Quasi-chemical Equilibrium Research Articles

Thermodynamics of high-temperature cuprous sulfide

AbstractPublished measurements of the diatomic sulfur fugacity were used to make a thermodynamic analysis of high-temperature cuprous sulfide between 789 K and 1321 K. Gibbs–Duhem integration of the fugacity data was used to determine the enthalpy of formation of stoichiometric Cu2S as – 123.8 kJ mol–1. Statistical thermodynamics was applied to find partition functions, interaction energies, and free energies to characterize the configurational aspects of the phase. Theoretical calculations indicated that Cu vacancies might be localized in one half of the Cu lattice sites under quasi-chemical equilibrium.

SO2 absorption in highly efficient chemical solvent AChBr + Gly compared with physical solvent ChBr + Gly

Deep eutectic solvents (DESs) have been identified as optimal gas absorbents. A tertiary amine-containing task-specific DES AChBr+Gly and a conventional DES ChBr+Gly have been designed, prepared and used to capture SO2. It is found that absorption capacity of 3.74 and 2.97 mol of SO2 per mole of DES can be obtained by AChBr+Gly and ChBr+Gly, respectively, at 293.2 K and 1 bar. When SO2 partial pressure was decreased to 0.01 bar, the capacity decreased to 0.93 and 0.13 mol SO2 of per mole of AChBr+Gly and ChBr+Gly, respectively. Mechanism and thermodynamic studies show that absorption by former absorbent includes physisorption, quasi-chemisorption (a strong physisorption) and chemisorption, while absorption by later absorbent only includes physisorption and quasi-chemisorption. Two equations were first proposed for the description of SO2 absorption. In these equations, the physisorption capacity is correlated with Henry's law, and the quasi-chemisorption and chemisorption are correlated with the quasi-chemical equilibrium constant of halogen···SO2 interaction and the chemical equilibrium constant of tertiary amine···SO2 interaction, respectively. In addition, the corresponding enthalpy change, entropy change, and Gibbs energy change have been calculated and discussed.

Annealing of indium-doped CdMnTe single crystals under Cd vapors

Indium-doped Cd1−xMnxTe (x=0.2, CdMnTe) crystals were annealed under Cd vapor atmosphere to improve the properties of CdMnTe. The quasichemical equilibrium model was adopted to calculate the point defect concentration of CdMnTe, and the annealing condition was obtained to maintain the minimum deviation from stoichiometry of CdMnTe. The Indium-doped CdMnTe wafers before and after Cd vapor annealing were characterized by near-infrared (NIR) transmission spectroscopy, IR transmission microscopy, I–V, and IR transmittance. The results indicated that, the Mn composition of the Indium-doped CdMnTe wafers remained unchanged, the concentrations of Te inclusions reduced from (1–5)×105cm−3 to (1–4)×104cm−3, the resistivity increased from (2.0–4.5)×108Ωcm to (2.7–5.3)×1010Ωcm, and the IR transmittance heightened from 17%–21% to 56%–59%. Therefore, it is concluded that the structural and electrical properties of the Indium-doped CdMnTe crystals were evidently improved by the stoichiometric Cd vapor annealing.

Molecular formations in ultracold mixtures of interacting and noninteracting atomic gases

Atom-molecule equilibrium for molecular formation processes is discussed for boson-fermion, fermion-fermion, and boson-boson mixtures of ultracold atomic gases in the framework of quasichemical equilibrium theory. After presentation of the general formulation, zero-temperature phase diagrams of the atom-molecule equilibrium states are calculated analytically; molecular, mixed, and dissociated phases are shown to appear for the change of the binding energy of the molecules. The temperature dependences of the atom or molecule densities are calculated numerically, and finite-temperature phase structures are obtained of the atom-molecule equilibrium in the mixtures. The transition temperatures of the atom or molecule Bose-Einstein condensations are also evaluated from these results. Quantum-statistical deviations of the law of mass action in atom-molecule equilibrium, which should be satisfied in mixtures of classical Maxwell-Boltzmann gases, are calculated, and the difference in the different types of quantum-statistical effects is clarified. Mean-field calculations with interparticle interactions (atom-atom, atom-molecule, and molecule-molecule) are formulated, where interaction effects are found to give the linear density-dependent term in the effective molecular binding energies. This method is applied to calculations of zero-temperature phase diagrams, where new phases with coexisting local-equilibrium states are shown to appear in the case of strongly repulsive interactions.

