Gibbs Energy Of Mixing Research Articles

Evaluation of Excess Gibbs Energy of Mixing in Extremely Dilute in Nonpolar Solvents Solutions of TRI-N-Butyl Phosphate

The excess gibbs energy of mixing in binary mixtures of TBP in nonpolar solvents viz. bcnzene, carbon disulphide, cyclohexane, n-heptane, n–hexane, p–xylene, tetrachloromethane at temperature 303°K is studied. The excess free energy of mixing (AGA8) is in the order, n–hexane < n–heptane < benzene < cyclohexane < p–xylene < CCI4 < CS2. The results corroborate the findings obtained through evaluation of the excess correlation Factor.

Excess thermodynamic properties of some binary solutions of ethylbenzene + n-alkanes

Abstract Some thermodynamic properties (excess enthalpies, entropies and Gibbs energies of mixing) have been determined for binary solutions of ethylbenzene + n -alkanes (eicosane, C 20 H 42 ; heneicosane, C 21 H 44 ; docosane, C 22 H 46 ; tricosane, C 23 H 48 ; and tetracosane, C 24 H 50 ), at crystallization temperatures in the (260–305) K range. The calculated properties vary with the chain lengths of the n -alkanes, and show the alternation effect occurring in the general behaviour of n -alkanes. Simple analytical expressions have been established to describe the excess properties.

Construction of a quasi-ternary phase diagram in the NdO 1.5BaOCuO system in the air atmosphere Part II. Phase equilibria of the neodymium-rich Nd 1+ xBa 2− xCu 3O z solid solution

In the present work phase relations in a copper-rich corner of the NdO 1.5BaOCuO system were studied at 970–1060°C in air by DTA, quenching experiments, EPMA, XRD, ICP AES and finally confirmed by growth of several test single crystals. It was found that in the analyzed region the Nd 1+ x Ba 2− x Cu 3O z solid solution (Nd123ss) with maximum x values co-exists at 970–1060°C with Cu-rich melt and different solid phases: CuO (970–990°C), Nd 2CuO 4 (990…995–1045°C) or Nd 4Ba 2Cu 2O 10 (1060°C). The decomposition temperature of Nd123ss decreases with increasing the neodymium content, and the limit composition of Nd123ss extends up to Nd 2BaCu 3O z at 990–995°C. The Nd123ss unit cell volume deviations from the ideal solution of the Nd123 and Nd213 phases were found positive by XRD, as well as their excess Gibbs energy of mixing, estimated thermodynamically using the experimental phase diagram. This provides a probability of a spinodal decomposition phenomena of such a solution.

Calculating binary and ternary multiphase equilibria: extensions of the integral area method

The area method was proposed in 1992 to calculate binary and ternary 2-phase equilibria. In its integral form, the method provides both the necessary and sufficient conditions required for the determination of the global minimum reduced Gibbs energy of mixing (Φ). The method has since been applied to the calculation of both pure component and ternary multiphase equilibria in a differential form. However, the extension of the original (2 point) integral area method to the direct calculation of both binary and ternary multiphase equilibria has not been completed. Direct 3 point and modified 2 point search methods have therefore been developed here and used to estimate the phase compositions of a representative binary vapour-liquid-liquid system. The 2 point area method principle has been extended and applied to the calculation of ternary multiphase equilibria using a net volume approach. However, this volume method was found to fail due to an underlying inconsistency in the bounding of the integrated Φ surface by the trial 3-phase region. A new method is proposed that overcomes this problem by minimising the area of intersection between a tangent plane and the Φ surface. This new method has successfully calculated the 3-phase compositions of two simple test systems from a variety of initial mixture starting points.

Viscosities of High Temperature Systems. A Modelling Approach.

A mathematical model for estimating the viscosities of multi-component metallic and ionic melts at high temperatures is presented. The reliability of the model in extrapolating the viscosity data as a function of temperature and composition has been demonstrated in the case of some metallic and slag systems. A correlation between the Gibbs energy of activation for viscosities and the Gibbs energy of mixing in the case of binary metallic systems is described. Preliminary results of the experimental measurements of viscosities of the system CaO-FeO-SiO2 are presented.

Improvement of polymer solubility: influence of shear and of pressure

Abstract

Calculation of miscibility behavior of multinary polymer blends

AbstractA method for the calculation of phase diagrams (tie lines and binodal, spinodal, critical points and their stability) based exclusively on the Gibbs energy of mixing, δG, is presented which does not require the calculation of the derivatives with respect to the composition. The method is demonstrated for ternary mixtures of two homopolymers and the corresponding copolymer, and for quaternary and quinternary blends of five polymers exhibiting a closed miscibility gap. The advantages of the presented method become most obvious in the mathematical description of measured phase diagrams, where complex composition dependencies of the interaction parameter are observed.

