Gibbs Free Energy Of Mixing Research Articles

Phase Behavior of System Carbon Dioxide + Hydrogen Sulfide

The global phase equilibrium behavior of the CO2+H2S system is discussed in this work for temperatures ranging from 160 K up to the critical region. Solid phases of CO2 and H2S and corresponding equilibria have been modeled by considering either a 4th-order equation of state (also used for the fluid phases) or a solid fugacity model for the pure components combined with an activity coefficient model (both coupled with a reference equation of state for the fluid phases).Phase equilibrium calculations have been performed by the minimization of the Gibbs Free Energy of mixing and compared to existing literature data.The types of pressure-mole fraction phase diagrams that can be encountered in the low-temperature thermodynamic region have been described. The temperature and pressure ranges where the phase behavior of the system changes have been identified and a representative phase diagram is presented for each range.

Model based study of temperature dependent thermodynamic and surface properties of Al-Ti-Ni-Cr system in liquid state

Thermodynamic and surface properties of Al-Ti-Ni liquid alloy with adding Cr, Al-Ti-Ni-Cr, were studied at 2000 K, 2100 K, 2200 K, 2300 K, and 2400 K using different theoretical models. The self-consistent energy interaction parameters of constituent binary subsystems were taken from the literature for the purpose. The thermodynamic properties like excess Gibbs free energy of mixing and the activities of the components in the alloy were investigated using the General Solution Model (GSM). Surface tension of the liquid alloy and surface concentrations of components in it were calculated using Butler's model with the aid of determined thermodynamic functions. The mixing tendency of the Al-Ti-Ni-Cr liquid alloy was found to decrease with the addition of Cr atoms for all compositions at its melting temperature, 2000 K. The activity of Cr decreased while those of the remaining components increased with the temperature rise. The surface tension of both Al-Ti-Ni and Al-Ti-Ni-Cr liquid alloys decreased linearly at elevated temperatures.

Interfacial bonding mechanism and mechanical properties of Cu-Ni-Si/1010 steel bimetallic laminated composites prepared by continuous solid/liquid bonding

The Cu-Ni-Si/1010 steel bimetallic laminated composites (BLCs) were prepared by continuous solid/liquid bonding, and the microstructure, mechanical properties and interfacial bonding mechanism were investigated. The results show that the microstucture of Cu-Ni-Si mainly consists of α-Cu, and a small quantity of Ni-Si rich phases which distribute at the grain boundaries. Meanwhile, the microstucture of 1010 steel is composed of ferrite (F), pearlite (P), and a small amount of bainite (B). A flat and well-bonded interface is formed between two layers due to the diffusion of elements. The diffusion layer is identified as the Fe based solid solution containing Ni and Si by TEM. The interfacial bonding mechanism is revealed using Fick's second law and thermodynamic methods. The results show that the diffusion coefficients of Ni and Si in Fe are higher than those of in Cu, and the molar Gibbs free energies of mixing (GmixM) of Fe-Ni and Fe-Si are lower than those of Cu-Ni and Cu-Si, indicating that Ni and Si tend to diffuse to Fe. The ultimate tensile strength, yield strength and elongation of Cu-Ni-Si/1010 steel BLC are 378 MPa, 233 MPa and 25.4 %, respectively, which lie between those of individual Cu-Ni-Si and 1010 steel. The tensile shear results show that the interface is always well bonded, and no cracks are found at the interface during the deformation. The fracture of the Cu-Ni-Si/1010 steel BLC occurs at the Cu-Ni-Si side, suggesting that the bonding strength is larger than that of the Cu-Ni-Si.

Thermodynamic, Structural and Surface Properties of Liquid Al-Sr Alloy at Different Temperatures

Thermodynamic functions like excess Gibbs free energy of mixing (∆GxsM) and activity (a) of liquid Al-Sr alloy were studied in the temperature range 1323-1623 K in the frame work of Redlich-Kister (R-K) polynomial. The compositional and temperature dependence of structural functions like concentration fluctuation in long wavelength limit (Scc(0)), Warren-Cowley short range order parameter (α) and ratio of mutual to intrinsic diffusion coefficients (Dm/Did) were computed and analysed using the same approach. The surface tension (σ) and surface segregation (xsi) tendencies of the atoms in the liquid mixture were computed and studied using Butler’s model. Present investigations revealed that association tendency among the atoms of metallic mixture gradually decreased with increase in temperature.

