Sign in to use this feature.

Years

Between: -

Subjects

remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline

Journals

remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline

Article Types

Countries / Regions

remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline

Search Results (864)

Search Parameters:
Keywords = gibbs free energy

Order results
Result details
Results per page
Select all
Export citation of selected articles as:
19 pages, 16517 KB  
Article
BaNb0.5In0.5(PO4)2 as an Efficient Inorganic Inhibitor for Mild Steel Corrosion in Acidic Media: Insights from Electrochemical Techniques and Surface Analyses
by Ahmed Griech, Marouane El-Alouani, Sami M. Alharbi, Zaidi Abderazzak, Issam Saber, Khattabi Mohamed, Khadija Dahmani, Mouhsine Galai, Helal S. Alharbi, Rachid Fakhreddine, Rida Allah Belakhmima and Mohamed Ebn Touhami
Corros. Mater. Degrad. 2026, 7(3), 50; https://doi.org/10.3390/cmd7030050 - 12 Aug 2026
Viewed by 17
Abstract
A novel orthophosphate compound, BaNb0.5In0.5(PO4)2 (FA31), was investigated as a corrosion inhibitor for mild steel in 1.0 M HCl using electrochemical techniques, adsorption studies, and surface characterization. Electrochemical impedance spectroscopy (EIS) and potentiodynamic polarization (PDP) measurements [...] Read more.
A novel orthophosphate compound, BaNb0.5In0.5(PO4)2 (FA31), was investigated as a corrosion inhibitor for mild steel in 1.0 M HCl using electrochemical techniques, adsorption studies, and surface characterization. Electrochemical impedance spectroscopy (EIS) and potentiodynamic polarization (PDP) measurements demonstrated that the inhibition efficiency increased with inhibitor concentration, reaching a maximum value of 94.8% at the optimal concentration. The charge-transfer resistance (Rct) increased significantly from that of the uninhibited solution to 427.2 Ω·cm2 in the presence of FA31, indicating the formation of a protective interfacial layer that effectively suppressed the corrosion process. The adsorption of FA31 on the mild steel surface followed the Langmuir adsorption isotherm, while the calculated standard Gibbs free energy of adsorption (ΔG°ads) indicated that the inhibition process was predominantly governed by physisorption. SEM/EDS analyses further confirmed the formation of a compact and homogeneous protective film on the steel surface. The combined electrochemical and surface analyses demonstrate that FA31 is an effective and environmentally promising corrosion inhibitor for mild steel in acidic media. Full article
Show Figures

Figure 1

15 pages, 1148 KB  
Article
Ro-Vibrational and Pure Vibrational Partition Functions and Thermodynamic Properties in an Eckart-like Potential Model
by Clement Atachegbe Onate, Matthew Olanrewaju Oluwayemi and Olumide Oyewale Ajani
AppliedMath 2026, 6(8), 130; https://doi.org/10.3390/appliedmath6080130 - 11 Aug 2026
Viewed by 44
Abstract
This study obtained the energy levels and examined the partition function (Z) of a quantum system described by an Eckart-like potential model. By adopting the Greene–Aldrich approximation scheme for the centrifugal term, the radial Schrödinger equation (SE) is solved and the analytic expression [...] Read more.
This study obtained the energy levels and examined the partition function (Z) of a quantum system described by an Eckart-like potential model. By adopting the Greene–Aldrich approximation scheme for the centrifugal term, the radial Schrödinger equation (SE) is solved and the analytic expression of the energy eigenvalues is obtained. The ro-vibrational Z is computed by explicitly incorporating the rotational quantum number, a feature often neglected or misapplied in many studies. This result is used to evaluate the key thermodynamic properties (TP), including the Gibbs free energy (G), entropy (S), and enthalpy (H). Numerical analysis reveals that the Z increases monotonically with temperature, while the G decreases in accordance with statistical thermodynamics. The S exhibits saturation-like behaviour at higher temperatures, while the H displays convex growth with increasing thermal energy. Parametric studies demonstrate that the Eckart-like potential allows for the controlled tuning of TP, with variations in the potential parameters, including the screening parameter, having distinct effects. The results generalise existing models, reproduce the Hulthén potential under specific conditions, show the effect of the rotational quantum number of TP, and provide new insights into the ro-vibrational statistical mechanics of exponential-type potentials. Full article
(This article belongs to the Section Deterministic Mathematics)
Show Figures