Thermodynamics and phase diagram of the binary system Bi 2O 3-B 2O 3

We analyzed the thermodynamic data of the binary system Bi 2O 3-B 2O 3. The phase diagram contains five compounds, of which four melt congruently, and a miscibility gap, close to pure B 2O 3. The three sets of transformation data of Bi 2O 3, the enthalpy of mixing data in the liquid, and the critical point of the miscibility gap gave five equations for the excess Gibbs energy of mixing and five sets of values for the enthalpies of formation of the binary compounds. The critical point data yielded another set of transformation data for Bi 2O 3. Using the monotectic composition and the enthalpy of mixing data also yielded a set of transformation data for Bi 2O 3. The values obtained using the enthalpy of mixing data are the most reliable values.

Molecular thermodynamic model for gibbs energy of mixing of nonionic surfactant solutions

AbstractA segment‐based molecular thermodynamic model for the Gibbs energy of polymer solutions or oligomer solutions is used to represent the Gibbs energy of mixing for aqueous nonionic surfactant solutions. In contrast to the mass‐action models and pseudophase models, which are often discussed in the literature, the Gibbs‐energy model provides an explicit account of the solution nonideality, including activity coefficients of monomeric amphiphiles in the aqueous phase. The equilibrium between monomeric amphiphiles and micellar amphiphiles is described by the equal‐activity relationship. The Gibbs‐energy model makes it possible to use a well‐accepted molecular thermodynamic framework to correlate and represent phase behaviors of aqueous nonionic surfactant solutions.

Calculation of multi-phase equilibria using the equal area rule with application to [formula omitted] mixtures

We have used an efficient, new Gibbs minimization method with an equation of state (EOS) model to predict phase equilibria for hydrocarbon water binary mixtures. The method utilizes the observation by Eubank and Hall (1995) that a plot of the derivative of the Gibbs energy of mixing against composition exhibits phase loops similar to those associated with the Maxwell rule. Equilibrium exists when the positive and negative areas are equal above and below a specific value of the derivative. Hence, we call the method the Equal Area Rule (EAR). The EAR application procedure automatically performs a stability analysis for the system. EAR also presents exciting possibilities when calculating phase equilibria for multi-component mixtures. Shyu et al. (1995) have applied the method to ternary liquid-phase systems using activity coefficient models.

Thermodynamics of polymer solutions and blends

AbstractTo describe the thermodynamic behavior of binary and larger polymer blends, the Hoch‐Arpshofen model is used to describe highly asymmetric phase diagrams, and asymmetric enthalpies of mixing, where the miscibility gap and the extremum of the enthalpy of mixing leans toward one of the components. The Gibbs energy of mixing of polymer blends is described as where z can be mole fraction, volume fraction, or weight fraction. The Hoch‐Arpshofen model contains an interaction parameter W = A + B*T independent of composition and an integer number n (2, 3, 4, …), which defines the asymmetricity of the binary phase diagram and of the Gibbs energy of mixing curve. In a binary system n defines the composition where the Gibbs energy of mixing is maximum or minimum or the composition is where the temperature of a miscibility gap is maximum or minimum. In a binary system A‐B the maximum effect occurs at An–1B. The disorder reaction in polymers is treated as a transformation temperature, and defines T0, the temperature where the ordered and disordered material is equal.

Thermodynamic activities and phase boundaries for the alloys of the Ni3Al-Ni3Ti pseudobinary section in the Ni-Al-Ti system

The pseudobinary section Ni3Al-Ni3Ti of the ternary Ni-Al-Ti system has been investigated by ther-mal analysis and Knudsen effusion mass spectrometry. The solidus of the pseudobinary section and the thermodynamic activities of Ni and Al have been determined in the alloys Ni0.75A10.25-xTix of the compositionsx = 0.00 to 0.21. Moreover, the thermodynamic activities of Ni and Ti in Ni3Ti (x = 0.25) as well as the Gibbs energy of mixing of the Ni0.75Ti0.25 phase resulted. The ionization cross-sectional ratio Σ(Ni)/Σ(Ti) = 0.77 has been evaluated for the electron impact energy of 50 eV.

Influence of Molar Mass Distribution on the Compatibility of Polymers

Abstract Phase equilibria were calculated by means of a new method (direct minimization of the Gibbs energy of mixing) for polymer blends consisting of monodisperse polymer A and polydisperse polymer B. The results obtained for a Schulz-Flory distribution of B (molecular nonuniformity U = (M w/M n) −1 = 1 and 100 components of model B) agree quantitatively with that of computations on the basis of continuous thermodynamics. The influence of U B on the miscibility of A and B in 1:1 mixtures was studied for constant M w of B, quantifying the incompatibility of the polymers by the length of the tie lines. The outcome of these calculations demonstrates that the typical effect of an augmentation of U B (keeping M w and the overall composition constant) consists in an enlargement of the mutual solubility of A and B. However, for an almost compatible pair of polymers (i.e., interaction parameters g are only slightly larger than the critical values for U B = 0), this statement remains true only in the case of suf...

