Phase Transitions and Critical Behaviour of Binary Liquid Mixtures

 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.     

Revised Phase Diagram of the System NaF–NaBF4

Summary. The phase diagram of the binary system NaF–NaBF₄ was determined using the thermal analysis method. Subsequent coupled analysis of the thermodynamic and phase diagram data was carried out to calculate the thermodynamically consistent phase diagram. The system NaF–NaBF₄ forms a simple eutectic phase diagram with the calculated coordinates of the eutectic point: 8.1 mol% NaF, 91.9 mol% NaBF₄, and 385.7°C. The probable inaccuracy in the calculated binary phase diagram is 9°C.     

Thermodynamic Investigation of Phase Equilibria in Metal Carbonate–Water–Carbon Dioxide Systems

Summary.  Solubility measurements as a function of temperature have been shown to be a powerful tool for the determination of thermodynamic properties of sparingly-soluble transition metal carbonates. In contrast to calorimetric methods, such as solution calorimetry or drop calorimetry, the evaluation of solubility data avoids many systematic errors, yielding the enthalpy of solution at 298.15 K with an estimated uncertainty of ±3 kJ · mol⁻¹. A comprehensive set of thermodynamic data for otavite (CdCO₃), smithsonite (ZnCO₃), hydrozincite (Zn₅(OH)₆(CO₃)₂), malachite (Cu₂(OH)₂CO₃), azurite (Cu₃(OH)₂(CO₃)₂), and siderite (FeCO₃) was derived. Literature values for the standard enthalpy of formation of malachite and azurite were disproved by these solubility experiments, and revised values are recommended. In the case of siderite, data for the standard enthalpy of formation given by various data bases deviate from each other by more than 10 kJ · mol⁻¹ which can be attributed to a discrepancy in the auxiliary data for the Fe²⁺ ion. A critical evaluation of solubility data from various literature sources results in an optimized value for the standard enthalpy of formation for siderite. The Davies approximation, the specific ion-interaction theory, and the Pitzer concept are used for the extrapolation of the solubility constants to zero ionic strength in order to obtain standard thermodynamic properties valid at infinite dilution, T = 298.15 K, and p = 10⁵ Pa. The application of these electrolyte models to both homogeneous and heterogeneous (solid-solute) equilibria in aqueous solution is reviewed. Received June 26, 2001. Accepted July 2, 2001     

Selected X-ray diffraction and differential scanning calorimetry investigations of the binary system K-palmitate/glycerol

Three mole fractions of the binary system K-palmitate/glycerol (KC₁₆/Gl) x_KC16 = 0.30, 0.37 and 0.50 have been investigated as a function of temperature by small- and wide-angle X-ray diffraction investigations and differential scanning calorimetry (DSC) measurements. The existence of a gel-like region, named G₁ in the preliminary binary phase diagram [4], could not be confirmed. Consequently, a corrected version of the phase diagram of the KC₁₆/Gl system is established. According to this corrected phase diagram at low K-palmitate concentrations, x_KC16 < 0.25, the transitions crystalline phase (C) ⇆ hexagonal phase, chains fluid (H_α) ⇆ isotropic, micellar phase (S) occur with rising temperature. At x_KC16 > 0.25 the transitions C ⇆ gel phase (G) ⇆ lamellar phase, chains fluid (L_α) were observed. X-ray diffraction and DSC measurements provided concordant results. Only differences in the phase transition temperatures from DSC curves obtained at rising and falling temperatures were observed. The phase transitions C ⇆ G, G ⇆ L_α and G ⇆ H_α correlate with a sharp shift in the d value of the first small-angle reflection. The occurrence of the G phase is accompanied by a distinct split of the first small-angle reflections. Simultaneously, the wide-angle reflections change and the peak intensity is reduced. Received: 14 April 1999 Accepted: 28 June 1999     

Theoretical study of group 11 metal–silonyl complexes: M–SiO and M–(SiO)2 (M = Cu, Ag, or Au)

 The spectroscopic properties of M–SiO and M–(SiO)₂ (1–1 and 1–2 complexes with M = Cu, Ag, or Au) have been theoretically studied. It has been shown that both M–SiO and M–(SiO)₂ compounds in their ground state are bent with a metal–Si bonded structure. The calculated M(ns) spin density agrees well with the electron spin resonance experimental data. From a topological analysis, it has been shown that a rather large charge transfer occurs from the metal towards the SiO moiety, and that the M–Si bond energy correlates with the electron density located at the M–Si bond path (bond critical point). Received: 6 July 2000 / Accepted: 11 October 2000 / Published online: 19 January 2001     