Figure 1

34 pages, 8706 KB  
Article
Sustainable Corrosion Mitigation Using Aqueous Spent Coffee Grounds Extract: Comparative Performance in Different Acidic Media
by Florina Brânzoi, Denisa-Ioana Răuță (Gheorghe), Roxana-Doina Truşcă and Sorin-Marius Avramescu
Molecules 2026, 31(16), 2771; https://doi.org/10.3390/molecules31162771 - 9 Aug 2026
Viewed by 158
Abstract
This study investigates the efficiency of green corrosion inhibitors derived from spent coffee grounds (SCGs) for OL 37 carbon steel in 0.5 M H2SO4 and 1 M HCl environments. The aqueous extracts, labeled K1 and K2, were obtained through specialized [...] Read more.
This study investigates the efficiency of green corrosion inhibitors derived from spent coffee grounds (SCGs) for OL 37 carbon steel in 0.5 M H2SO4 and 1 M HCl environments. The aqueous extracts, labeled K1 and K2, were obtained through specialized extraction techniques and characterized by HPLC. Their protective performance was investigated using potentiodynamic polarization and electrochemical impedance spectroscopy (EIS). FT-IR spectroscopy and SEM-EDX analysis confirmed the presence of a protective inhibitor film on the OL 37 surface, attributed to the adsorption of organic molecules from the SCGs extract (K1 and K2). The adsorption behavior followed the Langmuir isotherm, with high adsorption constants and standard free energy values (ΔG°ads), indicating a mixed-mode adsorption mechanism. Furthermore, the negative Gibbs free energy values of adsorption confirm the spontaneity of the adsorption process. Thermodynamic studies conducted between 293 K and 333 K demonstrated the temperature dependence of the inhibition process. Results showed that at a concentration of 800 ppm and 1000 ppm, both inhibitors exhibited high efficiency, reaching 96% for K1 and 95% for K2. Full article
Show Figures

Figure 1

22 pages, 2239 KB  
Article
Molecular Interactions and Antioxidant Properties of White Wine Phytochemicals: A Mechanistic Study of Serum Protein Binding
by Dinorah Barasch, Alina Nemirovski, Emmanuelle Merquiol, Joseph Deutsch, Dejian Huang, Pitipong Thobunluepop, Alma Leticia Martinez-Ayala, Patricia Arancibia-Avila, Fernando Toledo-Montiel, Paweł Paśko and Shela Gorinstein
Biomolecules 2026, 16(8), 1153; https://doi.org/10.3390/biom16081153 - 7 Aug 2026
Viewed by 178
Abstract
This study investigated the interactions between phenolic compounds from Israeli and Chilean white wines and human serum carrier proteins, including human serum albumin (HALB), gamma-globulin (HGLO), and fibrinogen (HFB), to characterize their antioxidant capacity and serum protein-binding behavior under controlled experimental conditions. The [...] Read more.
This study investigated the interactions between phenolic compounds from Israeli and Chilean white wines and human serum carrier proteins, including human serum albumin (HALB), gamma-globulin (HGLO), and fibrinogen (HFB), to characterize their antioxidant capacity and serum protein-binding behavior under controlled experimental conditions. The analyzed wines included Israeli Chardonnay (ICR), Chilean Chardonnay (CCR), Israeli Sauvignon Blanc (ISB), and Chilean Sauvignon Blanc (CSB). HPLC and FTIR fingerprinting revealed cultivar- and region-dependent differences in phenolic composition, with Chardonnay wines showing stronger protein-binding behavior and Sauvignon Blanc samples displaying high antioxidant efficiency relative to their phenolic content. ICR exhibited the highest total binding capacity, 46.44%, and the strongest albumin interaction, with a binding constant (Kb) of 8.44 × 104 M−1 and a Gibbs free energy (ΔG) value of −35.03 kJ/mol. Empirical fluorescence quenching kinetics demonstrated that white wine phenolics establish stable physical complexes with human serum proteins, displaying a distinct preferential affinity for HALB as the protein showing the strongest apparent interaction among the proteins tested. Two- and three-dimensional fluorescence spectroscopy confirmed substantial quenching of the intrinsic tryptophan and tyrosine residues, indicating meaningful microenvironmental alterations within the protein’s active transport sites. These empirical interactions were closely mirrored by complementary molecular docking simulations, which provided a structural visualization of the physical binding interactions. ICR also showed the highest antioxidant capacity, with DPPH and CUPRAC values of 1.66 and 2.91 mmol TE/L, respectively. Ethanol control showed negligible effects, indicating that the observed bioactivity was mainly associated with the polyphenolic matrix. Among the investigated samples, Chardonnay showed higher apparent protein-binding capacity, whereas Sauvignon Blanc showed relatively high antioxidant efficiency in relation to its phenolic content. Full article
Show Figures

