Excess Mixing Properties Research Articles

The Thermodynamic Properties of Dynol-604/AOT Mixed Reverse Micelles in Isooctane

The volumetric properties of the mixed surfactants bis(2-ethylhexyl) sodium sulfosuccinate and ethoxylated-2,5,8,11-tetramethyl-6-dodecyne-5,8-diol (Dynol-604) at various compositions in isooctane have been studied by density measurements at 303.15 K. The apparent specific volumes and the critical reverse micelle concentrations of the binary mixed surfactants were determined. The results were used to calculate the compositions, excess properties of mixing, activity coefficients and the interaction parameter between the two surfactants in the mixed micelles, based on Rubingh’s formalism.

Relationship between the thermodynamic excess properties of mixing and the elastic moduli in the monazite-type ceramics

Using ab initio quantum chemistry we computed the excess thermodynamic properties and the elastic moduli for a series of monazite-type single substitution solid solutions (Ln1−xLnxPO4). We found that the Margules interaction parameters of all the solid solutions can be described by a simple function of the endmembers volume mismatch ΔV, i.e. W(kJ/mol)=0.616(ΔV(cm3/mol))2. We show that the obtained relationship could be also derived by considering the strain energy resulting from the substitution of cations of different sizes, knowing the Young's modulus and the volumes of endmembers. This indicates that the strain resulting from the structural incorporation of cations is a major factor responsible for arising of the excess properties in monazite-type ceramics. Our results show thus a way to estimate the excess thermodynamic properties of solid solutions from the structural and elastic parameters, namely the endmembers volumes and the Young's modulus, which could be easily measured or computed.

Application of the SAFT-γ Mie group contribution equation of state to fluids of relevance to the oil and gas industry

The application of the SAFT-γ Mie group contribution approach [Papaioannou et al., J. Chem. Phys., 140 (2014) 054107] to the study of a range of systems of relevance to the oil and gas industry is presented. In particular we consider carbon dioxide, water, methanol, aromatics, alkanes, and their mixtures. Following a brief overview of the SAFT-γ Mie equation of state, a systematic methodology for the development of like and unlike group parameters relevant to the systems of interest is presented. The determination of group–group interactions entails a sequence of steps including: the selection of representative components and mixtures (in this instance carbon dioxide, water, methanol, aromatics, and alkanes); the definition of an appropriate set of groups to describe them; the collection of target experimental data used to estimate the group–group interactions; the determination of the group–group interaction parameters; and the assessment of the adequacy of the parameters and theoretical approach. The predictive capability of the SAFT-γ Mie group contribution approach is illustrated for a selection of mixtures, including representative examples of the simultaneous description of vapour–liquid and liquid–liquid equilibria, the densities of the coexisting phases, second derivative thermodynamic properties, and excess properties of mixing. Good quantitative agreement between the predictions and experimental data is achieved, even in the case of challenging mixtures comprising carbon dioxide and water, n-alkanes and water, and methanol and methane.

Composition dependence of thermodynamic, dynamic and dielectric properties of water–methanol model mixtures. Molecular dynamics simulation results with the OPLS-AA model for methanol

We have studied thermodynamic and dynamic properties, as well as the dielectric constant, of water–methanol model mixtures in the entire range of composition, by using constant pressure molecular dynamics simulations at room temperature and ambient pressure. The SPC-E and TIP4P-Ew water models are explored in combination with the OPLS-AA (all atom) model of methanol. Changes of the average number of hydrogen bonds between particles of different species and of the fractions of differently bonded molecules are put in correspondence with the evolution of excess mixing properties, of self-diffusion coefficients, reorientational relaxation times and power spectra. We were looking for the existence of correlations between properties of a different kind, in order to find reasons of satisfactory or dissatisfactory performance of the models applied. It seems that any improvement of the description of water–methanol mixtures requires a more sophisticated, carefully parametrized model for methanol and possibly, certain deviations in the combination rules.