Thermodynamic, structural, surface and transport properties of Au-Cu melt

Thermodynamic, structural, surface and transport properties of Au-Cu liquid alloy were calculated on the basis of different theoretical modeling equations. The thermodynamic properties, such as excess Gibbs free energy of mixing, enthapy of mixing and activity were estimated and compared with the available experimental and literature data on the basis of simple theory of mixing (STM). The best fit values of model parameters were estimated using the experimental values of excess Gibbs free energy of mixing and enthalpy of mixing of the system at 1550 K. Using the same model parameters and frame, the concentration fluctuation in long wave-length limit and Warren-Cowley short range order parameter were calculated and analysed to understand the local arrangement of atoms in the liquid mixture. The surface tension and extent of surface segregation of atoms in the initial melt were computed using Butler’s model. In transport properties, the ratio of mutual to intrinsic diffusion coefficients was calculated using STM and viscosity was calculated using Kaptay equation. The system showed complete ordering tendency at its melting temperature.

Size Matters: Unraveling the Nanoscale World of Actinide-Based High Entropy Alloys through Ab Initio Methods

Ab initio computational studies of size-dependent Actinide-based High Entropy Alloys (HEAs) nanomaterials (AHEANMs) have emerged as a powerful tool to unravel the fundamental properties and behaviors of these complex systems. AHEAs have demonstrated remarkable mechanical, thermal, and radiation-resistant characteristics making them promising candidates for advanced technological applications. In this context, the size-dependent properties like cohesive energy, melting temperature, Debye temperature, Gibbs free energy of mixing, Heat of mixing, entropy of mixing, etc., have been studied.

Molecular dynamics study of the thermodynamic properties of triglyceride/methanol mixtures in the presence of cosolvent

Biodiesel is a renewable source of energy that has the potential to replace fossil fuel-based resources. It is produced via the transesterification reaction in which a triglyceride reacts with methanol in the presence of a catalyst. Cosolvents are usually added to the reactants in transesterification to improve the mutual solubility of methanol and triglycerides and to create a single phase. The commonly used cosolvents in transesterification include tetrahydrofuran (THF) and diethyl ether (DEE). Understanding the thermodynamic properties of this system is important in the selection of cosolvent. In this study, molecular dynamics simulations were used to study the mixing behavior between the components of ternary mixtures of triolein/methanol/THF and triolein/methanol/DEE via the application of Flory-Huggins theory of solutions. A simple approach to calculation of the Flory-Huggins interaction parameters is used in which the mixing energy is derived from averaged non-bonded pair interaction energies. Apart from pure triolein, these ternary systems resemble the experimentally studied ternary systems employing various plant-based oils. The binary interaction parameters, Gibbs Free energy and chemical potentials of the components were calculated to study the mixing behavior. Our results show that along the experimental phase boundary the binary interaction parameters remain relatively unchanged with a deviation observed at the highest volume fractions of triolein where the highest binary interactions were observed indicating the possibility of phase separation. The Gibbs energy of mixing for the systems changed from positive to negative as one moves from two phase to single phase part of the ternary system as expected and in agreement with experimental data. The chemical potentials of the ternary mixture components were calculated from the partial derivatives of the Gibbs free energy of mixing. The activities calculated from Flory-Huggins chemical potentials were compared to those calculated using the UNIFAC model. There is good agreement between the two, with both able to predict a single and biphasic mixture. However, disagreements are noted at low and high concentrations of triolein.

Design of superhard high-entropy diborides [formula omitted] high-throughput DFT and thermodynamics calculations

We performed extensive high-throughput density functional theory (DFT) and thermodynamics calculations that led to the prediction of single-phase stability, mechanical properties, and melting points of a series of superhard high-entropy diborides (HEBs). We constructed a three-dimensional phase diagram using a unique combination of the mixing entropy, mixing enthalpy, melting point, and lattice size difference for the set of 56 equiatomic quinary diborides consisting of transition metals (TM = Ti, Zr, Hf, V, Nb, Ta, Mo, and W). The phase diagram allowed us to predict that all 56 quinary diborides are high-entropy materials, with fourteen already experimentally realized. Our calculations show that, for each of the quinary diborides, the driving force of the formation (the entropy term in the Gibbs free energy of mixing) suppresses the resistance of the formation (the enthalpy term) when the temperature is high (but still well below the melting point), suggesting that it is feasible to synthesize 42 new HEBs. Furthermore, all 56 quinary diborides exhibit high hardness, high fracture toughness, and ultrahigh melting points. In particular, we predict a new superhard high-entropy material, TiZrHfVTaB10, with a hardness of approximately 41 GPa.

