Gibbs Free Energy Model Research Articles

Kirkwood-Buff Analysis of Binary and Ternary Systems Consisting of Alcohols (Methanol, Ethanol, 1-Propanol, and 2-Propanol), Water, and n-Hexane to Understand the Formation of Surfactant-Free Microemulsions.

Surfactant-free microemulsion (SFME) represents a class of fluid mixtures that can form microheterogeneous structures without detergents, offering an environmentally benign alternative to traditional microemulsions. However, the formation mechanism is still elusive. This work applies the Kirkwood-Buff theory to mixtures of alcohols, water, and n-hexane to elucidate the SFME formation mechanism. To ensure robust calculation of the Kirkwood-Buff integrals (KBIs), we construct a data set of densities and excess free energies of binary and ternary systems. Multiple excess Gibbs free energy models are assessed against this data set to select the most suitable model reproducing the experimental results. In addition, we introduce statistical methods to determine the optimal polynomial order of the Redlich-Kister correlation for the excess volume data. We first validate our methodology in binary systems. Then, we extend the calculation method to ternary mixtures. The KBI calculation results reveal that the alcohol-hexane and water-hexane interactions do not significantly affect SFME formation. In contrast, the interplay among water-water, water-alcohol, and alcohol-alcohol interactions critically influences the ability of a liquid mixture to form SFME structures. SFME systems exhibit the facile formation of water aggregates enveloped by alcohols, whereas non-SFME systems demonstrate homogeneous alcohol/water droplets dispersed in an oil continuous medium.

Thermodynamic study of imidazolium halide ionic liquid–water binary systems using excess Gibbs free energy models

In this work, the excess Gibbs free energy models, i.e., non-random two-liquid (NRTL) model and electrolyte NRTL model, including the original one and those with new strategies (association or hydration), were used to describe the macroscopic properties and interpret the microstructure of ionic liquid (IL) - H2O binary systems, clarifying the role of IL association and ion hydration in model development. To provide systematic data for model development, the enthalpy of mixing of three imidazolium-based IL-H2O systems containing the same cation but different sizes of anions, i.e., Cl−, Br−, and I−, were measured. The models were developed and evaluated based on the newly measured data and the osmotic coefficient from the literature. The results reveal that the model reflecting the intrinsic mechanism of dissociation and hydration gives the best modeling results; and the ionic strength and the degree of IL dissociation as a function of water content can be predicted using the newly established model. The study clarifies the significance of IL association and anion hydration in model development and quantitatively demonstrates how water content influences the microstructure and real species in IL-H2O systems.

Formation and Evolution Mechanism of Intermetallic Compounds of Friction Stir Lap Welded Steel/Aluminum Joints.

Interfacial layers with brittle intermetallic compounds (IMC) greatly influence the performance of steel-aluminum friction stir lap welding (FSLW) joints. Thus, the formation and evolution of IMC between 7075-T6 aluminum alloy and galvanized DP590 steel in steel-aluminum FSLW joints were investigated. An FSLW numerical model was developed using the computational fluid dynamics method to analyze the interface temperature between the aluminum alloy and steel. Scanning electron microscopy (SEM) was conducted to observe the microstructure characterization and measure the IMC thickness. Phases among different joint zones were analyzed by X-ray diffraction (XRD) and energy dispersive spectroscopy (EDS). IMC layer formation was predicted by the effective Gibbs free energy model presented in this paper according to thermodynamic principles. The Monte Carlo method was utilized to predict the thickness of IMC layers. It was found that the IMC layer at the interface of the welded joint is composed of Fe2Al5, FeAl3, and Al-Zn eutectic. The IMC thickness decreased from 4.3 μm to 0.8 μm with the increasing welding speed, which was consistent with the Monte Carlo simulation results.

