Phase Transitions and Critical Behaviour of Binary Liquid Mixtures

Summary.  Compared to the simple one-component case, the phase behaviour of binary liquid mixtures shows an incredibly rich variety of phenomena. In this contribution we restrict ourselves to so-called binary symmetric mixtures, i.e. where like-particle interactions are equal (Φ₁₁(r) = Φ₂₂(r)), whereas the interactions between unlike fluid particles differ from those of likes ones (Φ₁₁(r) ≠ Φ₁₂(r)). Using both the simple mean spherical approximation and the more sophisticated self-consistent Ornstein-Zernike approximation, we have calculated the structural and thermodynamic properties of such a system and determine phase diagrams, paying particular attention to the critical behaviour (critical and tricritical points, critical end points). We then study the thermodynamic properties of the same binary mixture when it is in thermal equilibrium with a disordered porous matrix which we have realized by a frozen configuration of equally sized particles. We observe – in qualitative agreement with experiment – that already a minute matrix density is able to lead to drastic changes in the phase behaviour of the fluid. We systematically investigate the influence of the external system parameters (due to the matrix properties and the fluid–matrix interactions) and of the internal system parameters (due to the fluid properties) on the phase diagram. Received June 27, 2001. Accepted July 2, 2001     

Isothermal Phase Equilibrium Studies on the Binary Mixtures of some Alkylbenzenes

Abstract

The gas chromatographic method proposed by us for simple and accurate measurement of isothermal phase equilibria has been applied to the binary mixtures formed by alkylbenzenes amongst themselves. Results on the binary mixtures of: benzene - toluene, toluene + o-xylene, toluene + p-xylene, toluene + ethylbenzene, ethylbenzene + o-xylene and ethylbenzene + p-xylene are presented in this paper. The present measurements on benzene + toluene system at 40°C are in good agreement with the isothermal phase equilibrium data available in the literature.     

Association Model and Its Representation of Phase Equilibria and Excess Enthalpies of Alcohol, Aniline, and Acetonitrile Mixtures

An association model is presented to describe vapor–liquid equilibria,liquid–liquid equilibria, and excess enthalpies of binary and ternary liquid solutionscontaining alcohols, aniline, and/or acetonitrile using the concepts of linearself-association of associated components and of solvation between unlike molecules.Calculated results also show that the model works well in representing thethermodynamic properties for alcohol + aniline, alcohol + acetonitrile, andalcohol + alcohol mixtures.     

Prediction of phase equilibria in hydrocarbon + near-critical solvent systems

In this paper the Hole Quasichemical Group-Contribution model (HM) is used to describe phase diagram peculiarities of multicomponent aqueous systems containing hydrocarbons and alcohols. The model correctly describes liquid-liquid (LL), liquid-liquid-vapour (LLV), liquid-vapour (LV) and vapour-vapour equilibria (VVE), and critical and azeotrope curves. The potential use of the HM in the prediction of the solubilities of hydrocarbons in near-critical water and the densities of coexisting phases in the critical region of the system n-hexane-water are presented.     

Complex Permittivity Spectra of Binary Pyridine–Amide Mixtures Using Time–Domain Reflectometry

Frequency spectra of the complex permittivity for pyridine–amide binary mixtures have been determined over the frequency range 10 MHz to 10 GHz, at 5, 15, 25, and 40°C, using the time–domain reflectometry method, for 11 compositions of each pyridine–amide system, e.g., formamide, N-methylformamide, and N,N-dimethylformamide. The relaxation in these systems can be described by a single relaxation time using the Debye model. The static dielectric constant, relaxation time, the corresponding excess dielectric properties, Kirkwood correlation factor, and molar activation energy of the mixtures have been determined. The excess permittivity is found to be positive in the amide-rich region and negative in the pyridine-rich region. The excess inverse relaxation time is negative, except in the pyridine-rich region. The static dielectric constants for the mixtures have been fitted with the modified Bruggeman model. The temperature-dependent relaxation times show the expected Arrhenius behavior.     

