Redlich Kister Polynomial Expansions Research Articles

Measurements of the density and viscosity of binary mixtures of (hyper-branched polymer, B-H2004 + 1-butanol, or 1-hexanol, or 1-octanol, or methyl tert-butyl ether)

Density and viscosity were determined for binary mixtures of {hyper-branched polymer, Boltorn H2004 (B-H2004) + 1-alcohol (1-butanol, 1-hexanol, and 1-octanol)} at T = (298.15, 308.15, 318.15, 328.15, and 338.15) K and of {B-H2004 + methyl tert-butyl ether (MTBE)} at T = (298.15, 308.15, and 318.15) K and ambient pressure. The temperature dependence of density and viscosity is described by linear regression and by the Vogel–Fucher–Tammann equation, respectively. Excess volumes for the system {B-H2004 + MTBE} are presented as a function of mass fraction. Viscosity deviations were calculated and correlated by the Redlich–Kister polynomial expansions using also the mass fractions. The polynomial correlations describe the variation of viscosity with composition. A qualitative discussion on these quantities in terms of molecular interactions is reported.

Effect of Temperature and Composition on the Density and Viscosity of Binary Mixtures of Ionic Liquid with Alcohols

Density and viscosity were determined for the binary mixtures containing the ionic liquid 1-butyl-3-methylimidazolium thiocyanate ([BMIM][SCN]) and 1-alcohols (1-butanol, 1-pentanol and 1-hexanol) at six temperatures (298.15, 308.15, 318.15, 328.15, 338.15 and 348.15) K and ambient pressure. The density and viscosity correlation for these systems was tested by an empirical second-order polynomial and by the Vogel-Fucher-Tammann equation in wide ranges of temperatures. Excess molar volumes were described by the Redlich-Kister polynomial expansions. The density and viscosity variations with composition were described by polynomials. A qualitative analysis of the trend of the properties with solvent and temperature was performed. The obtained results indicate that ionic liquid interactions with 1-alcohols are strongly dependent on the special trend of packing of this ionic liquid into hydroxylic solvents. As previously observed, an increase of the 1-alcohol carbon-chain length leads to lower interactions on mixing.

Temperature and composition dependence of the density and viscosity of binary mixtures of (1-decanol + fragrance material)

Density and viscosity were determined for binary mixtures containing 1-decanol and three fragrance raw materials based on cyclohexane: cyclohexyl carboxylic acid (CCA), or cyclohexyl acetate (CA), or 2-cyclohexyl ethyl acetate (2CEA) in wide range of temperatures from 300 to 340 K and atmospheric pressure. Excess molar volumes were calculated and correlated by the Redlich–Kister polynomial expansions involving parameters dependent on temperature for the mixtures. The polynomial correlations describe the variation of density and viscosity with composition. The coefficient of thermal expansion, α was described for all pure fragrance raw materials and their mixtures and related excess property has been calculated. The temperature dependence of density and viscosity for these systems can be described by an empirical second-order polynomial and by the Vogel–Fulcher–Tammann equation, respectively. Comparison of the results for three binary systems elucidates the influence of the substituent at the cyclohexane ring on their physical and volumetric properties.

Temperature and composition dependence of the density and viscosity of binary mixtures of (hyperbranched polymer, B-U3000 + 1-alcohol, or ether)

Density and viscosity were determined for binary mixtures of {hyperbranched polymer, a fatty acid modified dendritic polymer Boltorn U3000 (B-U3000) + 1-alcohol (1-butanol, 1-hexanol, and 1-octanol)} at T = (298.15, 308.15, 318.15, 328.15, and 338.15) K and of {B-U3000 + tert-butyl-methylether (MTBE)} at T = (298.15, 308.15, and 318.15) K and ambient pressure. The temperature dependence of density and viscosity for these systems can be described by linear regression and by the Vogel–Fucher–Tammann equation, respectively. Excess volumes were discussed in a function of mass fractions. Viscosity deviations were calculated and correlated by the Redlich–Kister polynomial expansions using also the mass fractions. The polynomial correlations describe the variation of viscosity with composition. A qualitative discussion on these quantities in terms of molecular interactions is reported.