Effect of temperature on N-A-S-(H) and zeolite composition, solubility, and structure

This paper investigates the effect of temperature on the composition, solubility, and structure of sodium aluminosilicate hydrate (N-A-S-(H)) and zeolite synthesized using sodium silicate and sodium aluminate solutions across a range of bulk aqueous Si/Al ratios at different temperatures. It was found that temperature had minimal effect on the composition for both N-A-S-(H) and zeolite species. A decrease in N-A-S-(H) and zeolite solubility with increasing temperature was observed and attributed to the temperature-dependent pH. As expected, the solubility of N-A-S-(H) was higher than that of its crystalline counterpart. Estimation of thermodynamic properties also revealed that for both the N-A-S-(H) and zeolite phases, the Van't Hoff expression yielded similar enthalpy and Gibbs free energy of formation data as a three-parameter Gibbs free energy model that includes a heat capacity term. An additional benefit of the Van't Hoff approach is that it obviates the need for estimating the heat capacity from reference reactions.

An insight into the analogy between solute-solvent binding energy and solubility of acid gases in ionic liquids: Thermodynamic modeling versus molecular dynamic simulation

Ionic Liquids (ILs) have emerged as a promising generation of solvents for the absorption of acid gases (e.g., CO2 and H2S) due to their unparalleled physiochemical properties. This study focuses on thermodynamic modeling and molecular dynamic simulation approaches to estimate the solubility and interaction energies of CO2 and H2S gases in/with different frequently-used ILs. For thermodynamic modeling, the GE/EOS method was employed. This method allows for combining activity-coefficient models in the structure of the cubic equation of states. In the GE/EOS method, the modified Peng-Robinson equation of state (MPR2) together with the LCVM mixing rules was used. Excess Gibbs free energy models of Wilson, NRTL, and UNIQUAC were also applied for combination with the GE/EOS models. The prediction results of the combined models were compared with the experimental solubility data. The results demonstrated the capability of these models to predict the thermodynamic behavior of the acid gas-ILs systems. The results uncovered that the MPR2-LCVM-Wilson model can tabulate the highest correlation with the experimental data compared to the other model combinations. Results of the sensitivity analysis on the principal operational variables (temperature and pressure), showed superior effect of pressure on the gas solubility. In addition, the results of the molecular dynamic (MD) simulation disclosed an agreement between the trends of the solubility of acid gases in ILs with those of the released interaction energies of acid gases absorbed by the ILs. MD results also confirmed that the solubility of acid gases in ILs increases with an increase in the binding energy of the molecules with the ILs.

Interactions between carbon nanotubes and external structures of SARS-CoV-2 using molecular docking and molecular dynamics

Molecular modeling techniques are used to describe the process of interaction between nanotubes and the main structures of the Covid-19 virus: the envelope protein, the main protease, and the Spike glycoprotein. Molecular docking studies show that the ligands have interaction characteristics capable of adsorbing the structures. Molecular dynamics simulations provide information on the mean squared deviation of atomic positions ​​between 0.5 and 3.0 Å. The Gibbs free energy model and solvent accessible surface area approaches are used. Through the results obtained through molecular dynamics simulations, it is noted that the zig-zag nanotube prefers to interact with E-pro, M-pro, and S-gly, respectively. Molecular couplings and free energy showed that the S-gly active site residues strongly interact with zigzag, chiral, and armchair nanotubes, in this order. The interactions demonstrated in this manuscript may predict some promising candidates for virus antagonists, which may be confirmed through experimental approaches.

Senegalia Catechu activated carbon incorporated Ba-alginate composite beads for the removal of Safranine B: modeling studies

The present investigation depicts the removal of Safranine-Bdye from aqueous solution using senegalia Catechu activated carbon incorporated Ba-alginate composite beads. The alginate beads were synthesized by metal encapsulation technique using BaSO4 as an encapsulating agent. The Safranine-B dye removal efficiency was determinedby the modeling equations like Langmuir and Freundlich. The nature of physical, chemical force of attractionbetween the adsorbate vs. adsorbent and feasibility was determined using pseudo order equations of first andsecond. The progressiveness of the interaction process was predicted by intraparticle diffusion, enthalpy, entropy and Gibbs free energy model equations. Experimentally obtainedoutcomes were implied that the adsorption of Safranine-Bwas feasible for all the parameters used in this study. Furthermore, the predicted diffusion valueswere revealedthat the contact between Safranine-B versus composite beads was well diffused. The surface morphology of virgin and Safranine-B loaded images confirms that the Safranine-B was strappinglybind on outerlayer of the composite. The results of the FTIR spectrum indicatethe Safranine-Bwas intensively attached on thecomposite surface. The TGA result revealsthat the Ba composite bead has predominant temperature bearing nature.