Comparison of Prediction of Phase Equilibria in the Ag–In–Sb System at 200°C with Experimental Data

Summary. Binary thermodynamic data, successfully used for phase diagram calculations of binary systems Ag–In, Ag–Sb, and In–Sb, were used for prediction of phase equilibria in ternary Ag–In–Sb system at 200°C. Symmetrical Redlich–Kister–Muggianu model for ternary thermodynamic function calculation was proved to be best valid in this ternary system. Predicted equilibria were compared with experimentally (SEM, EDX) determined composition of phases in chosen alloys after long term annealing and with the results of DTA measurements.     

An atom-in-molecules and electron-localization-function study of the interaction between O2 and VxOy+/VxOy (x = 1, 2, y = 1–5) clusters

 The most stable structures of V _x O _y ⁺/V _x O _y (x=1, 2, y=1–5) clusters and their interaction with O₂ are determined by density functional calculations, the B3LYP functional with the 6-31G* basis set. The nature of the bonding of these clusters and the interaction with O₂ have been studied by topological analysis in the framework of both the atoms-in-molecules theory of Bader and the Becke–Edgecombe electron localization function. Bond critical points are localized by means of the analysis of the electron density gradient field, ∇ρ(r), and the electron localization function gradient field, ∇η(r). The values of the electron density properties, i.e., electron density, ρ(r), Laplacian of the electron density, ∇²ρ(r), and electron localization function, η(r), allow the nature of the bonds to be characterized, and linear correlation is found for the results obtained in both gradient fields. Vanadium-oxygen interactions are characterized as unshared-electron interactions, and linear correlation is observed between the electron density properties and the V–O bond length. In contrast, O₂ units involve typical shared-electron interactions, as for the dioxygen molecule. Four different vanadium–oxygen interactions are found and characterized: a molecular O₂ interaction, a peroxo O₂ ²⁻ interaction, a superoxo O₂ ⁻ interaction and a side-on O₂ ⁻ interaction. Received: 15 October 2001 / Accepted: 30 January 2002 / Published online: 24 June 2002     

Thermodynamic Investigation of Phase Equilibria in Metal Carbonate–Water–Carbon Dioxide Systems

 Solubility measurements as a function of temperature have been shown to be a powerful tool for the determination of thermodynamic properties of sparingly-soluble transition metal carbonates. In contrast to calorimetric methods, such as solution calorimetry or drop calorimetry, the evaluation of solubility data avoids many systematic errors, yielding the enthalpy of solution at 298.15 K with an estimated uncertainty of ±3 kJ · mol⁻¹. A comprehensive set of thermodynamic data for otavite (CdCO₃), smithsonite (ZnCO₃), hydrozincite (Zn₅(OH)₆(CO₃)₂), malachite (Cu₂(OH)₂CO₃), azurite (Cu₃(OH)₂(CO₃)₂), and siderite (FeCO₃) was derived. Literature values for the standard enthalpy of formation of malachite and azurite were disproved by these solubility experiments, and revised values are recommended. In the case of siderite, data for the standard enthalpy of formation given by various data bases deviate from each other by more than 10 kJ · mol⁻¹ which can be attributed to a discrepancy in the auxiliary data for the Fe²⁺ ion. A critical evaluation of solubility data from various literature sources results in an optimized value for the standard enthalpy of formation for siderite. The Davies approximation, the specific ion-interaction theory, and the Pitzer concept are used for the extrapolation of the solubility constants to zero ionic strength in order to obtain standard thermodynamic properties valid at infinite dilution, T = 298.15 K, and p = 10⁵ Pa. The application of these electrolyte models to both homogeneous and heterogeneous (solid-solute) equilibria in aqueous solution is reviewed.     

