Universal critical amplitude ratios in binary mixtures of {benzonitrile + alkane}

Turbidity in the one-phase region and the isobaric heat capacity per unit volume in both one-phase and two-phase regions for the critical solutions of {benzonitrile + n-alkane} were measured, from which the values of the system-dependent critical amplitudes for the correlation length, the osmotic compressibility, the heat capacity and the correction-to-scaling term of the heat capacity were deduced. The previously reported data of the coexistence curves for {benzonitrile + n-alkane} were also reanalyzed with the crossover model to obtain the crossover parameters. Subsequently, these results together with the values of the critical amplitude related to the coexistence curve reported previously were used to calculate some universal critical amplitude ratios, which showed reasonable agreement with the theoretical predictions.     

The liquid–liquid coexistence curves of {x dimethyl adipate + (1 − x) n-octane} and {x dimethyl adipate + (1 − x) n-nonane} in the critical region

The liquid–liquid coexistence curves of (dimethyl adipate + n-octane) and (dimethyl adipate + n-nonane) have been determined within about 10 K from the critical temperatures, from which the critical amplitudes and the critical exponents are deduced. The critical exponents corresponding to the coexistence curve β are consistent with the 3D-Ising values. The experimental results have been analyzed to determine Wegner-correction terms and to discuss the asymmetric behaviour of the diameters of the coexistence curves by the complete scaling theory. Molar mass-dependences of the critical amplitude and the critical volume fraction have been shown to be consistent with the theoretical prediction.     

The liquid–liquid coexistence curves of {x dimethyl adipate + (1 − x) n-hexane} and {x dimethyl adipate + (1 − x) n-heptane} in the critical region

The liquid–liquid coexistence curves for (dimethyl adipate + n-hexane), (dimethyl adipate + n-heptane) have been measured, from which the critical amplitudes and the critical exponents are deduced. The critical exponent β corresponding to the coexistence curves are consistent with the 3D-Ising value. The experimental results have also been analyzed to determine the critical amplitudes of Wegner-correction terms when β and Δ are fixed at their theoretical values, and to examine the asymmetry of the diameters for the coexistence curves.     

The critical behavior of {water + AOT + decane} microemulsion with various molar ratios of water to AOT

To examine the critical behavior of the microemulsion, we have determined the coexistence curves for two ternary microemulsion systems of {water + sodium di(2-ethylhexyl) sulfosuccinate (AOT) + n-decane} with the molar ratios ω = (45.2 and 50.0) of water to AOT, respectively, by measuring refractive index at a constant pressure in the critical region. The critical exponent β and the critical amplitude B have been deduced from the coexistence curves. It was found that the values of β for both systems were consistent with the 3D-Ising exponent in a critical region. By increasing ω, i.e. the droplet size, the critical temperature and, to a lesser extent, the critical concentration decrease. The region of coexisting two phases was drastically reduced by an increase in the droplet size.     

Liquid heat capacity of the solvent system (piperazine + 2-amino-2-methyl-l-propanol + water)

This report presents a new set of heat capacity data for the system piperazine {(PZ) + 2-amino-2-methyl-1-propanol (AMP) + water (H₂O)}, measured using the differential scanning calorimetry technique, over the temperature range 303.2 K to 353.2 K and at fourteen (14) different concentrations in which the water mole fractions, x₃’s, were fixed at 0.60, 0.70, 0.80, and 0.90. Heat capacity for the binary system {PZ (1) + AMP (2)} at x₁ = 0.05, 0.10, 0.15, and 0.20 were, likewise, measured to generate parameters necessary in the Redlich–Kister-type model, which was used to estimate excess molar heat capacities. Such estimates were then used to predict the values of the molar heat capacity at the corresponding sets of temperature and concentration. The predicted values were subsequently compared against the measured values and the results are satisfactory.     