Partitioning of oxygen between the Earth's mantle and core

Experiments to investigate the partitioning of oxygen between liquid iron and (Mg,Fe)O magnesiowüstite were conducted at 30–70 GPa and 2800–3500 K using a laser‐heated diamond anvil cell. A thin foil was prepared from the reacted regions in the recovered samples using a focused ion beam. The compositions of coexisting quenched iron and magnesiowüstite were measured using a transmission electron microscope equipped with energy dispersive X‐ray spectroscopy and electron energy‐loss spectroscopy. In order to understand and model the results, additional experiments were performed to determine the activity of oxygen, or rather FeO, in liquid Fe metal. Multianvil experiments to measure the oxygen contents of coexisting immiscible metallic and ionic liquids in the Fe‐FeO system were performed up to 25 GPa. The results were used to extract excess mixing properties for Fe‐FeO liquids at high pressure and temperature. These properties were used to derive a model that describes oxygen partitioning in the Fe‐Mg‐O system that is independent of the actual experimental partitioning data. The model indicates that the oxygen content of liquid Fe becomes a strong nonlinear function of the FeO content of magnesiowüstite at pressures greater than 25 GPa. This prediction is in excellent agreement with the experimental partitioning data, which is faithfully reproduced in most instances. The new results confirm that the Earth's core is undersaturated in oxygen with respect to the FeO content of the bulk mantle, which will result either in FeO being depleted from the very base of the mantle or lead to the development of an FeO‐enriched outer layer of the core. These possibilities are not mutually exclusive.

Thermodynamics of mixing in the ternary rhombohedral carbonate solid solution, [formula omitted], from atomistic simulations

The effective pairwise interactions in calcite–magnesite, calcite–rhodochrosite and magnesite–rhodochrosite binary systems were evaluated in the diluted limits from the excess enthalpies of supercell structures of the end-members in which pairs of the incoherent (admixed) atoms were inserted at all distinct distances available in a 3×3×1 supercell. The excess enthalpy of mixing within the ternary calcite–magnesite–rhodochrosite system was evaluated as a function of the pairwise interactions. Thermal averages of the enthalpy of mixing were calculated with the Monte Carlo method, while the free energies of mixing were obtained by thermodynamic integration. The convex-hull construction was used to visualize miscibility gaps within the ternary. The obtained agreement with the experimentally known phase relations shows that the excess mixing properties within the ternary can be successfully predicted from pairwise interactions calculated in the diluted limits. The method is expected to work only for systems in which many-body interactions can be ignored.

Computer modeling of the local structure, mixing properties, and stability of solid solutions of alkaline-earth metal oxides

A technique for the computer modeling of disordered binary oxide solid solutions MO-M′O in a wide composition range has been developed. The method of atomistic pair potentials was used for 4 × 4 × 4 supercells. The parameters of the potentials are optimized using the structural and elastic properties of pure components MgO, CaO, SrO, and BaO. The temperature dependences of the heat capacity and entropy are calculated for pure components. The excess mixing properties (enthalpy, volume, bulk modulus, vibrational entropy) are found for different compositions of MgxCa(1 − x)O, CaxSr(1 − x)O, and SrxBa(1 − x)O solid solutions. Temperature and composition dependences of the excess Gibbs energy were constructed, which made it possible to approximately estimate the critical decomposition temperatures and limits of component miscibility. Statistical analysis of lattice distortions in the first and second coordination spheres reveals a detailed picture of the solid-solution local structure.

Dielectric Properties in Ternary Mixtures of Ethane-1,2-diol + 1,2-Dimethoxyethane + Water

The static dielectric constant (e) of ethane-1,2-diol+1,2-dimethoxyethane + water ternary mixtures was measured as a function of temperature (263.15 ≤ T (K) ≤ 353.15) and composition, over the complete mole fraction range 0 ≤ x 1, x 2, x 3≤ 1. The experimental values were analyzed by empirical relationships that accounted for the dependence e = e(T) and Y = Y(x i). A comparison between calculated and experimental data shows that these fitting relationships can be reliably used to predict e values, along with other related properties, in areas of experimental data gaps. Starting from the experimental measurements, some derived quantities such as molar orientational polarization (P), dipolar interaction free energy ( F μ) and the relevant thermodynamic excess mixing properties (F μ E, F―E μ,i), were obtained. The values of the excess quantities are indicative of the presence of specific interactions between different components in the mixtures. A discussion of data in terms of the Kirkwood theory also provides information on the short-range intermolecular interactions, suggesting the formation of stable two-:component adducts rather than of more complex moieties involving all three molecular species.