Thermodynamics and defect structures of silver sulfide

Published measurements of sulfur vapor pressure and silver electromotive force were used to determine thermodynamic properties of silver sulfide above 379 K. They were Gibbs–Duhem integrated to estimate the formation properties of stoichiometric Ag 2S of fcc, bcc, and monoclinic crystal structures. Statistical thermodynamics was applied to estimate free energies and find possible atom arrangements in off-stoichiometric silver sulfide. Theoretical calculations show that silver vacancies and atoms may be in quasi-chemical equilibrium between tetrahedral and octahedral sites in the fcc structure and between two states of atoms within tetrahedral sites in the bcc structure and within octahedral sites in the monoclinic structure. A strong indication is that vacancy clusters should predominate, each containing four-atom vacancies in the fcc phase and three-atom vacancies in the bcc phase.

A general local composition and coordination number model for square-well fluids with variable well width and diameter ratio

A radial distribution function for attractive hard-core systems is obtained from the equilibrium of a molecular pair between local and bulk environments. With this function, a general model is established for the coordination number (CN) and local composition (LC) of square-well fluids. It meets the low-density, high-density and high-temperature limit conditions, as well as the unlike pair conservation and quasi-chemical equilibrium conditions. It also has some other features that many other models do not have: (1) its CN and LC expressions contain all pair potentials; (2) it yields temperature-dependent CN and LC for closely packed mixtures with different pair potentials; (3) its energy parameter is the difference of the total potentials of one pair in local and bulk environments, not the difference of two pair potentials. This model can accurately predict the CN, LC and compressibility factors of square-well fluids from computer simulation over a wide range of density, well width (λ = 1–2) and diameter ratio. For the case λ = 1.5, this model is better than or comparable with semi-empirical models; in other cases, it is far better than semi-empirical models. It does not need any empirical parameter for LC prediction. For the prediction of CN and compressibility factors, it only needs the smoothed radial distribution function of pure hard-sphere fluids. It also gives excellent results for lattice gases and highly nonideal lattice mixtures.

Composite boson dominance in many-fermion systems

I recently proposed a method of bosonization based on the use of coherent states of fermion composites, whose validity was restricted to smooth structure functions. In the present paper I remove this limitation and derive results which hold for arbitrary interactions and structure functions. The method respects all symmetries and in particular fermion number conservation. It reproduces exactly the results of the pairing model of atomic nuclei and of the BCS model of superconductivity in the number conserving form of the quasi-chemical equilibrium theory.

Thermodynamics of high-temperature cuprous sulfide

Abstract Published measurements of the diatomic sulfur fugacity were used to make a thermodynamic analysis of high-temperature cuprous sulfide between 789K and 1321K. Gibbs–Duhem integration of the fugacity data was used to determine the enthalpy of formation of stoichiometric Cu2S as −123.8kJmol−1. Statistical thermodynamics was applied to find partition functions, interaction energies, and free energies to characterize the configurational aspects of the phase. Theoretical calculations indicated that Cu vacancies might be localized in one half of the Cu lattice sites under quasi-chemical equilibrium.

Diquark Bose-Einstein condensation

Bose-Einstein condensation of composite diquarks in quark matter (the color superconductor phase) is discussed using the quasichemical equilibrium theory at a relatively low-density region near the deconfinement phase transition, where dynamical quark-pair fluctuations are assumed to be described as bosonic degrees of freedom (diquarks). A general formulation is given for the diquark formation and particle-antiparticle pair-creation processes in the relativistic framework, and some interesting properties are shown, which are characteristic for the relativistic many-body system. Behaviors of transition temperature and phase diagram of the quark-diquark matter are generally presented in model parameter space, and their asymptotic behaviors are also discussed. As an application to the color superconductivity, the transition temperatures and the quark and diquark density profiles are calculated in case with constituent/current quarks, where the diquark is in the bound/resonant state. We obtained ${T}_{C}\ensuremath{\sim}60--80\text{ }\text{ }\mathrm{MeV}$ for constituent quarks and ${T}_{C}\ensuremath{\sim}130\text{ }\text{ }\mathrm{MeV}$ for current quarks at a moderate density (${\ensuremath{\rho}}_{b}\ensuremath{\sim}3{\ensuremath{\rho}}_{0}$). The method is also developed to include interdiquark interactions into the quasichemical equilibrium theory within a mean-field approximation, and it is found that a possible repulsive diquark-diquark interaction lowers the transition temperature by $\ensuremath{\sim}50%$.