Figure 1

21 pages, 2462 KB  
Article
Experimental and Theoretical Insights on the Use of Expired Furosemide as Corrosion Inhibition for Cu in NaCl
by Dalia Garcia-Rosas, Alfredo Brito-Franco, Hugo Albeiro Saldarriaga-Noreña, Roy Lopez-Sesenes, America Maria Ramirez-Arteaga, Ana Karen Galvez-Larios, Jesus Porcayo-Calderon and Jose Gonzalo Gonzalez-Rodriguez
Materials 2026, 19(15), 3274; https://doi.org/10.3390/ma19153274 - 3 Aug 2026
Viewed by 192
Abstract
Copper and its alloys are extensively employed in a broad range of industrial applications owing to their outstanding mechanical, electrical, and thermal properties. However, their susceptibility to corrosion in aggressive environments remains a major challenge, making corrosion inhibitors one of the most practical [...] Read more.
Copper and its alloys are extensively employed in a broad range of industrial applications owing to their outstanding mechanical, electrical, and thermal properties. However, their susceptibility to corrosion in aggressive environments remains a major challenge, making corrosion inhibitors one of the most practical and cost-effective strategies for extending their service life. Nevertheless, conventional synthetic inhibitors are often limited by their high cost and adverse environmental and health impacts resulting from their toxicity. In this context, the present work provides a comprehensive experimental and theoretical assessment of the corrosion inhibition performance of Furosemide as an environmentally friendly inhibitor for copper in 3.5 wt.% NaCl solution. The corrosion inhibition performance was evaluated experimentally through gravimetric measurements, potentiodynamic polarization, and electrochemical impedance spectroscopy (EIS), while the adsorption behavior of Furosemide was investigated using density functional theory (DFT) calculations. The results demonstrated that expired Furosemide effectively reduced the corrosion rate of copper, with the inhibition efficiency increasing as the inhibitor concentration increased and decreased with increasing temperature. A maximum inhibition efficiency of 90% was achieved at an inhibitor concentration of 400 ppm. The calculated Gibbs free energy of adsorption indicated that Furosemide adsorbs onto the copper surface through a mixed physisorption–chemisorption mechanism, following the Langmuir adsorption isotherm. Potentiodynamic polarization measurements further revealed that Furosemide predominantly suppresses the anodic dissolution reaction, indicating that it behaves as an anodic-type corrosion inhibitor. In addition, the presence of Furosemide significantly decreased the passive current density and shifted the breakdown potential toward more positive values, demonstrating an enhancement in the stability and protective character of the passive film. Electrochemical impedance spectroscopy showed that the corrosion process was governed by diffusion-controlled kinetics in the uninhibited solution, whereas the addition of Furosemide changed the corrosion mechanism to a charge-transfer-controlled process. Density functional theory (DFT) calculations provided additional insight into the inhibition mechanism of Furosemide. The calculated EHOMO) and ELUMO values indicate that the molecule can both donate and accept electrons, reflecting its nucleophilic and electrophilic character and its strong affinity for adsorption on the copper surface. Furthermore, the relatively small energy gap (4.631 eV) suggests high molecular reactivity and facilitates electronic interactions with the metal surface. The estimated fraction of electrons transferred further supports the electron-donating ability of Furosemide during the adsorption process. Differences between the Fukui functions and the molecular electrostatic potential (MEP) maps are attributed to the distinct chemical information provided by each descriptor. Whereas the Fukui functions identify the most reactive atomic sites involved in soft donor–acceptor interactions, the MEP maps describe the molecular charge distribution governing electrostatic (hard–hard) interactions. Full article
Show Figures