High-pressure vapor–liquid equilibria in the nitrogen–n-pentane system

New experimental vapor–liquid equilibrium data of the N₂–n-pentane system were measured over a wide temperature range from 344.3 to 447.9 K and pressures up to 35 MPa. A static-analytic apparatus with visual sapphire windows and pneumatic capillary samplers was used in the experimental measurements. Equilibrium phase compositions and vapor–liquid equilibrium ratios are reported. The new results were compared with those reported by other authors. The comparison showed that the pressure–composition data reported in this work are in good agreement with those determined by others but they are closer to the mixture critical point at each temperature level. The experimental data were modeled with the PR and PC-SAFT equations of state by using one-fluid mixing rules and a single temperature independent interaction parameter. Results of the modeling showed that the PC-SAFT equation fit the data satisfactorily even at the highest temperatures of study.     

正已醇-邻、间、对二甲苯二元系固液相平衡

Melting temperatures have been measured and the solid-liquid phase diagrams constructed for 1-hexanol＋o-xylene, 1-hexanol＋m-xylene and 1-hexanol＋p-xylene. They are simple eutectic systems. Excess mole Gibbs free energies were calculated at 298.15K, showing larger positive deviations from ideal-solution behavior. The largest values of GmE are 711、 650 and 800 J•mol-1 for {o-C6H4(CH3)2＋C6H13OH}、 {m-C6H4(CH3)2 ＋ C6H13OH} and {p-C6H4(CH3)2＋C6H13OH} respectively.     

On the Validity of Stokes–Einstein and Stokes–Einstein–Debye Relations in Ionic Liquids and Ionic‐Liquid Mixtures

Stokes–Einstein (SE) and Stokes–Einstein–Debye (SED) relations in the neat ionic liquid (IL) [C₂mim][NTf₂] and IL/chloroform mixtures are studied by means of molecular dynamics (MD) simulations. For this purpose, we simulate the translational diffusion coefficients of the cations and anions, the rotational correlation times of the C(2)? H bond in the cation C₂mim⁺, and the viscosities of the whole system. We find that the SE and SED relations are not valid for the pure ionic liquid, nor for IL/chloroform mixtures down to the miscibility gap (at 50 wt % IL). The deviations from both relations could be related to dynamical heterogeneities described by the non‐Gaussian parameter α(t). If α(t) is close to zero, at a concentration of 1 wt % IL in chloroform, both relations become valid. Then, the effective radii and volumes calculated from the SE and SED equations can be related to the structures found in the MD simulations, such as aggregates of ion pairs. Overall, similarities are observed between the dynamical properties of supercooled water and those of ionic liquids.     

Measurement and modelling of binary (solid + liquid + vapour) equilibria involving lipids and CO2

The development of solid lipid nanoparticles (SLN) using supercritical fluid at room temperature is an innovative alternative compared to traditional pharmaceutical methods and the safety and drug efficacy of SLN made using supercritical CO₂ is increased. One of the micronization techniques which have provided the best results in the production of SLN is particles from gas-saturated solution (PGSS). The solid–liquid–vapour coexistence curve of a solid in a compressed gas is of primary importance in assessing the feasibility of PGSS and the selection of appropriate operating conditions. The objectives of this work are to perform experimental measurements using a high pressure differential scanning calorimeter (DSC) to obtain melting properties as a function of composition and develop a simplified approach to model multiphase equilibria of lipids in compressed CO₂. The selected lipid was tristearin. Before assessment of triestearin and CO₂ phase equilibrium, the performance of this thermodynamic model was evaluated in two other lipids which provided results with high accuracy.     