Group Contribution Theory for the Gibbs Energy of Solutions of Polyethers

The Gibbs energies of different oligoethers (oligomers of tetrahydrofuran and ethylene oxide and a block cooligomer of these ethers) with hydroxyl and acetyl end groups in tri- and tetrachloromethane are obtained by vapour pressure measurements. A group contribution theory, based on a quasichemical equilibrium between contacting segment surfaces, which was used so far only for calculating mixing enthalpies, is extended to Gibbs energies. The Gibbs energies predicted with this theoretical approach show a good agreement with the measured data of the tested polymer solutions. With this theory it is not only possible to describe but even to predict gaps in the mixing behaviour of polymer solutions.

The Eu1+xBa2-xCu3Oy system: oxygen content, phase transitions, point defect equilibria, and charge carriers

Single phase Eu1+xBa2−xCu3Oy materials with x = 0, 0.2, and 0.4 have been investigated with electrical conductivity and oxygen non-stoichiometry measurements at high temperatures (723–1073 K) and under various oxygen partial pressures. EuBa2Cu3Oy is an intrinsic semiconductor for 6<y<6.18, with a band gap close to 1 eV; for higher values of oxygen stoichiometry the crystal–gas equilibrium injects holes of different nature and mobility as extrinsic doping increases. This paper shows that the hole injection sequence and the variation of charge transport properties with different extrinsic and intrinsic doping levels can be effectively described by a quasi-chemical equilibrium approach if the particular features of the HOMO bands are considered. When the whole series of compounds is written as Eu1+xBa2−xCu3O6+x/2+z, the high temperature conductivity of the solid solutions is practically independent of x and shows a parallel dependence on oxygen excess z.

Thermodynamic and Textural Characterization of DPPG Phospholipid Monolayers

The phase properties of DPPG (dipalmitoyl-phosphatidylglycerol, sodium salt) monolayers are investigated at different temperatures 25 °C ≤ T ≤ 34 °C where the surface pressure−area (Π−A) isotherms have large two-phase coexistence regions. The studies are based on the thermodynamic and textural characterization of the monolayers. The main phase transitions obtained from the Π−A isotherms are in complete agreement with the Brewster angle microscopy results. In equilibrium, compact domains are formed which are never really circular. The domains differ from each other in the azimuthal tilt, but they have no inner texture. Over the entire region of the gaseous to the condensed state, the experimental Π−A isotherms are well described by an equation of state recently derived on the basis of the generalized Volmer's equation and the quasi-chemical equilibrium model of 2D aggregation. The possible dissociation effect on the monolayer properties of the ionic DPPG can be largely ignored, as clarified by extending th...

Calculation and Prediction of Thermodynamic Properties of Non-Electrolyte Mixtures with a New quasi-Chemical Approximation

Using the old, modified TASQUAC model [1–3], only small negative excess entropies of mixing can be described with model assumptions. Intra- and intermolecular vibrations and the rotation of molecules are also not considered. In this work, therefore, a new relationship for the interaction energy with an enthalpy (Δh) and an entropy parameter (Δs) in the quasi-chemical approximation is suggested. The exact solution for the quasi-chemical equilibrium in the two-component mixture is given, and a new model for describing and predicting phase equilibria in multi-component systems S-TASQUAC is developed. We examined the possibilities of using S-TASQUAC to predict VLE data and compared the results of binary systems to the results of other known models of liquid mixtures (Wilson, NRTL, UNIQUAC). The results of the calculated data demonstrate the usability of S-TASQUAC as a qualified tool to describe and predict phase equilibria.

Mixing enthalpies of polyethers in solvents of various polarity treated with a group contribution theory

The mixing enthalpies of different oligoethers (oligomers of tetrahydrofuran and ethylene oxide and a block cooligomer of these ethers) with hydroxyl and acetyl end groups in various solvents (2-propanol, tri- and tetrachloromethane) are obtained by microcalorimetry. An extended group contribution theory, based on a quasichemical equilibrium between contacting segment surfaces, is applied successfully for the description and prediction of the mixing enthalpies. The theory can be used for every kind of molecular interaction, for polar and non-polar interactions as well as for hydrogen bridges. In addition, it is possible to apply the theory to mixing enthalpies of polymer blends.