Generalized method of sensitivity analysis for uncertainty quantification in Calphad calculations

Calculation of Phase Diagrams (Calphad) is a method of using thermodynamic models obtained from experimental data to perform thermodynamic calculations. The next step to advancing this methodology is to account for the inconsistency or lack of data when assessing thermodynamic systems. A generalized method of propagating uncertainty through Calphad calculations by local expansion is proposed such that any type of Gibbs free energy model or number of components can be used. This method is faster than Monte Carlo approaches as only a single equilibrium calculation is needed for uncertainty propagation and also improves upon previous approaches to uncertainty propagation by its generalization to any thermodynamic system. As a case study, the Mg–Si system was assessed using a Bayesian approach and various thermodynamic calculations were performed comparing uncertainty quantification by Monte Carlo and the method in this work. Sensitivities (derivatives with respect to model parameters) were calculated on the Fe–Cr–Ni system and compared with sensitivities determined by finite different method.

Experimental and theoretical assessment of surface tension using different biodiesels at elevated temperature

The rheological property of biodiesel is determined by the methods of production, which constitute an important role in atomization, combustion, performance, and emission. Surface tension has a major contribution to droplet size in atomization characteristics. Therefore, it is necessary to examine the surface tension to enhance atomization. The surface tension of six biodiesels, Karanja, jatropha, soybean, palm, sunflower, and rapeseed oil, was measured experimentally and compared with three mathematical models, including the MacLeod–Sugden model, the Gibbs free energy model, and the Dalton type mass average model using MATLAB software. One more parameter was added to the Gibbs free model, which showed results that were more similar to experimental results. The proposed models use the temperature range of 300 to 360 K on changes in biodiesel properties. The study showed that the Gibbs free energy model exhibited a 1.6% to 6.8% error, the MacLeod–Sugden model 3.2% to 12.1%, and the Dalton type mass average model 9.52% to 14.16% with experimentation.

Vapor-liquid equilibrium predictions of refrigerant systems using COSMO based Gex-EoS methods

Combining COSMO-based excess Gibbs free energy models with the Peng-Robinson (PR) equation-of-state (EoS) via mixing rules has recently been shown as a promising method for satisfied VLE predictions on refrigerant systems by Mambo-Lomba and Paricaud. An extension is provided in this work for more systematic and dedicated evaluations focusing on a significantly larger refrigerant database and comparisons between different VLE modeling approaches. In particular, the COSMO-SAC-dsp model is combined with via the original Huron-Vidal (HVO), the modified Huron-Vidal (MHV1) and the Wong-Sandler (WS) mixing rules. Comprehensive model evaluation is performed on the basis of 447 vapor-liquid-equilibrium (VLE) experimental datasets for 233 refrigerant pairs. The results show that the combination of the COSMO-SAC-dsp with the PR yields satisfied and comparable prediction accuracy on the VLE in most cases comparing to the well-established group-contribution based Gex-EoS methods VTPR and PSRK. The performance of the three mixing rules on the studied database follows a decreasing order of MHV1 > HVO > WS but without qualitative difference. Large VLE prediction errors can appear between halogenated hydrocarbons and hydrocarbons. Moreover, errors become more significant and the VLE calculation cannot converge at all for mixtures involving R717 and R744 respectively. Improved predictive accuracy can be achieved by re-optimizing the atomic dispersion parameters of F and =O to 35.5 and 74.0 respectively.

Temperature Dependence of Solubility Predicted from Thermodynamic Data Measured at a Single Temperature: Application to α, β, and γ-Glycine.

