum increases significantly, and the T₂ mean value representing the T₂ spectrum characteristics becomes larger, which is presumed to be related to the increase in particle surface water. A comparative analysis suggests that cuttings with particle sizes larger than 2.4 mm can accurately characterize the NMR response characteristics of core samples. Full article

(This article belongs to the Special Issue Nuclear Magnetic Resonance (NMR) in the Petroleum Industry and Porous Media)

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28 pages, 5816 KB

Open AccessArticle

Low-Cost, Biodegradable, and Magnetic Biocomposite of Luffa cylindrica Fruit and Natural Magnetite by Removal of Microplastics

by Roberta Sorhaia Samayara Sousa Rocha de França, Rosangela Maria Ferreira da Costa e Silva, Ângela Leão Andrade, Daniel de Lima Silva, Rubens Lucas de Freitas Filho, Vinicius Veríssimo de Carvalho, Guilherme Oliveira Siqueira, Guilherme Jorge Brigolini Silva, Thiago Maturana Ribeiro, Diana Quintão Lima, José Agenor Carvalho Junior, Claudia Andrea Lima Cardoso, Vinicius de Oliveira Ribeiro, Leila Cristina Konradt-Moraes and Rozanna Marques Muzzi

Magnetochemistry 2026, 12(8), 86; https://doi.org/10.3390/magnetochemistry12080086 - 3 Aug 2026

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Abstract

Techniques such as adsorption have been widely adopted to remove residual microplastics (MPs) because they are efficient at removing contaminants from aqueous environments. In this study, we report a novel, low-cost, biodegradable, and scalable biocomposite (LCMAG NaOH) derived from Luffa cylindrica fruit (LC) [...] Read more.

Techniques such as adsorption have been widely adopted to remove residual microplastics (MPs) because they are efficient at removing contaminants from aqueous environments. In this study, we report a novel, low-cost, biodegradable, and scalable biocomposite (LCMAG NaOH) derived from Luffa cylindrica fruit (LC) and micrometric natural magnetite (MAG), prepared without organic solvents, for the removal of MPs. The performance of LCMAG NaOH was evaluated for the removal of polystyrene (PS) and polyethylene terephthalate (PET) MPs, with particle sizes ranging from 75 to 600 µm in three distinct aqueous media: drinking water, simulated seawater, and water collected from the eutrophic lake of Dourados, MS, Brazil. The material was also evaluated for capture capacity and for reutilization in drinking water over three cycles, using a neodymium magnet. The biocomposite exhibited maximum removal capacities of 163 mg g⁻¹ and 158 mg g⁻¹ for PS and PET, respectively, in drinking water. Additionally, it demonstrated high magnetic recovery efficiency (>90% of the initial mass) and good reusability after immersion (10 and 20 min) and a dry step during the first cycle. Full article

(This article belongs to the Special Issue Magnetic Nano- and Microparticles in Biotechnology)

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13 pages, 4408 KB

Open AccessArticle

Liquid-Film Temperature Regulates (222) Texture and Permeability–Frequency Response in Spin-Sprayed NiZn Ferrite Thin Films

by Hai Liu, Jinhua Zhu, Xinglian Song, Wenju Liao, Yu Liu and Ke Sun

Magnetochemistry 2026, 12(8), 85; https://doi.org/10.3390/magnetochemistry12080085 - 3 Aug 2026

Viewed by 397

Abstract

Spin-spray deposition is a low-temperature route for preparing crystalline ferrite films, but the actual liquid-film temperature has not been isolated from the nominal heater temperature. NiZn ferrite films were deposited at liquid-film temperatures of 87.6, 90.1, 92.7, and 95.0 °C. As the temperature [...] Read more.

Spin-spray deposition is a low-temperature route for preparing crystalline ferrite films, but the actual liquid-film temperature has not been isolated from the nominal heater temperature. NiZn ferrite films were deposited at liquid-film temperatures of 87.6, 90.1, 92.7, and 95.0 °C. As the temperature increased, the (222) Lotgering factor f_L decreased from 0.32 to 0.01, the triangular morphology weakened, and the growth rate declined. M_s remained nearly constant at 429–442 kA m⁻¹, whereas μ′_max increased from 44 to 83 and f_r decreased from 465 to 260 MHz. The structural and magnetic trends are consistent with a shift from surface-confined (222)-oriented growth toward less-oriented growth and a corresponding permeability–frequency trade-off. Unlike our previous studies of substrate and oxidant effects, this work isolates the measured liquid-film temperature and establishes its quantitative relationship with texture and dynamic magnetic response. This parameter provides a practical means of selecting the operating window of spin-sprayed NiZn ferrite cores for integrated high-frequency inductors. Full article

(This article belongs to the Special Issue Advances in Soft Magnetic Materials—2nd Edition)

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11 pages, 2003 KB

Open AccessArticle

Effect of Stress on Magnetic Property of the SiO₂-Added MnZn Ferrites

by Yao Ying, Yihao Zhu, Jingwu Zheng, Jing Yu, Liang Qiao, Juan Li, Naoki Wakiya and Shenglei Che

Magnetochemistry 2026, 12(8), 84; https://doi.org/10.3390/magnetochemistry12080084 - 3 Aug 2026

Viewed by 328

Abstract

In this work, the SiO₂-added MnZn power ferrites have been prepared by the conventional ceramic method, and the effect of stress on initial permeability and power loss has been investigated. With increasing SiO₂ content, initial permeability firstly increases and then [...] Read more.