Liquid heat capacity of the solvent system (piperazine + n-methyldiethanolamine + water)

A new set of values for the heat capacity of aqueous mixtures of piperazine (PZ) and n-methyldiethanolamine (MDEA) at different concentrations and temperatures are reported in this paper. The differential scanning calorimetry technique was used to measure the property over the range T = 303.2 K to T = 353.2 K for mixtures containing 0.60 to 0.90 mole fraction water with 15 different concentrations of the system (PZ + MDEA + H₂O). Heat capacity for four concentrations of the binary system (PZ + MDEA) was also measured. A Redlich–Kister-type equation was adopted to estimate the excess molar heat capacity, which was used to predict the value of the molar heat capacity at a particular concentration and temperature, which would then be compared against the measured value. A total of 165 data points fit into the model resulted in a low overall average absolute deviation of 4.6% and 0.3% for the excess molar heat capacity and molar heat capacity, respectively. Thus, the results presented here are of acceptable accuracy for use in engineering process design.     

(Solid + liquid) phase equilibria and heat capacity of (diphenyl ether + biphenyl) mixtures used as thermal energy storage materials

The (solid + liquid) phase equilibrium for eight {x diphenyl ether + (1 − x) biphenyl} binary mixtures, including the eutectic mixture were studied by using a differential scanning calorimetry (DSC) technique. A good agreement was found between previous literature and experimental values here presented for the melting point and enthalpy of fusion of pure compounds. The well-known equations for Wilson and the non-random two-liquid (NRTL) were used to correlate experimental solid liquid phase equilibrium data. Moreover, the predictive mixture model UNIFAC has been employed to describe the phase diagram. With the aim to check this equipment to measure heat capacities in the quasi-isothermal Temperature-Modulated Differential Scanning Calorimetry method (TMDSC), four fluids of well-known heat capacity such as toluene, n-decane, cyclohexane and water were also studied in the liquid phase at temperatures ranging from (273.15 to 373.15) K. A good agreement with literature values was found for those fluids of pure diphenyl ether and biphenyl. Additionally, the specific isobaric heat capacities of diphenyl ether and biphenyl binary mixtures in the liquid phase up to T = 373.15 K were measured.     

Temperature dependence on mutual solubility of binary (methanol + limonene) mixture and (liquid + liquid) equilibria of ternary (methanol + ethanol + limonene) mixture

Mutual solubility data of the binary (methanol + limonene) mixture at the temperatures ranging from 288.15 K close to upper critical solution temperature, and ternary (liquid + liquid) equilibrium (tie-lines) of the (methanol + ethanol + limonene) mixture at the temperatures (288.15, 298.15, and 308.15) K have been obtained. The experimental results have been represented accurately in terms of the extended and modified UNIQUAC models with binary parameters, compared with the UNIQUAC model. The temperature dependence of binary and ternary (liquid + liquid) equilibrium for the binary (methanol + limonene) and ternary (methanol + ethanol + limonene) mixtures could be calculated successfully using the extended and modified UNIQUAC model.     

The critical phenomena of (water + AOT + decane) microemulsion with the molar ratio (ω = 30.0) of water to AOT

The coexistence curves of a ternary microemulsion system of {water + sodium di(2-ethylhexyl) sulfosuccinate (AOT) + n-decane} with the molar ratio (30.0) of water to AOT have been determined by measurements of refractive index at constant pressure within about 8 K from the critical temperature T_c. The critical exponent β and the critical amplitude B have been deduced from the coexistence curves. The experimental results have been analysed and compared with the system with molar ratio of 40.8 studied previously. It was found that the critical exponents β for both systems were consistent with the 3D-Ising value in a region sufficiently close to the critical temperature. The critical concentration was slightly affected by the molar ratio ω, but the critical temperature significantly was raised as the molar ratio ω was decreased. The volume fraction ϕ was the better choice of the concentration variable than the effective volume fraction ψ and the refractive index n used for constructing the order parameter for both systems.     