Liquid–liquid and liquid–liquid–solid equilibrium in Na2CO3–PEG–H2O

The phase diagram was determined for the Na₂CO₃–PEG–H₂O system at 25°C using PEG (poly(ethylene glycol)) with a molecular weight of 4000. Compositions of the liquid–liquid and the liquid–liquid–solid equilibria were determined using calibration curves of density and index of refraction of the solutions, and atomic absorption (AA) and X-ray diffraction analyses were made on the solids. The solid phase in equilibrium with the biphasic region was Na₂CO₃·H₂O. Binodal curves were described using a three-parameter equation. Tie lines were described using the Othmer–Tobias and Bancroft correlation’s. Correlation coefficients for all equations exceeded 0.99. The effects of temperature (25 and 40°C) and the molecular weight of the PEG (2000, 3000, and 4000) on the binodal curve were also studied, and it was observed that the size of the biphasic region increased slightly with an increase in these variables.     

Aqueous Ammonia Vapor-Liquid Equilibria– Entropy and Temperature Dependence of Wilson Coefficients

This study extends a model for nonideal solution behavior by considering the temperature dependence of the coefficients in the Wilson equation for the aqueous ammonia system. Twenty-seven isothermal sets of experimental PXY data up to 2 MPa (20 atm) pressure (284 points) were analyzed using an objective function based on the excess Gibbs free energy to determine the pair of Wilson coefficients for each data set. Evaluation of these results supports the interpretation of the interaction parameters in Wilson's equation as temperature-dependent entropy functions. Comparison of computed results is made with four categories of vapor–liquid equilibrium (VLE) data: (1) primary PTXY, (2) refined PTXY, (3) secondary PTXY or PTM, and (4) partial. Excellent agreement is found with computed results for all but two of these VLE data sets in the region of rapidly changing vapor composition up to 90 mole % of ammonia. A comparison is also made to the only three previously published single-temperature (isothermal) pairs of Wilson coefficients with better agreement in Y, for all three cases, and in P, for two cases. A straightforward procedure is outlined to estimate any set of PTXY values (in the range P < 2 MPa, Y < 0.9) for the aqueous ammonia system.     

Molecular theory of phase equilibria in model and real associated mixtures III. Binary solutions of inert gases and n-alkanes in ammonia and methanol

Using new molecular models of ammonia and methanol and thermodynamic perturbation theory, the global phase diagrams of model mixtures of these compounds with a van der Waals fluid, representing a simple nonpolar fluid, have been calculated. The global phase diagram of these mixtures is much richer than that of corresponding aqueous mixtures. More types of critical line behavior are found, including the presence of van Laar points and a small region where the mixtures exhibit a closed liquid-liquid immiscibility loop (Type VI phase behavior). The individual mixture components are characterized by two molecular parameters, which can be adjusted to their critical temperature and critical volume; the mixture model itself contains no adjustable parameters. It is shown that the theory gives qualitatively correct predietions of mixtures with n-alkanes. This includes the prediction of Type III critical line behavior for small and large values of the ratio of the critical temperatures of the components, and Type II over a large range of conditions, including the presence or absence of absolute or limited azeotropy, and temperature and pressure extrema of critical lines and their dependence on the number of carbon atoms.     