Thermodynamic properties of liquid silver–indium alloys determined from e.m.f. measurements

The thermodynamic properties of the liquid Ag–In alloys were determined using solid oxide galvanic cells with zirconia electrolyte. The e.m.f.'s of the cells Re + kanthal, Ag x In (1− x) ,In 2O 3//ZrO 2 + (Y 2O 3)//NiO, Ni, Pt were measured in the temperature range from 950 to 1273 K, and in the molar fraction from x In = 0.15 to 1.0. At first, the Gibbs free energy of formation of pure solid indium oxide, In 2O 3, from pure elements was derived. Using values of the e.m.f.'s measured for the cell with x In = 1.0, the following temperature dependence was obtained: Δ f G m , In 2 O 3 0 ( ± 1000 mo l − 1 J ) = − 911570 + 313.10 T Next, the activities of indium were derived as a function of the alloy composition from measured e.m.f.'s. Activities of silver were calculated using Gibbs–Duhem equation. Also, using Darken's α-function formalism, activity coefficient of indium at infinite dilution in silver was calculated. These data taken together with the heat of mixing values which are available in the literature enabled the description of the thermodynamic properties of the liquid phase with Redlich–Kister polynomial expansion. Finally, the Ag–In phase diagram was recalculated using ThermoCalc software. The limiting value of the logarithm of the activity coefficient of indium in silver was also given as a function of temperature.

Thermodynamic properties of liquid silver–antimony alloys determined from emf measurements

The thermodynamic properties of the liquid Ag–Sb alloys were determined using solid oxide galvanic cells with zirconia electrolyte. The emfs of the cells: Ag x Sb (1−x), Sb 2 O 3/ O 2−/ air were measured in the temperatures range 950–1100 K in the whole range of the alloy compositions. First, the Gibbs free energy of formation of liquid Sb 2O 3 from pure elements was derived: ΔG° f( Sb 2 O 3) ( J/ mol)=−687100+243.23T. Next, the activities of antimony were measured as a function of the alloy compositions, x. Redlich–Kister polynomial expansion was used to describe the thermodynamic properties of the liquid phase. From the model equations the limiting value of the logarithm of activity coefficient of antimony in silver was obtained as a function of temperature: ln γ Sb 0=−3812.5/T+0.4112. The obtained results were compared with the experimental values reported in the literature.

Surface tension and thermodynamic properties of liquid Ag-Bi solutions

With the maximum bubble pressure method, the density and surface tension were measured for five Ag-Bi liquid alloys (XBi = 0.05, 0.15, 0.25, 0.5, and 0.75), as well as for pure silver. The experiments were performed in the temperature range 544-1443 K. Linear dependences of both density and surface tension versus temperature were observed, and therefore the experimental data were described by linear equations. The density dependence on concentration and temperature was derived using the polynomial method. A similar dependence of surface tension on temperature and concentration is presented. Next, the Gibbs energy of formation of solid Bi2O3, as well as activities of Bi in liquid Ag-Bi alloys, were determined by a solidstate electromotive force (emf) technique using the following galvanic cells: Ni, NiO, Pt/O �2 /W, AgXBi(1�X), Bi2O3(s). The Gibbs energy of formation of solid Bi2O3 from pure elements was derived: G 0�Bi2O3) = �598 148 + 309.27T [J mol �1 ] and G 0�Bi2O3) = �548 009 + 258.94T [J mol �1 ]; the temperature and the heat of the → transformation for this solid oxide were calculated as 996 K and 50.1 4J·m ol �1 . Activities of Bi in the liquid alloys were determined in the temperature range from 860-1075 K, for five Ag-Bi alloys (XAg= 0.2, 0.35, 0.5, 0.65, 0.8), and a Redlich-Kister polynomial expansion was used to describe the thermodynamic properties of the liquid phase. Using Thermo-Calc software, the Ag-Bi phase diagram was calculated. Finally, thermodynamic data were used to predict surface tension behavior in the Ag-Bi binary system.

Computer coupling of thermodynamics and phase diagrams: the gadolinium-magnesium system as an example

A thermodynamic analysis of the binary Gd-Mg system is presented, and its description is optimized using the experimental phase diagram and thermodynamic values. The excess Gibbs energies of the liquid and solid (α-Gd, β-Gd and Mg) solutions were described according to the Redlich-Kister polynomial expansion. The intermediate compounds (GdMg, GdMg 2, GdMg 3 and GdMg 5) were assumed to be stoichiometric phases. A good agreement between the experimental and the computed phase diagram is shown. The results are briefly discussed and compared with those for other binary rare earth-Mg alloys.