Figure 1

13 pages, 2280 KB  
Article
DFT Study on the Gas-Phase Cluster Formation Mechanism in SiC CVD
by Peng Su, Siyuan Tang, Liangcan Fu, Xinxin Yang and Lijun Liu
Crystals 2026, 16(8), 504; https://doi.org/10.3390/cryst16080504 - 1 Aug 2026
Viewed by 174
Abstract
This study employs density functional theory and quantum chemical calculations to investigate the gas-phase nucleation and growth mechanisms during chemical vapor deposition of silicon carbide. Based on thermodynamic stability evaluations of large clusters under various configurations, the lowest-energy ground-state structure was determined. The [...] Read more.
This study employs density functional theory and quantum chemical calculations to investigate the gas-phase nucleation and growth mechanisms during chemical vapor deposition of silicon carbide. Based on thermodynamic stability evaluations of large clusters under various configurations, the lowest-energy ground-state structure was determined. The Gibbs free energy (ΔG) calculations of pure silicon clusters (Sin), single-carbon silicon clusters (SinC), and double-carbon silicon clusters (SinC2) were conducted at different temperatures. The findings reveal that silicon atoms promote cluster growth. The special 2D-to-3D configurational transition attenuates the reaction’s spontaneity. During the initial nucleation stage, the system tends to form SinC; however, as the size increases, it evolves into the more stable SinC2. This study reveals gas-phase cluster formation at the atomic scale, providing a theoretical foundation for suppressing detrimental gas-phase nucleation. Full article
(This article belongs to the Section Inorganic Crystalline Materials)
Show Figures

Figure 1

27 pages, 27631 KB  
Article
Determination of the Formation Constants of Copper(II) Complexes Using Quantum Chemical Calculations
by Nikita S. Aksenin, Mikhail S. Bukharov, Valery G. Shtyrlin and Nikita Yu. Serov
Inorganics 2026, 14(8), 202; https://doi.org/10.3390/inorganics14080202 - 28 Jul 2026
Viewed by 258
Abstract
Gibbs free energy values obtained from quantum-chemical calculations were used to determine the formation constants of homo- and heteroligand copper(II) complexes with various ligands (amino acids, diimines, and phosphorylated dithiocarbamates) in an aqueous medium. A computationally robust, yet moderately expensive, level of theory—B3LYP/def2-TZVPPD—was [...] Read more.
Gibbs free energy values obtained from quantum-chemical calculations were used to determine the formation constants of homo- and heteroligand copper(II) complexes with various ligands (amino acids, diimines, and phosphorylated dithiocarbamates) in an aqueous medium. A computationally robust, yet moderately expensive, level of theory—B3LYP/def2-TZVPPD—was employed. Solvent effects were accounted for using two models: C-PCM and SMD. A key prerequisite for obtaining reliable results is the use of a reference complex with a known formation constant that is structurally and solvation-wise similar to the compound under study. In this context, “similarity” implies identical stoichiometry, the same coordination number, the same number of water molecules in the inner coordination sphere; matching charges, however, is considerably less critical. The importance of considering conformers and isomers to obtain the most accurate values is demonstrated. The more rigid the structure and the greater the degree of similarity between the studied and reference compounds, the better the agreement between calculated and experimental data; the discrepancy can be as low as 0.1–0.2 logarithmic units. When an appropriate reference is selected, the average deviation of the calculated stability constants is less than 1 logarithmic unit. Full article
(This article belongs to the Special Issue Copper(II) Complexes and Their Properties)
Show Figures

Figure 1

14 pages, 5701 KB  
Perspective
Hidden Order in the Apparent Chaos of Bias Temperature Instability
by Joseph B. Bernstein
Micromachines 2026, 17(8), 903; https://doi.org/10.3390/mi17080903 - 28 Jul 2026
Viewed by 252
Abstract
Bias Temperature Instability (BTI) remains one of the principal reliability challenges limiting advanced CMOS technologies. Although degradation is commonly described by an empirical power–law relationship, the power–law exponent is generally regarded only as a fitting parameter used for lifetime extrapolation. This Perspective reexamines [...] Read more.
Bias Temperature Instability (BTI) remains one of the principal reliability challenges limiting advanced CMOS technologies. Although degradation is commonly described by an empirical power–law relationship, the power–law exponent is generally regarded only as a fitting parameter used for lifetime extrapolation. This Perspective reexamines a previously published Multiple-Temperature Operational Life (MTOL) dataset to investigate whether the measured exponent contains previously overlooked physical information. Individual ring oscillators stressed under identical voltage and temperature conditions exhibit substantially different, yet reproducible, power–law exponents. When these measurements are analyzed over a broader temperature range, the apparent statistical scatter reveals a systematic kinetic dependence that produces a remarkably consistent lifetime relationship after incorporating the experimentally measured exponent into the Arrhenius analysis. The resulting intrinsic activation energy is significantly smaller than values obtained using conventional extrapolation methods, suggesting that part of the apparent activation energy arises from neglecting the temperature dependence of the degradation exponent. A recently proposed thermodynamic formulation based on Gibbs free energy and correlation entropy is presented as one possible physical interpretation of these observations, in which the power–law exponent reflects the correlation between successive degradation events rather than merely an empirical fitting constant. More generally, this Perspective suggests that the power–law exponent should be regarded as a measurable kinetic quantity whose systematic variation may provide additional insight into degradation mechanisms in BTI and other reliability phenomena. Full article
(This article belongs to the Section D1: Semiconductor Devices)
Show Figures