Shear flow and the phase behaviour of polymer blends

The effect of simple shear flow on the phase diagram of partially miscible polymer blends has been analysed through the use of a generalised Gibbs energy of mixing, modified by a stored energy term. The latter is defined as the energy stored by the polymeric molecules during flow, and is seen to have a significant influence on the magnitude and direction of the change in the phase boundary caused by shear. Computer simulations indicate that flow induces mixing when the excess stored energy is negative and phase separation when the excess stored energy is positive. The dependence of the stored energy on the viscosity of the polymer blend was investigated for seven model blends exhibiting different viscosity-composition behaviours. A negative deviation of the viscosity-composition curve from the linear mixing rule was found to be a sufficient condition for a negative excess stored energy, resulting in shear-induced mixing. This prediction is in qualitative agreement with the experimental results on the effect of shear on the phase diagram of poly(styrene-co- acrylonitrile) poly(methymethacrylate) blends. In contrast, a positive deviation of the viscosity-composition curve from additivity was found to be a necessary but not sufficient condition for a positive excess stored energy which would cause shear-induced phase separation. This analysis seems to indicate that the viscosity-composition behaviour of a polymer blend could be used to qualitatively anticipate the change in the phase diagram of a polymer blend upon flow.

Phase behavior of the ternary system water/hydroxyethyl cellulose/nonionic surfactant

The phase behavior of ternary aqueous solutions of two samples of hydroxyethyl cellulose (HEC) and oligoethylene glycol mono(n-alkyl) ethers CxEy (x: 11;y: 28, 40) at 25°C has been studied above the CMC of CxEy. The influence of molar mass of HEC and the number of ethylene glycol units on the phase diagram has been investigated. Both binary systems water/HEC and water/CxEy are completely miscible. The ternary mixture of water/polymer/nonionic surfactant is homogeneous if the weight fraction of water is larger than 0.93, or else it can separate segregatively, i.e., HEC is enriched in one phase, the surfactant in the other. The theoretical description is based on an equation for the Gibbs energy of mixing which takes polar conformations into account. The phase diagrams are calculated by means of a new method which does not require the derivatives of the Gibbs energy of mixing.

Thermodynamic Analysis of the Metastable Regions for the AI2O3‐SiO2 System

The paper offers a short review of investigations conducted on the Al2O3‐SiO2 system, particularly from the point of view of an appearance of immiscibility gaps, below the liquidus temperatures. Based on theoretical criteria and using the data along the liquidus curves (for mullite and corundum), this investigation suggests immiscibility regions at both ends of the phase diagram. That is, it defines the Margules polynomials for calculation of the activity coefficients necessary for determining the Gibbs energy of mixing. Obtained results are in good agreement with the results reported by Risbud and Pask and other investigators who have found immiscibility gaps at rather high temperatures.

Prediction of the enthalpy of transfer of alkali-metal halides in binary mixtures

The quasi-lattice quasi-chemical model has been modified in order to predict the enthalpy of transfer of alkali-metal halides in binary solvent mixtures from the solvation properties in the pure solvents and from the excess enthalpy and Gibbs energy of mixing of the solvents. In mixtures with a negative Gibbs energy of mixing, there is an approximately linear dependence of the enthalpy of transfer on the mole fraction. In mixtures with a positive Gibbs energy of mixing, the occurrence of an extremum in the enthalpy of transfer is predicted.

A Simplified Model for Calculation of the Gibbs Energy of Mixing in Crystals: Thermodynamic Theory, Restrictions and Applicability

A simplified model has been set up for calculation of the molar Gibbs energy of mixing ∆mixGm(s) in crystals based on the assumption of a complete liquid-solid thermodynamic equilibrium in the water-salt systems. The procedure allows the ∆mixGm(s) values to be calculated from the experimental solubility data for the saturated binary and ternary solutions. The ∆mixGm(s) values and the excess Gibbs energy of mixing ∆mixGEm(s) were calculated for six alkali-halide systems (KCl-RbCl-H2O, KBr-RbBr-H2O, KI-RbI-H2O, NH4Cl-NH4Br-H2O, RbCl-RbBr-H2O and CsCl-CsBr-H2O). The results obtained were compared with experimental data taken from the literature and values calculated based on various theoretical approaches.

Activities of Components in the Ca2MgSi2O7-CaSiO3Molten System

Activities of the components, the Gibbs energy of mixing, and the excess entropy of mixing have been calculated for the Ca2MgSi2O7-CaSiO3 system. The mole fractions of the components were calculated assuming that in the point of the formal component Ca2MgSi2O7, the molar mass of the quasi-real particle in the melt corresponds to its formula molar mass, whereas in the point of the formal component CaSiO3 the molar mass of the quasi-real particle in the melt is 8.5 times higher than as corresponds to its formula. The fact that the enthalpy of mixing is zero whereas the excess entropy of mixing is non-zero suggests that Ca2MgSi2O7-CaSiO3 melts behave as athermal solutions.

Mass-Spectrometric Study of Thermodynamic Properties in the RbBO2-SiO2 System.

Partial pressures of RbBO2 (g) and Rb2(BO2)2 (g) in the RbBO2-SiO2 system are measured by a mass-spectrometric Knudsen effusion method. On the basis of the partial pressures, chemical activities of the RbBO2 and SiO2 components and molar Gibbs energies of mixing are determined in the whole composition range. The chemical activities of both RbBO2 and SiO2 show negative deviation from Raoult's law at 1000 K. From low molar Gibbs energies of mixing, the melts in the RbBO2-SiO2 system are concluded to be very stable thermodynamically.