Thermodynamic evaluation and optimization of the (NaCl + KCl + MgCl2 + CaCl2 + MnCl2 + FeCl2 + CoCl2 + NiCl2) system

A complete critical evaluation of all available phase diagram and thermodynamic data has been performed for all condensed phases of the (NaCl + KCl + MgCl₂ + CaCl₂ + MnCl₂ + FeCl₂ + CoCl₂ + NiCl₂) system, and optimized model parameters have been found. The (MgCl₂ + CaCl₂ + MnCl₂ + FeCl₂ + CoCl₂ + NiCl₂) subsystem has been critically evaluated in a previous article. The model parameters obtained for the binary subsystems can be used to predict thermodynamic properties and phase equilibria for the multicomponent system. The Modified Quasichemical Model was used for the molten salt phase, and the (MgCl₂ + MnCl₂ + FeCl₂ + CoCl₂ + NiCl₂) solid solution was modeled using a cationic substitutional model with an ideal entropy and an excess Gibbs free energy expressed as a polynomial in the component mole fractions. Finally, the (Na,K)(Mg,Ca,Mn,Fe,Co,Ni)Cl₃ and the (Na,K)₂(Mg,Mn,Fe,Co,Ni)Cl₄ solid solutions were modeled using the Compound Energy Formalism.     

Hydrate phase equilibrium and structure for (methane + ethane + tetrahydrofuran + water) system

The separation of methane and ethane through forming hydrate is a possible choice in natural gas, oil processing, or ethylene producing. The hydrate formation conditions of five groups of (methane + ethane) binary gas mixtures in the presence of 0.06 mole fraction tetrahydrofuran (THF) in water were obtained at temperatures ranging from (277.7 to 288.2) K. In most cases, the presence of THF in water can lower the hydrate formation pressure of (methane + ethane) remarkably. However, when the composition of ethane is as high as 0.832, it is more difficult to form hydrate than without THF system. Phase equilibrium model for hydrates containing THF was developed based on a two-step hydrate formation mechanism. The structure of hydrates formed from (methane + ethane + THF + water) system was also determined by Raman spectroscopy. When THF concentration in initial aqueous solution was only 0.06 mole fraction, the coexistence of structure I hydrate dominated by ethane and structure II hydrate dominated by THF in the hydrate sample was clearly demonstrated by Raman spectroscopic data. On the contrary, only structure II hydrate existed in the hydrate sample formed from (methane + ethane + THF + water) system when THF concentration in initial aqueous solution was increased to 0.10 mole fraction. It indicated that higher THF concentration inhibited the formation of structure I hydrate dominated by ethane and therefore lowered the trapping of ethane in hydrate. It implies a very promising method to increase the separation efficiency of methane and ethane.     

Phase equilibrium data and thermodynamic modeling of the system (CO2 + biodiesel + methanol) at high pressures

The main objective of this work was to investigate the high pressure phase behavior of the binary systems {CO₂(1) + methanol(2)} and {CO₂(1) + soybean methyl esters (biodiesel)(2)} and the ternary system {CO₂(1) + biodiesel(2) + methanol(3)} were determined. Biodiesel was produced from soybean oil, purified, characterized and used in this work. The static synthetic method, using a variable-volume view cell, was employed to obtain the experimental data in the temperature range of (303.15 to 343.15) K and pressures up to 21 MPa. The mole fractions of carbon dioxide were varied according to the systems as follows: (0.2383 to 0.8666) for the binary system {CO₂(1) + methanol(2)}; (0.4201 to 0.9931) for the binary system {CO₂(1) + biodiesel(2)}; (0.4864 to 0.9767) for the ternary system {CO₂(1) + biodiesel(2) + methanol(3)} with a biodiesel to methanol molar ratio of (1:3); and (0.3732 to 0.9630) for the system {CO₂ + biodiesel + methanol} with a biodiesel to methanol molar ratio of (8:1). For these systems, (vapor + liquid), (liquid + liquid), (vapor + liquid + liquid) transitions were observed. The phase equilibrium data obtained for the systems were modeled using the Peng–Robinson equation of state with the classical van der Waals (PR-vdW2) and Wong-Sandler (PR–WS) mixing rules. Both thermodynamic models were able to satisfactorily correlate the phase behavior of the systems investigated and the PR–WS presented the best performance.     