Figure 1

29 pages, 8291 KB  
Article
Assessment of Co-Pyrolysis of a Cyanobacterium and Waste Textile Polymer: Investigating Kinetics, Thermodynamics, Reaction Mechanism and Synergism
by Kaustav Nath, Biswajit Debnath, Ranjana Chowdhury, Somil Thakur and Rajnish Kaur Calay
Clean Technol. 2026, 8(4), 112; https://doi.org/10.3390/cleantechnol8040112 - 22 Jul 2026
Viewed by 384
Abstract
Algal cultivation has attracted significant attention due to CO2 biocapture and potential for biofuel generation. Enormous generation of waste polymer often poses an environmental problem due to non-biodegradability. This study comprehensively analyses the thermal degradation characteristics of blue–green alga, Leptolyngbya subtilis JUCHE1 [...] Read more.
Algal cultivation has attracted significant attention due to CO2 biocapture and potential for biofuel generation. Enormous generation of waste polymer often poses an environmental problem due to non-biodegradability. This study comprehensively analyses the thermal degradation characteristics of blue–green alga, Leptolyngbya subtilis JUCHE1 (LS) and waste textile polyester (WTP) and their mixtures (LS1P3 (1:3); LS1P1 (1:1); LS3P1 (3:1)) during co-pyrolysis. The interaction between LS and WTP during co-pyrolysis has been assessed through the verification of synergism using different blending ratio and through the comparison of the corresponding values of the Comprehensive Pyrolysis Index (CPI). The composite, LS1P3, exhibited the highest synergism and the maximum value of CPI. Isoconversional models (FWO, Starink, Bosewell and Tang) have been used to predict the activation energies (Ea). Thermodynamic parameters, namely, heat of reaction (ΔH), Gibbs free energy change (ΔG) and entropy change (ΔS), have also been determined for all. The average value of Ea for LS1P3 is also the lowest (96.015 kJ/mol) among all composites. The Master plot method identifies that there is a shift of reaction mechanism from phase boundary type (R2 and R3) for LS and WTP to a P2-type acceleratory reaction rate mechanism for LS1P3. The lowest average value of ΔH and the highest values of ΔG and ΔS for LS1P3 co-pyrolysis also support the least consumption of energy and the highest favorability under present conditions. The product yield distribution of co-pyrolysis in the isothermally operated conditions (450 °C) also establishes the superiority of LS1P3. Yields of pyro-oil and pyro-gas are the highest among all composites. The study ensures the future application prospects of co-pyrolysis of LS and WTP as a means for generation of energy resources (pyro-oil and pyro-gas) and chemicals (pyro-char). Full article
Show Figures