Understanding of solid–liquid equilibria for polymorphic systems is crucial for rational design and efficient operation of crystallization processes. In this work, we present a framework to determine the temperature dependent solubility based on experimentally accessible thermodynamic data measured at a single temperature. Using this approach, we investigate aqueous solubility of α, β, and γ-glycine, which, despite numerous studies, have considerable quantitative uncertainty, in particular for the most stable (γ) and the least stable (β) solid forms. We benchmark our framework on α-glycine giving predictions in excellent agreement with direct solubility measurements between 273–340 K, using only thermodynamic data measured at the reference temperature (298.15 K). We analyze the sensitivity of solubility predictions with respect to underlying measurement uncertainty, as well as the excess Gibbs free energy models used to derive required thermodynamic quantities before providing solubility predictions for β and γ-glycine between 273–310 and 273–330 K, respectively. Crucially, this approach to predict solubility as a function of temperature does not rely on measurement of solute melting properties which will be particularly useful for compounds that undergo thermal decomposition or polymorph transition prior to melting.

Thermodynamics of solvent-driven water extraction from hypersaline brines using dimethyl ether

Solvent-driven water extraction (SDWE) has promising applications in hypersaline brine desalination, including zero-liquid discharge processing for industrial wastewaters, and resource recovery, such as the extraction of lithium and rare earth elements from solution mining leachates. In this study, we develop a computational thermodynamic framework to analyze the liquid–liquid extraction of water from hypersaline brines using dimethyl ether (DME), an aprotic solvent that is partially miscible with water. The high volatility of DME enables its rapid separation from water–DME mixtures after water absorption, while its low polarity minimizes the organic-phase solubility of electrolytes, such as sodium chloride (NaCl). We first build a thermodynamic model based on the LIQUAC excess Gibbs free energy model for water–DME–NaCl mixtures. Maximum likelihood estimators for water–DME–NaCl interaction parameters are calculated through the nonlinear regression of fluid phase equilibrium and osmotic coefficient data using metaheuristic global optimization techniques. A multistage counter-current liquid–liquid separator (LLS) model is then developed to explore the water recovery and brine concentration ratios achievable as a function of feed molality and DME to feed water flow rate ratio. For a saline feed with a molality of 2.0molkg−1 (over three times the salinity of seawater) our analysis demonstrates that a one-stage LLS can achieve a water recovery ratio of 0.51 with an initial DME to saline feed molar flow rate ratio of 4.0, rising to 0.63 with a second equilibrium stage. We conclude by quantifying the amount of DME required to reach zero-liquid discharge brine salinities and analyzing the impact of staging and temperature on separation performance. Our thermodynamic model enables the rapid evaluation of SDWE systems for emerging hypersaline brine desalination and valorization applications.

The Na–H system: from first-principles calculations to thermodynamic modeling

Abstract The Na–H system thermodynamic properties were assessed using Gibbs free energy model parameters obtained from best fit optimizations to combined experimental and first-principles predicted data. The first-principles finite temperature thermodynamic property predictions, based upon density functional theory ground state minimizations and direct method lattice dynamics, were used to supplement the Na–H dataset wherever experimental information was unavailable or unattainable. The predictions proved to be important for extending the evaluation of the heat capacity of the stable NaH phase to cover the complete 0 – 2000 K temperature range. The predicted thermodynamic properties of the hypothetical NaH3 end-member representing complete interstitial H substitution in solid body-centered cubic Na, provided a physical basis for modeling H dissolution in the Na lattice. The modeling also showed satisfactory agreement with experimental measurements of NaH enthalpies of formation, NaH decomposition pressures, and H solubility in liquid Na.

Energy and exergy analysis of parallel flow double effect H2O-[mmim][DMP] absorption refrigeration system for solar powered district cooling