Frequency dispersion of the viscoelastic properties of solutions of electrolytes

Analytical expressions obtained earlier are used to numerically calculate the dynamic coefficients of the bulk η_ν(ω) and shear η _s (ω) viscosity and the corresponding modules of their bulk K(ω) and shear μ(ω) elasticity at a certain choice of the model of solution structure in an approximation of the osmotic solution theory. The potential energy of the interaction between ions Φ _ab (r) was taken as the sum of the Lennard-Jones potential and the generalized Debye potential, taking into account the configuration and size of ions. In this approximation, the viscoelastic properties of the NaCl water solution were numerically calculated over a wide interval of change in the thermodynamic parameters and frequency ranges. Satisfactory agreement with the literature experimental data was obtained.     

Thermal Analysis of the System Na3AlF6–NaVO3

Summary. The phase diagram of the system Na₃AlF₆–NaVO₃ was determined by means of thermal analysis. The system is a simple binary eutectic one. The eutectic point was estimated at x(NaVO₃) = 0.975 and t _eut = 617°C. The XRD patterns of samples after thermal analysis revealed the presence of cryolite and NaVO₃ only supporting the above assumption of a simple eutectic binary system.     

Statistical–mechanical models with separable many-body interactions: especially partition functions and thermodynamic consequences

We start from a classical statistical–mechanical theory for the internal energy in terms of three- and four-body correlation functions g ₃ and g ₄ for homogeneous atomic liquids like argon, with assumed central pair interactions f(r_ij){\phi(r_{ij})} . The importance of constructing the partition function (pf) as spatial integrals over g ₃, g ₄ and f{\phi} is stressed, together with some basic thermodynamic consequences of such a pf. A second classical example taken for two-body interactions is the so-called one-component plasma in two dimensions, for a particular coupling strength treated by Alastuey and Jancovici (J Phys (France) 42:1, 1981) and by Fantoni and Tellez (J Stat Phys 133:449, 2008). Again thermodynamic consequences provide a particular focus. Then quantum–mechanical assemblies are treated, again with separable many-body interactions. The example chosen is that of an N-body inhomogeneous extended system generated by a one-body potential energy V(r). The focus here is on the diagonal element of the canonical density matrix: the so-called Slater sum S(r, β), related to the pf by pf(b) = òS(r, b)d[(r)\vec]{{\rm pf}(\beta) = \int {S({\bf r}, \beta)}d\vec {r}}, β = (k _B T)⁻¹. The Slater sum S(r, β) can be related exactly, via a partial differential equation, to the one-body potential V(r), for specific choices of V which are cited. The work of Green (J Chem Phys 18:1123, 1950), is referred to for a generalization, but now perturbative, to two-body forces. Finally, to avoid perturbation series, the work concludes with some proposals to allow the treatment of extended assemblies in which regions of long-range ordered magnetism exist in the phase diagram. One of us (Z.D.Z.) has recently proposed a putative pf for a three-dimensional (3D) Ising model, based on two, as yet unproved, conjectures and has pointed out some important thermodynamic consequences of this pf. It would obviously be of considerable interest if such a pf, together with conjectures, could be rigorously proved.     

Optimization and Calculation of the EuCl<Subscript>3</Subscript>–MCl (M = Na,K, Rb,Cs) Phase Diagrams

By using the CALPHAD technique, an optimization of the binary EuCl₃–MCl (M = Na, K, Rb, Cs) systems has been carried out. To describe the Gibbs energies of liquid phases in these systems the new modified quasi-chemical model was used in the pair-approximation for short-range ordering. From the measured phase equilibrium data and the experimental thermo-chemical properties, the EuCl₃–MCl phase diagrams were optimized and calculated. A set of thermodynamic functions has been optimized based on an interactive computer-assisted analysis. The calculated phase diagrams and thermodynamic data are self-consistent.     

Spin Crossover Properties of the [Fe( PM - BiA )2(NCS)2] Complex – Phases I and II