Determination of Pair Interaction Parameters of Multicomponent Polymer Systems.

From the examples of three and four-component polymer-polymer systems characterized by amorphous separation, an original technique for determining the pair parameters of interaction between components based on the sorption isotherms of common solvent vapor, particularly water vapor, has been developed. The possibility of calculating thermodynamic characteristics of multicomponent polymer compositions with specific interactions of functional groups from experimentally obtained sorption isotherms is shown. An algorithm for calculating pair interaction parameters, estimating concentration dependences of chemical potential and Gibbs free energy of mixing, and predicting the phase state of polymer mixtures was presented for the first time for such systems. The technique was tested on the example of systems poly(N-vinylpyrrolidone) (PNVP)-polyethylene glycol (PEG), PNVP-PEG-Poly(acrylic acid) (PAA), poly(N-vinylcaprolactam) (PNVCL)-PEG, and polyvinyl alcohol (PVA)-PEG.

Theoretical Investigation of the Thermodynamic Properties of Lead-free Ternary Alloys Sn-Sb-Bi and their Subsystems

The concentration-dependent properties, like the constituents’ activities for the binary liquid alloys like Sb-Sn at 905 K, Bi-Sn at 600 K, and Bi-Sb at 1200 K, and the integral Gibbs free energy of mixing, ΔGXS, of the correspondent alloys were computed using the molecular interaction volume model (MIVM). Further, the model has been used to compute the activities of the component Sn in the ternary Sn-Sb-Bi system at 900K at the three cross-sections, i.e., Sb:Bi = 1:3, 1:1, and 3:1. The theoretical data have been analyzed with the corresponding experimental data accessible in the literature. An acceptable concurrence has been obtained, with some inconsistencies. The activities of the ternary alloys along the three cross-sections, i.e., Sb:Bi = 1:3, 1:1, and 3:1, show that the deviations change from positive to negative with increasing Sb content. The results confirm that MIVM is a good model for estimating the thermodynamic properties of binary and ternary systems.

Cohesive, elastic and anisotropic properties of s-, p- and d-block fission metals substituted Fe–Zr intermetallics

Density functional theory (DFT) based calculations are performed to study cohesive, elastic and anisotropic properties of c-Fe2Zr, t-FeZr2 and o-FeZr3 phases in the presence of s-, p- and d-block fission metals (FMs), viz. Rb, Sr, Cs, Ba, In, Sn, Sb, Te, Y, Nb, Mo, Tc, Ru, Rh, Pd, Ag and Cd. The FM substituted intermetallics are found to be thermodynamically stable owing to their negative formation energy. The Gibbs free energy of mixing is calculated to find the solubility of these FMs in these intermetallics. The calculated single crystal elastic constants suggest that all the FM substituted phases are mechanically stable. We also report the change in polycrystalline elastic moduli, viz. bulk, shear and Young moduli of the pristine intermetallics on incorporation of these FMs. The substitution of FMs in the FeZr2 phase increases its intrinsic ductility; while that in FeZr3 phase decreases it. The degree of anisotropy exhibited by the intermetallics follow the order FeZr2> FeZr3> Fe2Zr. The substitution of FMs does not affect the anisotropic behavior of Fe2Zr and FeZr2 phases, but slightly changes that of FeZr3 phase. Finally, the potential of these intermetallics to incorporate the FMs is discussed.

Thermodynamic, structural and surface properties of rare earth metallic alloys: Au-La liquid system

A complete information related to the mixing behaviours of Au alloyed with rare earth metals or lanthanides is very scarce. Therefore, an attempt has been made in this work to compute and study the temperature and concentration dependent thermodynamic, structural and surface properties of Au-La liquid alloy using different theoretical approaches. The thermodynamic properties, such as excess Gibbs free energy of mixing, enthalpy of mixing, excess entropy of mixing and activity of the system were computed using available coefficients of interaction energy parameters in the framework of Redlich-Kister polynomial. Taking these as reference values, model parameters for quasi-lattice model were optimised at 1473 K. The model parameters were then determined at higher temperatures assuming them to be linear temperature-dependent. The thermodynamic and structural properties were then computed in the temperature range 1473 K-1773 K. The surface properties of the system were computed using Bulter’s model using determined values of partial excess Gibbs free energy of its components. Present investigations revealed that the compound forming tendency of the system gradually decreased with increase in temperature of the system.