Thermodynamic evaluation and optimization of the (MgCl2 + CaCl2 + MnCl2 + FeCl2 + CoCl2 + NiCl2) system

A complete critical evaluation of all available phase diagram and thermodynamic data has been performed for all condensed phases of the (MgCl₂ + CaCl₂ + MnCl₂ + FeCl₂ + CoCl₂ + NiCl₂) system, and optimized model parameters have been found. The model parameters obtained for the binary subsystems can be used to predict thermodynamic properties and phase equilibria for the multicomponent system. The Modified Quasichemical Model was used for the molten salt phase, and the (MgCl₂ + MnCl₂ + FeCl₂ + CoCl₂ + NiCl₂) solid solution was modeled using a cationic substitutional model with an ideal entropy and an excess Gibbs free energy expressed as a polynomial in the component mole fractions. This is the first of two articles on the optimization of the (NaCl + KCl + MgCl₂ + CaCl₂ + MnCl₂ + FeCl₂ + CoCl₂ + NiCl₂) system.     

Volumetric properties of ternary (IL + 2-propanol or 1-butanol or 2-butanol + ethyl acetate) systems and binary (IL + 2-propanol or 1-butanol or 2-butanol) and (1-butanol or 2-butanol + ethyl acetate) systems

The experimental densities for the binary or ternary systems were determined at T = (298.15, 303.15, and 313.15) K. The ionic liquid methyl trioctylammonium bis(trifluoromethylsulfonyl)imide ([MOA]⁺[Tf₂N]⁻) was used for three of the five binary systems studied. The binary systems were ([MOA]⁺[Tf₂N]⁻ + 2-propanol or 1-butanol or 2-butanol) and (1-butanol or 2-butanol + ethyl acetate). The ternary systems were {methyl trioctylammonium bis(trifluoromethylsulfonyl)imide + 2-propanol or 1-butanol or 2-butanol + ethyl acetate}. The binary and ternary excess molar volumes for the above systems were calculated from the experimental density values for each temperature. The Redlich–Kister smoothing polynomial was fitted to the binary excess molar volume data. Virial-Based Mixing Rules were used to correlate the binary excess molar volume data. The binary excess molar volume results showed both negative and positive values over the entire composition range for all the temperatures.The ternary excess molar volume data were successfully correlated with the Cibulka equation using the Redlich–Kister binary parameters.     

Critical behaviour of { water + n-nonane + sodium di(2-ethyl-1-hexyl)sulphosuccinate } microemulsions

Coexistence curves of ( T, n), ( T, ϕ), and ( T, Ψ), where n, ϕ, and Ψ are the refractive index, volume fraction and effective volume fraction ψ = ϕ / {ϕ +  [(1  − ϕ )ϕ_c / (1  − ϕ_c )]}, respectively, for ternary microemulsion systems of {water  + n -nonane  +  sodium di(2-ethyl-1-hexyl)sulphosuccinate} have been determined at temperatures within 8.7 K above the critical temperature by measurements of refractive index at constant pressure and a constant molar ratio of water to sodium di(2-ethyl-1-hexyl)sulphosuccinate. The critical exponent β deduced from ( T,n ), ( T, ϕ), and ( T, Ψ) coexistence curves was found consistent with nonmonotonic crossover observed in all aqueous ionic solutions. The values of β deduced from the experimental data in the range of 1 K above T_cwere consistent with the universality class of three-dimensional Ising-like systems. The coexistence curves have been interpreted by a combination of the Wegner expansion and the rectilinear diameter. The present results indicate that the molar mass dependence of critical amplitudes, we proposed recently, is valid for microemulsion systems.     