Graphical abstract

28 pages, 1259 KB  
Article
Effect of β-Cyclodextrin on the Mixed Micellization of Triton X-100 and Brij S20: A Thermodynamic Study
by Kosta Popović, Zita Farkaš Agatić, Ana Pilipović and Mihalj Poša
Int. J. Mol. Sci. 2026, 27(14), 6284; https://doi.org/10.3390/ijms27146284 - 15 Jul 2026
Viewed by 317
Abstract
The micellization behavior of binary mixtures of the nonionic surfactants Triton X-100 and Brij S20 was investigated in aqueous solution in the absence and presence of β-cyclodextrin (βCD) over the temperature range 283.15–318.15 K. Critical micelle concentrations (CMC) were determined and [...] Read more.
The micellization behavior of binary mixtures of the nonionic surfactants Triton X-100 and Brij S20 was investigated in aqueous solution in the absence and presence of β-cyclodextrin (βCD) over the temperature range 283.15–318.15 K. Critical micelle concentrations (CMC) were determined and analyzed using regular solution theory to evaluate mixed micelle composition, interaction parameters, activity coefficients, and excess Gibbs free energies. The Triton X-100/Brij S20 system exhibited pronounced synergistic interactions, reflected by negative interaction parameters, reduced CMC values, and negative excess Gibbs free energies over the entire composition range. The addition of βCD systematically increased CMC values and reduced the magnitude of the interaction parameters, indicating that inclusion complex formation competes with micellization and weakens surfactant–surfactant interactions. Corrected micellar compositions revealed significant redistribution of surfactants between the aqueous phase and mixed micelles due to host–guest complexation. Thermodynamic analysis demonstrated spontaneous formation of βCD inclusion complexes with both surfactants, characterized by negative Gibbs free energy, enthalpy, and entropy changes. Triton X-100 exhibited a higher affinity toward βCD than Brij S20. The results demonstrate that coupled equilibria between micellization and inclusion complex formation govern the behavior of the system and suggest that conformational contributions should be considered when interpreting interaction parameters in cyclodextrin–surfactant systems. Full article
Show Figures

Figure 1

13 pages, 2791 KB  
Article
First-Principles Insights into I Doping Effects on the Electronic Structure, Optical Properties, and CO2 Photoreduction Performance of Bi4O5Br2
by Juan Guo, Shuaishuai Liu, Chenxi Wang, Haocheng Wang and Gaihui Liu
Catalysts 2026, 16(7), 622; https://doi.org/10.3390/catal16070622 - 9 Jul 2026
Viewed by 343
Abstract
To address the insufficient visible-light absorption of Bi4O5Br2 photocatalysts, first-principles density functional theory (DFT) calculations were employed to systematically investigate the effects of I doping at different concentrations (12.5%, 25%, 50%, 75%, 87.5%, and 100%) on the geometric [...] Read more.
To address the insufficient visible-light absorption of Bi4O5Br2 photocatalysts, first-principles density functional theory (DFT) calculations were employed to systematically investigate the effects of I doping at different concentrations (12.5%, 25%, 50%, 75%, 87.5%, and 100%) on the geometric structure, electronic structure, optical properties, and photocatalytic CO2 reduction performance of Bi4O5Br2. Formation energy calculations and Ab initio molecular dynamics (AIMD) simulations indicate that the I-doped systems possess good thermodynamic and kinetic stability. Geometric analysis shows that I doping leads to a gradual expansion of lattice parameters along the c-axis (from 14.80 Å to 15.16 Å), due to the larger ionic radius of I compared to Br. Electronic structure results reveal that all doped systems remain indirect band gap semiconductors, with the band gap decreasing from 2.56 eV for the pristine system to 2.25 eV at 87.5% doping. This reduction is mainly attributed to the progressive substitution of Br 4p states by I 5p states near the valence band maximum, which modifies the valence band structure. Differential charge density analysis shows electron transfer from Bi to I, enhancing local polarization effects. Optical property calculations demonstrate a pronounced red shift in the absorption edge and significantly enhanced absorption intensity in the visible region after I doping. The real and imaginary parts of the dielectric function also exhibit red shifts and increased peak intensities in the low-energy region. Gibbs free energy analysis indicates that the Gibbs free energy for *COOH formation decreases from 2.83 eV in the pristine system to 2.68 eV after I doping, while the free energy of the *CO intermediate decreases from 1.28 eV to 0.98 eV, significantly improving the CO2 reduction pathway. This study provides a theoretical basis for improving the optical response and the thermodynamics of the CO2 reduction reaction through halogen substitution, suggesting a promising strategy for enhancing the photocatalytic potential of Bi4O5Br2. Full article
Show Figures