The ternary system cerium–palladium–silicon

Phase relations in the ternary system Ce–Pd–Si have been established for the isothermal section at 800 °C based on X-ray powder diffraction and EMPA techniques on about 130 alloys, which were prepared by arc-melting under argon or powder reaction sintering. Eighteen ternary compounds have been observed to participate in the phase equilibria at 800 °C. Atom order was determined by direct methods from X-ray single-crystal counter data for the crystal structures of τ₈—Ce₃Pd₄Si₄ (U₃Ni₄Si₄-type, Immm; a=0.41618(1), b=0.42640(1), c=2.45744(7) nm), τ₁₆—Ce₂Pd₁₄Si (own structure type, P4/nmm; a=0.88832(2), c=0.69600(2) nm) and also for τ₁₈—CePd_1−xSi_x (x=0.07; FeB-type, Pnma; a=0.74422(5), b=0.45548(3), c=0.58569(4) nm). Rietveld refinements established the atom arrangement in the structures of τ₅—Ce₃PdSi₃ (Ba₃Al₂Ge₂-type, Immm; a=0.41207(1), b=0.43026(1), c=1.84069(4) nm) and τ₁₃—Ce_3−xPd_20+xSi₆ (0≤x≤1, Co₂₀Al₃B₆-type, Fm3¯m; a=1.21527(2) nm). The ternary compound Ce₂Pd₃Si₃ (structure-type Ce₂Rh_1.35Ge_4.65, Pmmn; a=0.42040(1), b=0.42247(1), c=1.72444(3) nm) was detected as a high-temperature compound, however, does not participate in the equilibria at 800 °C. Phase equilibria in Ce–Pd–Si are characterized by the absence of cerium solubility in palladium silicides. Mutual solubility among cerium silicides and cerium–palladium compounds are significant whereby random substitution of the almost equally sized atom species palladium and silicon is reflected in extended homogeneous regions at constant Ce-content such as for τ₂—Ce(Pd_xSi_1−x)₂ (AlB₂-derivative type), τ₆—Ce(Pd_xSi_1−x)₂ (ThSi₂-type) and τ₇—CePd_2−xSi_2+x. The crystal structures of compounds τ₄—Ce_~8Pd_~46Si_~46, τ₁₂—Ce_~29Pd_~49Si_~22, τ₁₅—Ce_~22Pd_~67Si_~11, τ₁₇—Ce_~5Pd_~77Si_~18 and τ₁₈—CePd_1−xSi_x (x~0.1) are still unknown.     

Use of Kirkwood–Buff Integrals for Extracting Distinct Diffusion Coefficients in Macromolecule–Solvent Mixtures

The possibility to extract velocity correlation quantities from fluctuation thermodynamic properties is explored in the case of macromolecule–solvent mixtures. Indeed, Kirkwood–Buff integrals, G_ij, together with self‐diffusion and viscosity data can provide an approximation for distinct diffusion coefficients (DDCs), D^d_ij. Herein, D^d_ij for binary polyethyleneglycol (PEG)(i)–water(0) systems is calculated. These systems show positive values of D^d_ii coefficients, indicating strong PEG–PEG interaction, and providing marker of water mediated PEG–PEG networks. The efficiency of several standard DDCs present in literature for D^d_ij analysis is compared, summarizing the usefulness of each one, depending on the nonideality degree.

     

Prediction of vapor–liquid and liquid–liquid equilibria for polymer systems: Comparison of activity coefficient models

A large number of equations of state and activity coefficient models capable of describing phase equilibria in polymer solutions are available today, but only a few of these models have been applied to different systems. It is therefore useful to investigate the performance of existing thermodynamic models for complex polymer solutions which have not yet been widely studied. The present work studies the application of several activity coefficient models [P.J. Flory, Principles of Polymer Chemistry, Cornell University Press, New York, NY, 1953; T. Oishi, J.M. Prausnitz, Estimation of solvent activities in polymer solutions using a group-contribution method, Ind. Eng. Chem. Process Design Dev. 17 (1978) 333; H.S. Elbro, A. Fredenslund, P. Rasmussen, A new simple equation for the prediction of solvent activities in polymer solutions, Macromolecules 23 (1990) 4707; G.M. Kontogeorgis, A. Fredenslund, D. Tassios, Simple activity coefficient model for the prediction of solvent activities in polymer solutions, Ind. Eng. Chem. Res. 32 (1993) 362; C. Chen, A segment-based local composition model for the Gibbs energy of polymer solutions, Fluid Phase Equilib. 83 (1993) 301; A. Vetere, Rules for predicting vapor–liquid equilibria of amorphous polymer solutions using a modified Flory–Huggins equation, Fluid Phase Equilib. 97 (1994) 43; C. Qian, S.J. Mumby, B.E. Eichinger, Phase diagrams of binary polymer solutions and blends, Macromolecules 24 (1991) 1655; Y.C. Bae, J.J. Shim, D.S. Soane, J.M. Prausnitz, Representation of vapor–liquid and liquid–liquid equilibria for binary systems containing polymers: applicability of an extended Flory–Huggins equation, J. Appl. Polym. Sci. 47 (1993) 1193; G. Bogdanic, J. Vidal, A segmental interaction model for liquid–liquid equilibrium calculations for polymer solutions, Fluid Phase Equilibria 173 (2000) 241] and activity coefficient from equations of state [F. Chen, A. Fredenslund, P. Rasmussen, Group-contribution Flory equation of state for vapor–liquid equilibria en mixtures with polymers, Ind. Eng. Chem. Res. 29 (1990) 875; M.S. High, R.P. Danner, Application of the group contribution lattice—fluids EOS to polymer solutions, AIChE J. 36 (1990) 1625]. The evaluation of these models was carried out both at infinite dilution and at finite concentrations and the results compared to experimental data. Furthermore, liquid–liquid equilibrium predictions for binary polymer solutions using six activity coefficient models are compared in this work. The parameters were estimated for all the models to achieve the best possible representation of the reported experimental equilibrium behavior.     