In this work, the SiO₂-added MnZn power ferrites have been prepared by the conventional ceramic method, and the effect of stress on initial permeability and power loss has been investigated. With increasing SiO₂ content, initial permeability firstly increases and then decreases, whereas power loss firstly decreases and then increases. The sample with 50 ppm SiO₂ additive exhibits optimal magnetic performance, including the highest initial permeability and the lowest power loss. This optimal sample also exhibits the wide-temperature characteristics of power loss. Initial permeability decreases and power loss increases under the applied stress. The sample with 75 ppm SiO₂ additive exhibits the best stress insensitivity of initial permeability and power loss. Through the loss separation method, it is revealed that magnetic hysteresis loss is more sensitive whereas eddy current loss remains almost unchanged with stress. An appropriate addition of SiO₂ reduces the stress sensitivity of the initial permeability and power loss of MnZn ferrites. Full article

(This article belongs to the Special Issue Magnetic Materials: From Fundamentals to Cutting-Edge Applications)

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12 pages, 2464 KB

Open AccessArticle

From NMR Signals to Fracture Size: Capillary-Controlled Conversion for Shale

by Xu Dong, Wenqi Shi, Xueying Shi, Peidong Liu, Jiahui Zhang, Zhiyuan Chen and Jingjie Zhang

Magnetochemistry 2026, 12(8), 83; https://doi.org/10.3390/magnetochemistry12080083 - 1 Aug 2026

Viewed by 425

Abstract

Fracture size governs fluid mobility in shale, yet its direct quantification remains challenging. Nuclear Magnetic Resonance (NMR) transverse relaxation time (T₂) offers a unique, non-destructive probe of fracture size distributions; however, a physically grounded conversion from transverse relaxation time to [...] Read more.

Fracture size governs fluid mobility in shale, yet its direct quantification remains challenging. Nuclear Magnetic Resonance (NMR) transverse relaxation time (T₂) offers a unique, non-destructive probe of fracture size distributions; however, a physically grounded conversion from transverse relaxation time to pore radius r (T₂−r) is essential to translate NMR signals into quantitative geometric constraints on fluid mobility. This study introduces a capillary-constrained experimental method for T₂−r transformation into shale fractures. The workflow uses computed tomography (CT) scanning to extract fracture geometry. The gas-displacing-water process is precisely controlled by integrating the pore capillary pressure and back-pressure feedback algorithm. The NMR-CT conversion method performed in this study differs significantly from the T₂−r transformation based on conventional MICP. Differential spectral analysis isolates fracture-specific T₂ responses, and least-squares fitting derives the T₂−r conversion. Constraining displacement pressure and controlling segmental pressure are effective methods for ensuring the accuracy of fracture displacement. By emphasizing the governing role of capillary pressure during displacement, this method achieves accurate fracture-targeted displacement and reliable T₂−r mapping. The results significantly advance the use of NMR for quantifying fracture size and evaluating fluid transport in shale. Full article

(This article belongs to the Special Issue Nuclear Magnetic Resonance (NMR) in the Petroleum Industry and Porous Media)

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18 pages, 3190 KB

Open AccessArticle

Local Structural Distortions and Frustrated Magnetism in Slag-Derived Lithium Borate Glasses

by Kawtar Khattab, Abdellah El Boukili, Lahcen Boudad, Jacem Zidani, Naji AlDahoudi, Arash Jamali, Mimoun El Marssi, Mohamed Saadi, M’hamed Taibi and Abdelilah Lahmar

Magnetochemistry 2026, 12(8), 82; https://doi.org/10.3390/magnetochemistry12080082 - 30 Jul 2026

Viewed by 595

Abstract

This study analyzes the structural and magnetic properties of a new composite material with a lithium borate glass matrix loaded with electric arc furnace slag, with a composition of 50Li₂O-50B₂O₃-80 wt.% slag. The amorphous nature of the [...] Read more.

This study analyzes the structural and magnetic properties of a new composite material with a lithium borate glass matrix loaded with electric arc furnace slag, with a composition of 50Li₂O-50B₂O₃-80 wt.% slag. The amorphous nature of the obtained glass is confirmed by X-ray diffraction analysis (XRD). Differential scanning calorimetry (DSC) indicates that the material has an extremely high thermal stability as evidenced by its high glass transition temperature which is due to the reinforcing role of the slag metallic oxides. Additionally, magnetic studies reveal a highly frustrated magnetic state in the disordered system. The significant addition of mixed-valence iron ions (Fe²⁺/Fe³⁺) in the slag forms antiferromagnetic interactions in the system. These factors result in the stabilization of the spin-glass-like state. The incorporation of slag within the lithium borate matrix is a promising route to valorize this industrial by-product and to develop new functional materials. Full article

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79 pages, 933 KB

Open AccessArticle

The Zeta-Minimizer Theorem as a Deductive Variational Foundation for HOR and ORR Kinetics in Proton Exchange Membrane Fuel Cells

by Muhamad Fouad

Magnetochemistry 2026, 12(8), 81; https://doi.org/10.3390/magnetochemistry12080081 - 26 Jul 2026

Viewed by 548

Abstract

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 [...] Read more.

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

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Magnetochemistry, Volume 12, Issue 8 (August 2026) – 13 articles

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