Graphical abstract

16 pages, 4580 KB  
Perspective
A Thermodynamic Framework for Reliability Kinetics
by Joseph B. Bernstein
Micromachines 2026, 17(7), 817; https://doi.org/10.3390/mi17070817 - 7 Jul 2026
Viewed by 350
Abstract
Empirical power-law relationships are widely used in reliability physics to describe degradation kinetics and predict lifetime. Such behavior appears across diverse failure mechanisms, including time-dependent dielectric breakdown (TDDB), hot-carrier injection (HCI), bias temperature instability (BTI), electromigration (EM), and fatigue. In this work, a [...] Read more.
Empirical power-law relationships are widely used in reliability physics to describe degradation kinetics and predict lifetime. Such behavior appears across diverse failure mechanisms, including time-dependent dielectric breakdown (TDDB), hot-carrier injection (HCI), bias temperature instability (BTI), electromigration (EM), and fatigue. In this work, a thermodynamic framework for reliability kinetics is developed from Gibbs free energy and entropy partitioning, leading to a generalized kinetic equation that incorporates thermal activation, stress acceleration, and accumulated degradation. The formulation introduces two parameters: a stress coefficient, γ, which describes the influence of externally applied stress, and a correlation coefficient, χ, which describes how accumulated degradation influences subsequent degradation. Negative values of χ correspond to self-limiting evolution, positive values correspond to self-amplifying evolution, and χ=0 represents statistically independent accumulation. Representative reliability mechanisms are interpreted within this framework, with TDDB approaching independent evolution, HCI exhibiting weak self-limiting behavior, BTI showing strong self-limiting behavior, and fatigue exhibiting self-amplifying behavior. Electromigration illustrates the complementary role of stress acceleration through γ. The proposed framework provides a common thermodynamic interpretation of empirical power-law degradation kinetics and introduces degradation correlation as a complementary descriptor for reliability modeling and lifetime prediction. Full article
Show Figures

Figure 1

32 pages, 968 KB  
Article
Bounds for General Zagreb Indices and Improved Topological Coindices with QSPR Benchmarking on Octane Isomers
by Suha Wazzan and Abdu Alameri
Symmetry 2026, 18(7), 1139; https://doi.org/10.3390/sym18071139 - 3 Jul 2026
Viewed by 263
Abstract
Topological descriptors play an important role in chemical graph theory and QSPR/QSAR studies by relating molecular structure to measurable physicochemical properties. Among standard benchmark families, octane isomers are frequently used to evaluate the behavior of degree-based descriptors because of their rich branching patterns [...] Read more.
Topological descriptors play an important role in chemical graph theory and QSPR/QSAR studies by relating molecular structure to measurable physicochemical properties. Among standard benchmark families, octane isomers are frequently used to evaluate the behavior of degree-based descriptors because of their rich branching patterns and well-documented physicochemical data. Although many studies have examined topological indices for octane isomers, comparatively fewer works have focused on topological coindices and derived coindex-based descriptors. In this work, we study several known topological coindices and four derived descriptors, denoted by KJ1,KJ2,KJ3, and KJ4, for comparative analysis on the octane-isomer benchmark. We also present a unified treatment of lower and upper bounds for the first and second (α,β)-general Zagreb indices, together with their reduced and expanded variants, in terms of basic graph parameters, such as the minimum degree, maximum degree, order, and size. These bounds cover a range of familiar special cases, including classical Zagreb, forgotten, Sombor, and Randić-type indices, thereby placing several known descriptors within a common framework. For the application part, the original octane-isomer analysis is retained as a controlled benchmark for the proposed descriptors. In addition, an expanded QSPR experiment is added using a Zenodo molecular dataset containing 90 organic compounds and nine physicochemical endpoints. SMILES strings were converted into hydrogen-suppressed molecular graphs, graph-theoretical descriptors were computed, and ordinary least squares, ridge regression, and PLS(2) models were evaluated using an 80:20 train/test split and five-fold cross-validation. The expanded results show strong or useful performance for selected endpoints, especially critical volume, molecular volume, standard Gibbs free energy of formation, and logarithmic water solubility, whereas some temperature-related endpoints remain less stable. The results therefore support the usefulness of degree-based and coindex-based descriptors as compact exploratory QSPR variables while also emphasizing the need for cautious interpretation, redundancy analysis, and external validation on broader chemical families. Full article
(This article belongs to the Special Issue Mathematics: Feature Papers 2026)
Show Figures