Solar thermal energy-driven double effect absorption refrigeration system (DE-ARS) for district cooling in smart cities is an efficient, and sustainable alternative for centralized air conditioning and concurrently harnesses low-grade solar energy. This work investigates ionic liquid based H2O-[mmim][DMP] mixture as an alternative working fluid to overcome the drawback of H2O–LiBr driven DE-ARS. The thermodynamic properties of H2O-[mmim][DMP] mixture is evaluated using the excess Gibbs free energy model. Performance modeling and simulation of DE-ARS is based on both energy and exergy analysis by applying the first and second laws of thermodynamic. The performance, and solution circulation ratio of parallel flow DE-ARS is assessed and optimized under various temperatures and solution distribution ratios. In comparison to the conventional H2O–LiBr, the proposed H2O-[mmim][DMP] working fluid achieves 5.22% and 4.95% improvement in COP and ECOP, respectively at Th/Te/Ta/Tc of 140/5/30/30°C . An optimization of generator temperature to achieve maximum COP and ECOP is performed for a wide range of evaporation temperature from 5 to 20°C and Ta/Tc from 30 to 40°C. An optimization of H2O-[mmim][DMP] mixture driven DE-ARS reveals the uppermost COPmax and ECOPmax of 1.81 and 0.69 for Te of 20°C and TaTc=30°C.

Estimating a Stoichiometric Solid’s Gibbs Free Energy Model by Means of a Constrained Evolutionary Strategy

Modeling of thermodynamic properties, like heat capacities for stoichiometric solids, includes the treatment of different sources of data which may be inconsistent and diverse. In this work, an approach based on the covariance matrix adaptation evolution strategy (CMA-ES) is proposed and described as an alternative method for data treatment and fitting with the support of data source dependent weight factors and physical constraints. This is applied to a Gibb’s Free Energy stoichiometric model for different magnesium sulfate hydrates by means of the NASA9 polynomial. Its behavior is proved by: (i) The comparison of the model to other standard methods for different heat capacity data, yielding a more plausible curve at high temperature ranges; (ii) the comparison of the fitted heat capacity values of MgSO4·7H2O against DSC measurements, resulting in a mean relative error of a 0.7% and a normalized root mean square deviation of 1.1%; and (iii) comparing the Van’t Hoff and proposed Stoichiometric model vapor-solid equilibrium curves to different literature data for MgSO4·7H2O, MgSO4·6H2O, and MgSO4·1H2O, resulting in similar equilibrium values, especially for MgSO4·7H2O and MgSO4·6H2O. The results show good agreement with the employed data and confirm this method as a viable alternative for fitting complex physically constrained data sets, while being a potential approach for automatic data fitting of substance data.

Research on transient multi-field coupling model of GMM under variable pressure in embedded GMA

To improve the output performance of embedded giant magnetostrictive actuators (GMAs) for non-circular hole precision machining and to describe the transient nonlinear hysteresis behavior of giant magnetostrictive material (GMM), the magnetostrictive process of GMM is analyzed in detail in this paper. Based on the J–A model and the Gibbs free energy model, a transient multi-field coupling model of GMM is developed by considering the eddy current effect, compression stress variation, and ΔE effect. The simulation results show that the hysteresis loop area increases with increasing driving frequency. The strain of GMM increases first and then decreases with increasing preloading stress. If the stiffness of the deformable bar is too large, the stress of GMM will increase rapidly, thus hindering the elongation of GMM. The simulation process combines the magneto-mechanical coupling model and the dynamic model of embedded GMAs. The simulation results at different excitation frequencies are basically consistent with the experimental data, indicating that the proposed model can predict the output displacement well and provide a theoretical basis for the optimized design of magneto-mechanical coupling for high-performance embedded GMAs.

Assessment of the SM12, SM8, and SMD Solvation Models for Predicting Limiting Activity Coefficients at 298.15 K

The SMx (x = 12, 8, or D) universal solvent models are implicit solvent models which using electronic structure calculations can compute solvation free energies at 298.15 K. While solvation free energy is an important thermophysical property, within the thermodynamic modeling of phase equilibrium, limiting (or infinite dilution) activity coefficients are preferred since they may be used to parameterize excess Gibbs free energy models to model phase equilibrium. Conveniently, the two quantities are related. Therefore the present study was performed to assess the ability to use the SMx universal solvent models to predict limiting activity coefficients. Two methods of calculating the limiting activity coefficient where compared: (1) the solvation free energy and self-solvation free energy were both predicted and (2) the self-solvation free energy was computed using readily available vapor pressure data. Overall the first method is preferred as it results in a cancellation of errors, specifically for the case in which water is a solute. The SM12 model was compared to both the Universal Quasichemical Functional-group Activity Coefficients (UNIFAC) and modified separation of cohesive energy density (MOSCED) models. MOSCED was the highest performer, yet had the smallest available compound inventory. UNIFAC and SM12 exhibited comparable performance. Therefore further exploration and research should be conducted into the viability of using the SMx models for phase equilibrium calculations.