Phase Stability of Hydrogen-Bonded Polymer Mixtures. III. Spinodal Diagrams

Relations derived on the basis of the Barker-Guggenheim quasichemical theory were used for construction of spinodal diagrams (temperature versus composition) of a mixture of two polymers in which hydrogen bonds and other strong interactions exist. A function dependence of parameters of quasichemical equilibrium, η, was proposed, which has the form of the Boltzmann function at lower temperatures, but at higher temperatures corresponds to random mixing. The spinodal diagrams were constructed for several sets of dependences of η on temperature in a wide temperature range for different chain lengths, r, or for different values of the content of polar groups in one of the polymers. According to circumstances, the phase diagram shows one or two temperature regions of phase instability or the phase instability occurs in a certain range of composition at any temperature. Though the chain length was chosen equal for both polymers, the phase diagrams are asymmetric in the sense that the critical points are shifted towards that border of the diagram which corresponds to the component with a larger relative content of the polar group. The temperature range of phase instability is strongly influenced by small changes in the relative surface area of polar groups in the molecules.

Phase Stability of Hydrogen-Bonded Polymer Mixtures. II. Mixtures of Intercomplexing Polymers

Equations for the second derivative of the Gibbs energy of mixing with respect to composition were derived on the basis of the Barker-Guggenheim theory of quasichemical equilibrium for mixtures of two polymers containing polar groups and a nonpolar rest. Using equations derived, conditions for the phase separation in mixtures of two strongly intercomplexing polymer components were evaluated. The phase instability appears when the components differ in their polar group contents (strictly speaking, in their surface fractions in respective macromolecules), or due to an unfavorable interaction between nonpolar groups of the components. The effect is conditioned by small affinity of polar to nonpolar groups and may be influenced by the difference in this affinity between both components; nevertheless, the latter factors are not sufficient for a phase instability to occur.

Calculations of multicomponent phase equilibria with a new group contribution method

The present paper introduces a new group contribution model (GTASQUAC) for calculations of multicomponent phase equilibria of organic compounds. The method is based on the concept of quasi-chemical equilibrium using the TASQUAC formalism for determination of contact numbers in the liquid mixture. GTASQUAC has two adjustable parameters for describing the temperature dependent interchange energy and was applied to the description of VLE and heat of mixing data. The results are compared to those of other '‘local composition models'' like UNIFAC, ASOG or mod. UNIFAC using two, four or six adjustable parameters, respectively. GTASQUAC can also be applied for true prediction of thermodynamic excess properties. A comparison with simulated heat of mixing data shows good agreement. Moreover, the method provides a high flexibility.

Thermodynamics of mixing of propylene oxide oligomers with different end groups and of statistical and block cooligomers of ethylene oxide and propylene oxide in tetrachloromethane

AbstractMixing enthalpies and Gibbs energies of liquid propylene oxide oligomers with hydroxyl and methoxy end groups and of block and statistical cooligomers of ethylene oxide and propylene oxide in tetrachloromethane are obtained by microcalorimetry and vapour pressure measurements. The thermodynamic excess quantities ΔH, ΔGE and ΔSE of mixing are influenced by induced dipol interactions of the ether segments with CCl4 and by the hydrogen bond interactions of the OH end groups. An expanded theoretical treatment using the Huggins approach of quasichemical equilibrium between the contacting segment surfaces is successfully applied on the experimental results.

Thermodynamics of mixing of ethylene oxide oligomers with different end groups in tetrachloromethane: theoretical treatment

AbstractIn a previous paper we reported the enthalpies of mixing of oligomers of ethylene oxide with different end groups in tetrachloromethane. This paper shows the applicability of the modified theoretical treatment, based on a quasichemical equilibrium of the contacting segmental surfaces originated from Huggins, to our experimental results. The experimental data of ethylene oxide oligomers with methoxy end groups can be described with the energy parameter Δεαβ, the equilibrium constant Kαβ and the surface ratio rσ assuming a chemically uniform surface of the oligomer in CCI4. Ethylene oxides with strong polar OH end groups can be treated successfully with an extended version of the theory with two additional parameters K and ΔΔε for systems containing three different kinds of chemical units.

On the liquidus curve for GaN

Abstract A Quasi-Chemical Equilibrium approach was used to discuss the experimental results of three phase (Ga-GaN-N2) equilibrium conditions for the temperature range 1200-1580°C and pressure 0. 1-1. 45 GPa. The best fitting was obtained for the melting temperature of 2531 K which is in reasopable agreement with the value of 2791 K calculated by Van Vechten1.