Dynamic properties of water/alcohol mixtures studied by computer simulation

We have studied mixtures of alcohol and water in an extensive series of 465 molecular-dynamics simulations with an aggregate length of 713 ns, in order to study excess properties of mixing, in particular the relation between mobility and viscosity. Methanol/water, ethanol/water, and 1-propanol/water mixtures were simulated using an alcohol content of 0–100 mass % in steps of 10%, using the OPLS (optimized potential for liquid simulations) force field for the alcohol molecules and the TIP4P (transferable intermolecular potential with four particles) water model. Computed densities and energies show very good agreement with experimental data for bulk simulations and the mixtures are satisfactory as well. The shear viscosity was computed using nonequilibrium molecular-dynamics simulations. Other properties studied include diffusion constants and rotational correlation times. We find the mobility to correlate well with the viscosity data, i.e., at intermediate alcohol concentrations the viscosity is maximal and the mobility is minimal. Furthermore, we have combined the viscosity and diffusion calculations in order to compute an effective hydrodynamic radius of the particles in the mixtures, using the Stokes–Einstein relation. This analysis indicates that there is no collective diffusion of molecular clusters in these mixtures. For all properties we find that the excess values are underestimated in the simulations, which, given that the pure liquids are described rather well, raises the question whether the potential function is too simplistic to describe mixtures quantitatively. The set of simulations presented here can hence be regarded as a force-field benchmark.

Mixing properties of the enstatite-ferrosilite solid solution: II. A microscopic perspective

Infrared spectra of natural, synthetic and heat treated orthopyroxene samples belonging to the enstatite-ferrosilite join were investigated in the range 70–1400 cm −1 . Correlations of the wavenumber shifts and line broadening systematics with the thermodynamic mixing properties were found. Wavenumber shifts of the highest energy modes correlate closely with the Si-O bond lengths and give an indirect view of the distortions of tetrahedra across the solid solution. One phonon line dominated by the bending of the tetrahedral chains is sensitive to changes in the degree of cation order and correlates with the average of the kinking angles of the same samples determined by X-ray diffraction. All the other wavenumber shifts (at lower energies) are correlated linearly with compositional changes only. A phonon line shift at low energy correlates with unit cell volume. Local strains arising from cation substitution and ordering have been quantified by means of an autocorrelation function. Local heterogeneities are associated with Fe/ Mg substitution and disordering in samples at intermediate composition. Line broadening is more pronounced in the energy region of the spectra, corresponding to modes involving primarily the M cations. The shape of line broadening in this region is similar to the enthalpy of mixing, ΔH mix . Ordering reduces broadening and hence local strains and excess mixing properties. A fully ordered orthopyroxene at En 50 Fs 50 would be collinear with pure En and pure Fs, implying that ordering eliminates the local heterogeneities which arise due to Fe/Mg mixing.

Viscosity of (ethane-1,2-diol + 1,2-dimethoxyethane + water) at temperatures from 263.15 K to 353.15 K

The kinematic viscosity ν for (ethane-1,2-diol + 1,2-dimethoxyethane + water) was measured at 14 different ternary compositions covering the whole miscibility field, and at 19 temperatures in the range 263.15 ⩽T/ K ⩽ 353.15. The experimental values were fitted using empirical equations of the type ν=ν (T) and ν=ν (xi), respectively, in order to provide reliable models to account for the behaviour of the system. The excess kinematic viscosity νEhas been determined and interpreted in terms of the type and nature of the interactions among the components of the mixture. Using the experimental ν data, the thermodynamic properties ( ΔG*, ΔH*,ΔS* ) of the viscous flow have been obtained from the Eyring’s approach and standard thermodynamic equations. Furthermore, excess mixing functions, such asΔG*E , have been determined, and found to evidence the existence of quite strong specific interactions among the components, probably due to the formation of hydrogen bonds and dipolar networks. However, all the calculated excess mixing properties suggest the absence of stable three-component adducts.