Summary.  In the present review, we reexamine the photomagnetic properties of the [Fe(PM-BiA)₂(NCS)₂], cis-bis(thiocyanato)-bis[(N-2′-pyridylmethylene)-4-(aminobiphenyl)]iron(II), compound which exhibits, depending on the synthetic method, an exceptionally abrupt spin transition (phase I) with a very narrow hysteresis (T _1/2↓ = 168 K and T _1/2↑ = 173 K) or a gradual spin conversion (phase II) occurring at 190 K. In both cases, light irradiation in the tail of the ¹MLCT-LS absorption band, at 830 nm, results in the population of the high-spin state according to the light-induced excited spin-state trapping (LIESST) effect. The capacity of a compound to retain the light-induced HS information, estimated through the T(LIESST) experiment, is determined for both phases. Interestingly, the shape of the T(LIESST) curve is more gradual for the phase II than for the phase I and the T(LIESST) value is found considerably lower in the case of the phase II. The kinetics parameters involved in the photoinduced high-spin→low-spin relaxation process are estimated for both phases. From these data, the experimental T(LIESST) curves are simulated and the particular influence of the cooperativity as well as of the parameters involved in the thermally activated and tunneling regions are discussed. The Light-Induced Thermal Hysteresis (LITH), originally described for the strongly cooperative phase I, is also reinvestigated. The quasi-static LITH loop is determined by recording the photostationary points in the warming and cooling branches. Corresponding authors. E-mail: letard@icmcb.u-bordeaux.fr Received August 26, 2002; accepted August 30, 2002     

Thermodynamics of the interaction of liquid-crystalline polypropyleneimine dendrimer with low-molecular-weight compounds studied by reversed-phase gas chromatography

The thermodynamic functions of dissolution of n-alkanes (C₇–C₉) and n-alkanols (C₅–C₈) in the liquid-crystalline and isotropic phases of polypropyleneimine dendrimer of the first generation at infinite dilution were determined by the reversed-phase gas chromatography. The dependences of the thermodynamic parameters of sorbates on the phase state of the dendrite solvent, hydrocarbon chain length, and polarity of low-molecular-weight components of mesogenic—nonmesogenic binary systems were considered. The role of dispersion forces and specific intermolecular interactions in the solutions under study was estimated. Saturated hydrocarbons are more compatible with columnar phases of the dendrimer than alcohols.     

The Potential Energies of Cohesion of a Crystalline Organic Enantiomer and the Racemate; on the Energy for the Liquid Racemate [1]

Summary. The cohesion potential energy of the crystal of one enantiomer of ethyl 3-cyano-3-(3,4-dimethyloxyphenyl)-2,2,4-trimethylpentanoate, −47.7 ± 0.1 kJ mol⁻¹ (0–90°C), was found out from the heat of sublimation (123.2 ± 5.1 kJ mol⁻¹, 78.6°C) and the kinetic energies for the gas phase and the crystal. It was found that the entropy function of Debye’s theory of solids mathematically agreed with the vibrational entropy of the gas (variationally obtained), allowing to disclose the vibrational energy using the Debye energy function (E _vib 835.0 kJ mol⁻¹ (78.6°C), E ⁰ included). E _kin for the crystal (771.1 kJ mol⁻¹ (78.6°C)) was obtained by Debye’s theory with the experimental heat capacity. The cohesion energy represented a moderate part of the sublimation energy. The cohesion energy of the racemic crystal, −44.2 kJ mol⁻¹, was obtained by the heat of formation of the crystal in the solid state (3.0 kJ mol⁻¹, 83.3°C) and E _kin for the crystal (by Debye’s theory). The decrease in cohesion on formation of the crystal accounted for the energy of formation. The change in potential energy on liquefaction of the racemate from the gas state was disclosed obtaining added-up E _{vib + rot} for the liquid in the way as to E _vib for the gas, the Debye entropy function being increasedly suited for the liquid (E _{vib + rot} 763.4 kJ mol⁻¹ (115.4°C)). Positive ΔE _pot, 13.0 kJ mol⁻¹, arised from the increase in electronic energy (Δ _l ν_mean − 154.3 cm⁻¹, by the dielectric nature of the liquid), added to the cohesion energy.     

Complexation of M–(buffer) x –(OH) y Systems Involving Divalent Ions (Cobalt or Nickel) and Zwitterionic Biological Buffers (AMPSO, DIPSO, TAPS and TAPSO) in Aqueous Solution