Hydrate phase equilibrium for the (hydrogen + tert-butylamine + water) system

The three-phase equilibrium conditions of ternary (hydrogen + tert-butylamine + water) system were first measured under high-pressure in a “full view” sapphire cell. The tert-butylamine–hydrogen binary hydrate phase transition points were obtained through determining the points of intersection of three phases (H–L_w–V) to two phases (L_w–V) experimentally. Measurements were made using an isochoric method. Firstly, (tetrahydrofuran + hydrogen) binary hydrate phase equilibrium data were determined with this method and compared with the corresponding experimental data reported in the literatures and the acceptable agreements demonstrated the reliability of the experimental method used in this work. The experimental investigation on (tert-butylamine + hydrogen) binary hydrate phase equilibrium was then carried out within the temperature range of (268.4 to 274.7) K and in the pressure range of (9.54 to 29.95) MPa at (0.0556, 0.0886, 0.0975, and 0.13) mole fraction of tert-butylamine. The three-phase equilibrium curve (H + L_w + V) was found to be dependent on the concentration of tert-butylamine solution. Dissociation experimental results showed that tert-butylamine as a hydrate former shifted hydrate stability region to lower pressure and higher temperature.     

Isothermal and isobaric (vapour + liquid) equilibria of (N,N- dimethylformamide + 2-propanol + 1-butanol)

The isothermal and isobaric (vapour  +  liquid) equilibria (v.l.e.) for (N, N - dimethylformamide  +  2-propanol  +  1-butanol) and the binary constituent mixtures were measured with an inclined ebulliometer. The experimental results are analyzed using the UNIQUAC equation with temperature-dependent binary parameters. The comparison between the experimental and literature results for binary systems is given. The ternary v.l.e. values are predicted from the binary results.     

Thermodynamic evaluation and optimization of the (NaCl + KCl + MgCl2 + CaCl2 + ZnCl2) system

A complete critical evaluation of all available phase diagram and thermodynamic data has been performed for all condensed phases and relevant gaseous species of the (NaCl + KCl + MgCl₂ + CaCl₂ + ZnCl₂) system, and optimized model parameters have been found. The (NaCl + KCl + MgCl₂ + CaCl₂) subsystem has been critically evaluated in a previous article. The model parameters obtained for the binary and ternary subsystems can be used to predict thermodynamic properties and phase equilibria for the multicomponent system. The Modified Quasichemical Model for short-range ordering was used for the molten salt phase.     

Critical behaviour of binary mixture of {xC6H5CN + (1 − x)CH3(CH2)7CH3}: Measurements of coexistence curves,light scattering,and heat capacity

Liquid + liquid coexistence, light scattering, and isobaric heat capacity per unit volume for the critical solutions of (benzonitrile + n-nonane) have been measured. The critical exponents relating to the coexistence curve β, the osmotic compressibility γ, the correlation length ν, and the heat capacity α have been deduced and the values are consistent with the 3D-Ising values in the range close to the critical point. The experimental results of the liquid + liquid coexistence were analyzed to examine the Wegner correction terms and the behaviour of the diameter of the coexistence curves. The light scattering data were well described by the crossover model proposed by Anisimov and Sengers, and showed a tendency of monotonic crossover of the critical exponents γ and ν from the 3D-Ising values to the mean-field values as the temperature departures from the critical point. From calorimetric measurements, the amplitude A^± and the critical background B_cr of the heat capacity in the critical region have been deduced and some universal ratios are tested.     

Isopiestic studies on the saturated systems {H2O + BaCl2(sat) + NaCl + NH4Cl} and {H2O + BaCl2(sat) + mannitol(sat) + NaCl + NH4Cl} at the temperature 298.15 K: Comparison with the ideal-like solution model

Isopiestic measurements have been carried out at the temperature 298.15 K for two saturated aqueous solutions: {H₂O + BaCl₂(sat) + NaCl + NH₄Cl} saturated with barium chloride and {H₂O + BaCl₂(sat) + mannitol(sat) + NaCl + NH₄Cl} saturated with barium chloride and mannitol. Taking sodium chloride (aq) as reference solutions, osmotic coefficients of the aqueous solutions were determined. The experimental results are well represented by the ideal-like solution model.