Kinematic Viscosities of Binary Liquid Mixtures of 2-Butanone with 1,2-Propanediol

Kinematic viscosities of the binary 2-butanone (1) + 1,2-propanediol (2) solvent system have been measured for mixtures covering the whole miscibility range expressed by 0 ≤ xi ≤ 1, at 19 temperatures in the range −10 ≤ t/°C ≤ 80. The measured values have been used to test empirical equations that express the kinematic viscosities as functions of the composition and temperature. Excess kinematic viscosities (νE) have also been calculated. Sign and magnitude of these quantities are discussed in terms of type and nature of specific intermolecular interactions. Furthermore, derived quantities such as thermodynamic parameters of viscous flow (ΔG‡, ΔH‡ and ΔS‡), are analyzed on the basis of Eyring's model. All the investigated excess mixing properties indicate the probable existence of stable two-component adducts in this binary solvent system.

Densities, refractive indices and excess properties of mixing of the n-octanol + 1,4-dioxane + 2-butanol ternary system at 298.15 K

Excess molar volumes and excess refractive indices of the n-octanol + 1,4-dioxane + 2-butanol system and the three corresponding binary mixtures have been determined at 298.15 K by measuring densities and refractive indices. Different expressions exist in the literature to predict these excess properties from binary data. An estimation of excess molar volumes is also evaluated using a modified Heller equation which depends on the refractive indices of the mixtures. A comparison of the predictions of different methods with the experimental values of the physical properties has been made.Key words: excess molar volumes, densities, refractive indices, n-octanol, 1,4-dioxane, 2-butanol, ternary system.

Kinematic viscosities of ternary mixtures containing ethane-1,2-diol, 2-methoxyethanol and water from −10°C to 80°C

Kinematic viscosities ( ν) of the ternary ethane-1,2-diol (1)+2-methoxyethanol (2)+water (3) solvent system have been measured for 36 ternary mixtures covering the whole miscibility range expressed by the condition 0< X 1, X 2, X 3<1, at 19 temperatures in the range −10≤ t (°C)≤80. The measured values have been used to test some empirical equations of the type ν= ν( t) and ν= ν( X i ), in order to provide for useful interpolation procedures to obtain calculated values in correspondence to the experimental data gaps. From the experimental data, the excess kinematic viscosities ( ν E) have been calculated. Sign and magnitude of these quantities have been discussed in terms of type and nature of specific intermolecular interactions. Furthermore, derived quantities such as thermodynamic parameters of the viscous flow (Δ G*, Δ H* and Δ S*), have been analysed on the basis of the Eyring's model. All the investigated excess mixing properties indicate the probable absence of stable three-component adducts in this ternary solvent system.

Densities, Refractive Indexes, and Excess Properties of Mixing of the n-Hexanol + Ethanenitrile + Dichloromethane Ternary System at 25°C

Excess molar volumes and excess refractive indexes of the n-hexanol + ethanenitrile + dichloromethane system and the three corresponding binary mixtures have been determined at 25°C, by measuring densities and refractive indexes. Different expressions exist in the literature to predict these excess properties from binary data. The empirical correlation of Cibulka is shown to be the best in this system. An estimation of excess molar volumes is also evaluated using a modified Heller equation, which depends on the refractive indexes of the mixtures. Comparison of the predictions by different methods with the experimental values of the physical properties has been made.