The miscibility gap between the rock salt and wurtzite phases in the MgO–ZnO binary system to 3.5 GPa

Abstract. At ambient pressure, MgO crystallizes in the rock salt (B1) structure, whereas ZnO crystallizes in the wurtzite structure (B4). The asymmetric miscibility gap between these two structures in the MgO–ZnO binary system narrows with increasing pressure, terminating at the wurtzite-to-rock-salt phase transition in pure ZnO, which occurs at approximately 5 GPa at 1000 ∘C. Despite their essential simplicity, the pressure–temperature–composition (P–T–X) relations in the MgO–ZnO binary system have been sparsely studied experimentally, with disparate results that are inconsistent with available thermodynamic data. Here we report the experimental determination of the P–T–X relations of the miscibility gap from 940 to 1500 ∘C and 0 to 3.5 GPa, which we combine with calorimetric and equation-of-state data from the literature and on the transition in endmember ZnO, to build a thermodynamic model that resolves many of the inconsistencies. The model treats the rock salt phase as an ideal solution (no excess Gibbs free energy of mixing), while in the wurtzite phase the MgO component follows Henry's law and the ZnO component Raoult's law in the range of compositions accessed experimentally. However, there is an inconsistency between the partial molar volume of wurtzite-structured MgO deduced from this model and that inferred from lattice parameter measurements by X-ray diffraction in the quenched samples. This discrepancy may be caused by unquenchable disordering of some significant fraction of the substituting Mg2+ into normally vacant octahedral interstices of the wurtzite structure.

A multifaceted approach for grading of polymers for the development of stable amorphous solid dispersion of Riluzole

The current work involves grading three widely used polymers for preparing a kinetically and thermodynamically stable amorphous solid dispersion (ASD) of a neuroprotective drug Riluzole (RLZ) by evaluating the drug-polymer interactions. Polymers were screened based on their chemical interaction with RLZ and their ability to inhibit the crystallization of the drug. Detailed computational studies were performed to quantify the non-covalent interactions between RLZ and the modelled structures of polymers; polyacrylic acid (PAA), polyvinylpyrrolidone vinyl acetate (PVP VA), and hydroxypropyl methyl cellulose acetate succinate (HPMC AS) for calculating the interaction energies of drug-polymer complexes. Experimental characterization of drug-polymer complexes through analytical techniques further validated the formation of the drug-polymer complexes. The results indicated that RLZ interacts with the polymers in the order PAA > PVP VA > HPMC AS, giving an insight into the stability of drug-polymer complexes. In vitro dissolution study also showed higher dissolution profile of RLZ with PAA. Further, the drug-polymer miscibility was determined by employing Flory-Huggins theory and stability in accordance with Gibbs free energy of mixing and phase diagram. This work presented a multi-technique approach for the grading of polymers in search of a stable ASD of the poorly water-soluble drug RLZ.

Thermodynamics of compound forming CdHg liquid alloys at 600 K

The quasi-lattice model has been applied to analyze the alloying behavior of the compound forming CdHg liquid alloys at 600 K. In solid state, CdHg liquid alloys exhibit the existence of Cd2Hg and CdHg2 complexes. In present study, it is considered that Cd2Hg complex also exists in liquid state near the melting temperature. The investigative equations for the thermodynamic and structural functions have been derived for a binary molten alloy having the existence of A2B complex where A and B are constituent elements. The theoretical data for the excess Gibbs free energy of mixing, Gibbs free energy of mixing, thermodynamic activity, entropy of mixing, enthalpy (i.e. heat) of mixing, concentration fluctuations and short-range order (SRO) parameter are compared with the corresponding experimental values. A well agreement have been observed between the theory and experiment. The present study reveals that CdHg system at 600 K in molten state is a weakly interacting ordered system. Further, the order energy parameters are temperature dependent.

Multicomponent solutions: Combining rules for multisolute osmotic virial coefficients.

This paper presents an exploration of a specific type of a generalized multicomponent solution model, which appears to be first given by Saulov in the current explicit form. The assumptions of the underlying theory and a brief derivation of the main equation have been provided preliminarily for completeness and notational consistency. The resulting formulae for the Gibbs free energy of mixing and the chemical potentials are multivariate polynomials with physically meaningful coefficients and the mole fractions of the components as variables. With one additional assumption about the relative magnitudes of the solvent-solute and solute-solute interaction exchange energies, combining rules were obtained that express the mixed coefficients of the polynomial in terms of its pure coefficients. This was done by exploiting the mathematical structure of the asymmetric form of the solvent chemical potential equation. The combining rules allow one to calculate the thermodynamic properties of the solvent with multiple solutes from binary mixture data only (i.e., each solute with the solvent), and hence, are of practical importance. Furthermore, a connection was established between the osmotic virial coefficients derived in this work and the original osmotic virial coefficients of Hill found by employing a different procedure, illustrating the equivalency of what appears to be two different theories. A validation of the combining rules derived here has been provided in a separate paper where they were successfully used to predict the freezing points of ternary salt solutions of water.