An improved perturbed hard-sphere equation of state

The Carnahan–Starling–Patel–Teja (CSPT) equation of state was revisited to improve the fitting accuracy of vapour–liquid equilibrium data of pure fluid substances. By setting the pseudo-critical compressibility factor and the correction coefficient in the attractive parameter as the temperature-dependent variables, the fitting accuracies of the vapour pressures and the saturated liquid-phase densities from the new CSPT increased significantly compared with the Patel–Teja equation of state (PT) and the Peng–Robinson equation of state (PR) and the original CSPT model. The new CSPT combined with temperature-dependent functions was applied to the vapour–liquid equilibrium data available for 45 pure substances. The results indicate that the new CSPT model can accurately reproduce the experimental vapour–liquid equilibria in the whole temperature and pressure range. The successful calculations of the PVT in the critical region suggest the new CSPT has wide applicability. The new CSPT model is also superior to PR and the original CSPT for calculating the phase behaviour of binary mixtures.     

A study on the liquid–liquid equilibria of 1-alkyl-3-methylimidazolium hexafluorophosphate with ethanol and alkanes

This work demonstrates the ability of the 1-alkyl-3-methylimidazolium hexafluorophosphate to act as an extraction solvent in petrochemical processes for the removal of alkanes from their azeotropic mixture with ethanol. LLE (liquid–liquid equilibrium) of the ternary systems hexane + ethanol + 1-hexyl-3-methylimidazolium hexafluorophosphate (HMIM PF₆) or 1-octyl-3-methylimidazolium hexafluorophosphate (OMIM PF₆) and heptane + ethanol + OMIM PF₆ are carried out at 298.15 K and atmospheric pressure. Experimental liquid–liquid data are correlated by using different equations. The solute distribution ratio and the selectivity, determined from tie-line data, suggest the efficiency of the ILs used as solvents. A comparison with other IL, in terms of solvent capacity, is included. The liquid–liquid extraction process is simulated by using conventional software and the obtained results are shown.     

Nanostructured Ni2P as a Robust Catalyst for the Hydrolytic Dehydrogenation of Ammonia–Borane

Ammonia–borane (AB) is a promising chemical hydrogen‐storage material. However, the development of real‐time, efficient, controllable, and safe methods for hydrogen release under mild conditions is a challenge in the large‐scale use of hydrogen as a long‐term solution for future energy security. A new class of low‐cost catalytic system is presented that uses nanostructured Ni₂P as catalyst, which exhibits excellent catalytic activity and high sustainability toward hydrolysis of ammonia–borane with the initial turnover frequency of 40.4 mol_(H2) mol_(Ni2P)^?1 min^?1 under air atmosphere and at ambient temperature. This value is higher than those reported for noble‐metal‐free catalysts, and the obtained Arrhenius activation energy (E_a=44.6 kJ mol^?1) for the hydrolysis reaction is comparable to Ru‐based bimetallic catalysts. A clearly mechanistic analysis of the hydrolytic reaction of AB based on experimental results and a density functional theory calculation is presented.