Figure 1

30 pages, 1867 KB  
Article
Improvement of PC-SAFT-Based Asphaltene Prediction Model and Simulation of Phase Behavior Under Multiple Operating Conditions
by Jianyi Liu and Minjian Gun
Appl. Sci. 2026, 16(13), 6437; https://doi.org/10.3390/app16136437 - 28 Jun 2026
Viewed by 381
Abstract
This study, based on phase equilibrium theory, uses reservoir crude oil systems as the research object and adopts the Perturbed Chain-Statistical Associating Fluid Theory (PC-SAFT) equation of state. By combining the Panuganti characterization method with the three-phase Rachford–Rice algorithm, an integrated RRPC-SAFT engineering [...] Read more.
This study, based on phase equilibrium theory, uses reservoir crude oil systems as the research object and adopts the Perturbed Chain-Statistical Associating Fluid Theory (PC-SAFT) equation of state. By combining the Panuganti characterization method with the three-phase Rachford–Rice algorithm, an integrated RRPC-SAFT engineering workflow is established, which effectively addresses the drawbacks of traditional PC-SAFT models, including low computational efficiency and poor convergence under extreme working conditions. On this basis, systematic performance comparisons are conducted between the RRPC-SAFT workflow and classical cubic equations of state (PR and SRK). Furthermore, the asphaltene phase behavior under gas injection development conditions is simulated, and the quantitative effects of the four SARA fractions on the critical precipitation conditions and precipitation intensity of asphaltenes are determined, clarifying the evolution rules and main controlling factors of asphaltene phase instability under various development scenarios. The research results reveal that the average relative errors of bubble point pressure and asphaltene onset precipitation pressure (AOP) for the three crude oil samples are all less than or equal to 5%. Compared with the PR and SRK models, the average prediction errors are reduced by 1.27% and 2.01%, respectively. Gas injection simulation results demonstrate that nitrogen poses the highest risk of triggering asphaltene precipitation under equimolar injection, with the asphaltene onset precipitation pressure increasing up to 114.94%. Single-factor analysis of SARA fractions verifies that saturates and asphaltenes aggravate precipitation, while aromatics and resins suppress asphaltene destabilization. In terms of computational efficiency, the computational speed of the RRPC-SAFT algorithm is four times higher than that of the traditional Gibbs free energy minimization algorithm. This model can be applied to calculate the thermodynamic critical equilibrium conditions of asphaltene precipitation, providing a thermodynamic basis for early screening of asphaltene deposition risks, optimization of gas injection schemes, and design of deposition prevention and control technologies. Full article
Show Figures

Figure 1

20 pages, 3739 KB  
Article
Dracaena fragrans Extract as a Corrosion Inhibitor for SAE 1025 Steel Used in Aircrafts
by Sury Saday Arizmendi Gómez, María Guadalupe Valladares Cisneros, Víctor Martínez Calzada, Alonso Saldaña Heredia, Jorge Guillermo Alonso Alfaro and Adriana Rodríguez Torres
Processes 2026, 14(13), 2079; https://doi.org/10.3390/pr14132079 - 26 Jun 2026
Viewed by 591
Abstract
This study evaluated the corrosion inhibition performance of Dracaena fragrans extract for SAE 1025 steel in artificial seawater. Inhibition efficiency was assessed using weight loss measurements, potentiodynamic polarization, and electrochemical impedance spectroscopy (EIS). The results showed that inhibition efficiency increased with higher extract [...] Read more.
This study evaluated the corrosion inhibition performance of Dracaena fragrans extract for SAE 1025 steel in artificial seawater. Inhibition efficiency was assessed using weight loss measurements, potentiodynamic polarization, and electrochemical impedance spectroscopy (EIS). The results showed that inhibition efficiency increased with higher extract concentrations, reaching a maximum of 97% at 500 ppm. Potentiodynamic polarization measurements indicated that the extract acts as a mixed-type inhibitor, affecting both anodic and cathodic reactions. EIS analysis revealed an increase in charge transfer resistance and a decrease in double-layer capacitance, confirming the formation of a protective adsorbed film on the steel surface. Adsorption studies indicated that the process followed the Frumkin isotherm and was predominantly governed by physisorption, with a standard Gibbs free energy of adsorption Gads° of approximately −12.33 kJ mol−1. Surface analyses confirmed enhanced protection of the steel substrate in the presence of the extract. Moreover, toxicity tests yielded a germination index (GI) of 35.1% and a relative germination (RG) of 45.6% at 500 ppm. These findings demonstrate the potential of Dracaena fragrans extract as an environmentally friendly corrosion inhibitor for steel exposed to chloride-containing environments in marine and aeronautical applications. Full article
Show Figures

Graphical abstract

Back to TopTop