Axial-torsion behavior of superelastic tubes: Part I, proportional isothermal experiments

The tensile response of superelastic shape memory alloys (SMAs) has been widely studied, but detailed experimental studies under multi-axial loading are relatively rare. In Part I, we present the isothermal responses of commercially-available superelastic NiTi tubes for a series of proportional stretch-twist controlled histories, spanning pure tension to simple torsion to pure compression. These axial-shear responses are used to quantify the onset and saturation during forward (loading) and reverse (unloading) stress-induced transformations for the first time. Each of the four transformation surfaces is well-captured by a smooth (three-parameter) ellipse in both strain and stress space. A simple Gibbs free energy model is presented to show how the driving force for phase transformation is approximately constant across all proportional strain paths and how the stress and strain transformation surfaces are conjugate to one another. In addition, transformation kinetics and surface strain morphologies are characterized by stereo digital image correlation (DIC). Under extension at low amounts of twist, stress-induced transformation involves strain localization in helical bands that evolve into axial propagation of ring-like transformation fronts with fine criss-crossing fingers (similar to those seen by Q. P. Sun and co-workers in pure extension). However, at large amounts of twist, including simple torsion and pure torsion, we report a new transformation morphology, involving strain localization along nearly longitudinal bands in the tube. The sequel (Part II) will address the response to non-proportional stretch-twist paths. Together, these detailed multi-axial results advance the scientific understanding of superelasticity and inform efforts to develop high-fidelity SMA constitutive models and simulation tools.

An improved equation of state of binary CO2–N2 fluid mixture and its application in the studies of fluid inclusions

An equation of state (EOS) in the form of Helmholtz free energy for fluid mixtures was improved by using four mixing parameters. It can calculate the pressure-volume-temperature-composition (PVTx) and vapor-liquid equilibrium (VLE) properties of the CO2–N2 fluid mixture. This EOS is based on highly accurate EOSs of pure CO2 and N2 fluids and contains a simple generalized departure function of Lemmon and Jacobsen (1999). This EOS can reproduce experimental PVTx and VLE data available up to 673 K and 1000 bar, with an accuracy within or close to experimental uncertainties. The EOS of CO2–N2 fluid mixture and an updated Gibbs free energy model of solid CO2, can be combined to determine the compositions and molar volumes of CO2–N2 fluid inclusions with the melting temperature of solid CO2 and the vapor-liquid homogenization temperature which can be directly obtained from experimental microthermometric analysis. Isochores of CO2–N2 inclusions can be easily calculated from this EOS.

Performance modelling and validation on co-gasification of coal and sawdust pellet in research-scale downdraft reactor

Co-gasification of the fossil fuel with the biomass is considered a very promising clean energy opt-in reduce the greenhouse gas emission. The main objective of this research is to develop a simple and reliable model provided as a preliminary tool to evaluate the performance of the co-gasification of sub-bituminous coal with densified biomass (sawdust pellet, SP). The simulation model using Aspen Plus was validated with the experimental data for minimization of the Gibbs free energy model. Three performance parameter; the calorific value of the syngas (CVsyngas), syngas yield (Ysyngas) and gasification efficiency (ŋGE) were studied along with three different control parameter. The increase of the sawdust pellet blending ratio denoted in a decrease of the CVsyngas, Ysyngas and ηGE ranged from 3.00-6.00 MJ/Nm3, 1.20-2.20 Nm3/kg and 25%-37%, respectively. On the contrary, effect of the gasification temperature at the various blending ratio exhibits an increase for all the performance parameters. In addition, ERair resulted in the decline of the CVsyngas from 8.50 to 1.58 MJ/Nm3 and ηGE from 52 to 15% while vice versa for Ysyngas. Furthermore, it is found that the result obtained from the developed model agrees well with the experimental data that have been conducted in replicate.