Dielectric Characterization of Binary Solvents Containing 1,2-Dichloroethane and 2-Chloroethanol

Abstract Static dielectric constants (ε) were determined for the 1,2-dichloroethane (DCE, 1)/2-chloroethanol (CE, 2) binary solvent system at 19 temperatures ranging from −10 to +80 °C and in the whole composition range expressed by the mole fraction 0 ≤ X1 ≤ 1. The experimental values have been fitted to some equations that could be usefully employed for predictive ε calculations. Furthermore, the excess mixing properties (εe) have been evaluated in order to point out the presence of solvent–cosolvent adducts in the binary mixtures mentioned above. The values of εe have been generally found to be negative and only slightly positive under a few experimental conditions in the CE rich-region, thus giving evidence of a close interaction network probably via hydrogen bonding as well as other interactions of every kind in this solvent system.

Thermodynamic study of glass transitions in miscible polymer blends

Contemporary theoretical considerations of glass transitions in miscible binary polymer blends give the thermodynamic functions associated with the excess properties of mixing in liquid and glass states. A striking feature of the present analysis is that fewer assumptions are involved in the derivations. The values of the new parameters are reported for a number of polymer pairs, representing various types of intermolecular interactions. It is demonstrated that the enthalpy and entropy of mixing are virtually discontinuous at the glass transition temperature of the blend, Tgb, particularly for the cases of large deviations of Tgb from the weight-average values. In addition, the difference between the polymer-polymer interaction parameters of the blend in the liquid and glassy states, Δχ, is indeed linearly related to the reciprocal of Tgb. Other implications of the results are discussed.

Molecular dynamics studies of polar/nonpolar fluid mixtures. I. Mixtures of Lennard-Jones and Stockmayer fluids

The results of canonical ensemble molecular dynamics calculations of mixtures of Lennard–Jones and Stockmayer fluids are reported. To study solely the influence of the polarity, the Lennard-Jones parameters were identical for both components. The excess mixing properties show a strong asymmetry with respect to composition for large dipolar strength. The free energy of mixing is obtained through a thermodynamic integration procedure. The results strongly suggest that, for reduced dipolar strengths μ2&amp;gt;3.15, demixing occurs into a phase rich in polar component and an almost pure Lennard-Jones fluid. It is shown that perturbation theory yields fairly accurate results for the dipolar energy and free energy of the mixture. For the free energy of mixing, qualitatively correct results are obtained. The structure and orientational correlation functions of the mixture are discussed. The radial distribution function for pairs of polar molecules show a marked increase in local ordering with dipolar strength for low concentrations of the polar component, indicating that strong clustering of polar molecules occurs at these concentrations. The orientational order is also seen to increase very strongly with dipole moment at these concentrations. The pair correlation function for pairs of Lennard-Jones atoms shows little dependence on dipolar strength of Stockmayer molecules at these concentrations. The distribution function for pairs of unlike molecules reflects the increasingly dissimilar character of these molecules as the dipolar strength increases. For large concentrations of Stockmayer molecules, the opposite effect is observed, albeit less pronounced, in that the pair-correlation function for Lennard-Jones atoms shows an increase in local ordering as μ increases, whereas the radial distribution function for Stockmayer pairs remains relatively unaffected with increasing μ. These results are interpreted in terms of a frustation model. Results are given for the variation of the dielectric constant of the mixture with composition and dipolar strength.

Geothermobarometry of high-grade metapelites: simultaneously operating reactions

Summary Experimental data on equilibria involving rock-forming minerals in high-grade metapelites (garnet, orthopyroxene, cordierite and plagioclase) have been used to derive an internally consistent system of mineralogical thermometers and barometers based on component reactions and excess mixing properties of solid solutions. Application of these data to a granulite-facies metapelite sample reveals that compositional inhomogeneity of minerals on a thin-section scale is likely to be a result of several reactions opening simultaneously at the retrograde stage of metamorphic evolution. The widely accepted practice of estimating pressure and temperature from separate reactions may thus lead to errors and misinterpretation of P-T paths.

Mixing rules for the back equation of state

Van der Waals type of mixing rule for the energy parameter us together with the mixing rules introduced previously for parameters αs and Vs0 of the BACK equation were employed in evaluating excess properties of mixing, Henry's law constant and high pressure vapour-liquid equilibria. A comparison with the experimental data reveals that the BACK equation together with the suggested mixing rules could provide good prediction of equilibrium properties of mixtures of relatively simple molecules.