Computational assessment of Sn activities and integral excess free energy change for mixing in the Sn-Au-Cu ternary liquid alloys using the molecular interaction volume model

The activities of Sn in the liquid solder ternary alloy Sn-Au-Cu at 900 K have been computed using the molecular interaction volume model (MIVM). The calculated values have been compared with the experimental data for three cross-sections, i.e., for three different ratios of aurum to copper (XAu:XCu) = 3:1, 1:1, and 1:3. In addition, the excess Gibbs free energy of mixing, ΔGEx, for these ternary liquid alloys has been determined using the same model parameters to assess their validity. The resulting values have then been compared with the corresponding experimental data found in the literature. The agreement between the theoretical and experimental results has been found to be satisfactory.

Ternary Mixed Micelle Hexadecyltrimethylammonium Bromide-Dodecyltrimethylammonium Bromide-Sodium Deoxycholate: Gibbs Free Energy of Mixing and Excess Gibbs Energy of Mixing.

Pharmaceutical, food, and cosmetic formulations often contain binary or ternary surfactant mixtures with synergistic interactions amongst micellar building blocks. Here, a ternary mixture of the surfactants hexadecyltrimethylammonium bromide, dodecyltrimethylammonium bromide, and sodium deoxycholate is examined to see if the molar fractions of the surfactants in the ternary mixed micellar pseudophase are determined by the interaction coefficients between various pairs of the surfactants or by their propensity to self-associate. Critical micelle concentrations (CMC) of the analyzed ternary mixtures are determined experimentally (spectrofluorimetrically using pyrene as the probe molecule). Thermodynamic parameters of ternary mixtures are calculated from CMC values using the Regular Solution protocol. The tendency for monocomponent surfactants to self-associate (lower value of CMC) determines the molar fractions of surfactant in the mixed micelle if there is no issue with the packing of the micelle building units of the ternary mixed micelle. If a more hydrophobic surfactant is incorporated into the mixed micelle, the system (an aqueous solution of surfactants) is then the most thermodynamically stabilized.

Temperature-Dependence of Mixing Properties of Cu-Ti Liquid Alloy

In this study, the temperature-dependence of thermodynamic and surface properties of Cu-Ti binary liquid alloy were studied. In thermodynamic properties, excess Gibbs free energy of mixing, enthalpy of mixing, excess entropy of mixing, and activity of the system were computed at 1873 K. The surface properties were analyzed by computing the surface tension and surface concentration of the system. Thermodynamic properties were computed in the framework of the Redlich-Kister polynomial, and the surface properties were computed using the Butler model. At its melting point, the system exhibited a tendency for the formation of compounds, and as the Cu concentration was increased, the surface tension of the system gradually decreased. The excess Gibbs free energy of mixing, activity and surface tension of the system were also computed at different temperatures, in the range 1873-2173 K. With the increase in temperature of the system, the compound forming tendency of the system gradually decreased.

Estimation of excess Gibbs free energy of multicomponent biofuel mixtures of Butan-1-ol using machine learning methods based on modified Raoults law models

In biofuels, the excess Gibbs free energy of mixing is a very important thermodynamic property as it is used in evaluating the efficiency and sustainability in terms of energy conversion. Multiple biofuel systems containing butan-1-ol were examined with oxygenate ether additives such as MTBE and DIPE using isothermal vapour-liquid equilibrium data at different temperatures (298.15K, 313.15K, 318.15K). Two activity coefficient models, Wilson and van Laar model were compared by determining the bubble pressure and vapor mole fractions of each system using Modified Raoults Law and Machine Learning techniques. Besides, mole fractions and activity coefficients were used to identify the excess property. Results showed that Wilson model is appropriate for all the biofuel systems when using the Artificial Neural Network (ANN) resulting in an MSE of 3.2010e-09, 4.6792e-10, 1.6186e-10, and 5.3461e-07. In addition, van Laar model is more acceptable when Rational Quadratic GPR or Fine Tree algorithm were used with an average RMSE of 0.005820.01 and 0.020950.03 respectively. Lastly, the generated data for both activity coefficient models were also used to estimate the systems excess Gibbs free energy of mixing across varying mole fraction of its components.