The complexation behavior of eight M–(buffer) _x –(OH) _y systems involving two divalent ions (cobalt and nickel) and four zwitterionic biological buffers (AMPSO, DIPSO, TAPS and TAPSO) were characterized. Complex formation was detected for all eight M–(buffer) _x –(OH) _y systems studied, but fully defined final models were obtained for only four of these systems. For systems involving cobalt or nickel with AMPSO or TAPS, a complete characterization of the systems was not possible in the studied buffer pH-range. Metal complexation was studied by glass-electrode potentiometry (GEP) and UV-Vis spectroscopy at 25.0 °C and I=0.1 mol⋅dm⁻³ KNO₃ ionic strength. For the Ni–(L) _x –(OH) _y and Co–(L) _x –(OH) _y systems, with L = TAPSO or DIPSO, the proposed final models and overall stability constants were obtained by combining results from both techniques. For the Ni–(L) _x –(OH) _y systems, the measured values of the stability constants are log ₁₀ β _NiL=3.0±0.1 and log ₁₀ β _NiL2=4.8±0.1 for L = TAPSO, and log ₁₀ β _NiL=2.7±0.1 and log ₁₀ β _NiL2=4.6±0.1 for L = DIPSO. For the Co–(L) _x –(OH) _y systems, the overall stability constants are log ₁₀ β _CoL=2.2±0.1, log ₁₀ β _CoL2=3.6±0.2 and log ₁₀ β _CoL(OH)=7.6±0.1 for L = TAPSO, and log ₁₀ β _CoL=2.0±0.1 and log ₁₀ β _CoL(OH)=7.8±0.1 for L = DIPSO. For both buffers, the CoL(OH) species is characterized by a major structural rearrangement.     

Raman scattering spectra and molecular conformations of bis(quaternaryammonium bromide)-water systems

The dimeric bis(quaternaryammonium bromide) surfactants, [Br⁻(CH₃)₂N⁺(C _m H_{2 m +1})—(CH₂) _s —(C _m H_{2 m +1})N⁺(CH₃)₂Br⁻, s = 2, 3 and m = 4, 6, 10 and 12, s = 6 and m = 8, 10, 12], have been synthesized and the phase maps of the sm6-8-water, sm6-10-water and sm6-12-water binary systems have been determined (sm6-8 implies s = 6, m = 8). In order to examine the molecular structures of these solid samples and of their dimeric surfactant-water binary systems, Raman spectra of the simple dimeric surfactants, sm2-4 and sm3-4, in which crystal structures of the trans- and cis-type conformations have been determined by single-crystal X-ray diffraction analysis, have been investigated, and Raman bands characteristic of these skeletal structures were found in the skeletal deformation region. On the basis of these characteristic Raman bands for the two conformations, it has been concluded that the dimeric surfactants, sm6-8, sm6-10 and sm6-12 also take up a cis-type conformation in the crystalline state. Furthermore, it has been found that the Raman bands in the C—H stretching, skeletal stretching and CH₂ scissoring regions are sensitive to phase structure. Received: 21 July 1998 Accepted in revised form: 9 November 1998     

Influence of the Phase Morphology on the Viscoelastic Behaviour of Polymer Blends (PP-EPR)

Summary. Melts of polyethylene-propylene-rubber (EPR, blends of linear polyethylene, linear polypropylene, and PE-PP copolymer) show phase separation. The influence of the phase morphology on the viscoelastic behaviour is studied with the aid of the dynamical moduli. The measured moduli of the fraction of the linear homopolymer of an EPR agree with the moduli calculated from the molar mass distribution of this fraction. In contrast, the copolymer fraction shows a strong rubber-like behaviour (represented by a characteristic relaxation time spectrum). Mixtures of 80 wt% linear PP and of EPRs with low copolymer content are not rubber-like liquids. In addition, the moduli from them can be calculated from the moduli of the components with the aid of Palierne’s emulsion model. This clearly reveals that the linear PP forms the matrix in this case. Mixtures of 80 wt% linear PP and of EPRs with high copolymer content show rubber-like behaviour and Palierne’s emulsion model is not applicable on them. Obviously, the copolymer fraction forms a physical network.     

Thermodynamic characteristics of the acid dissociation of dopamine hydrochloride in water-ethanol solutions

Enthalpies of the interaction of protonated dopamine with a hydroxide ion in water-ethanol mixtures in the concentration range of 0–0.8 EtOH mole fractions are measured calorimetrically. The neutralization process of dopamine hydrochloride is shown to occur endothermally in solvents with an ethanol concentration of ≥0.5 mole fractions. Standard thermodynamic characteristics (Δ_r H ^○, Δ_r G ^○, and Δ_r S ^○) of the first-step acid dissociation of dopamine hydrochloride in solutions are calculated with regard to the autoprotolysis enthalpy of binary solvents. It is found that dissociation enthalpies vary within 9.1–64.8 kJ/mol, depending on the water-ethanol solvent composition.