Molar Free Energies Of Mixing Research Articles

Phase equilibria and thermodynamic description of solid dispersions of 8-hydroxyquinoline – 4-chlorobenzoic acid drug system

In present article 8-hydroxyquinoline (HQ)-4-chlorobenzoic acid (CBA) binary drug system has been undertaken to study phase diagram and thermodynamic contribution in the system in terms of partial and integral mixing and excess functions. The phase equilibria of the system undertaken shows the formation of 1:1 addition compound C and its eutectic E at 214º and199º c respectively. The negative value of molar free energy of mixing (∆GM) of solid dispersion at 0.810 and 0.895 mole fraction of CBA suggests that the mixing in these cases is spontaneous. The integral molar enthalpy of mixing value corresponds to the value of excess integral molar free energy of the system favors the regularity in the binary solutions. The positive value of excess free energy (gE) for all the eutectic and noneutectic solid dispersion suggests an association of weaker nature between unlike molecules and of stronger nature between like molecules. Gibbs-Duhem equation gives the graphical solution of partial molar heat of mixing (Hi-M), activity and activity coefficient of a particular constituent in the binary mix. Interfacial roughness of the binary solid dispersion has also been explained. Keywords: Binary drug dispersion, phase diagram, activity, activity coefficient, mixing and excess function.

Compatibility between Paclitaxel and Polymer Carrier

Several polymer-based drug delivery systems are being developed to enhance the extremely low water-solubility of paclitaxel (PTX). It is believed that there is a positive correlation between the compatibility of polymer-drug and the solubilization. In recent years, solubility parameters for polymer and drug were used to evaluate degree of compatibility between a drug and a polymer, which were measured using various experimental methods or estimated using the group contribution menthod (GCM). In this study, degree of compatibility between PTX and polymers were estimated by molar free energy of mixing (Δ̗mix) that was calculated through computer simulation. It is found that the degree of compatibility is: PTX-PTRP > PTX-PLBG > PTX-PLGA > PTX-PCL > PTX-PLA. It has been demonstrated that the result of this study is in accord with the Similar Dissolve Mutually Theory.

Gas–liquid chromatographic study of polystyrene–n‐alkane interactions

AbstractGas–liquid chromatography is used to study the thermodynamic interactions between polystyrene and n‐alkanes (C6–C10). Polystyrene is used as a stationary phase with n‐alkanes as the probe molecules. Retention times and specific retention volumes are measured over the temperature interval of 60 to 170°C. Partial molar free energy of mixing, polymer–solvent interaction parameter, glass‐transition temperature, and solubility parameter of polystyrene at infinite dilution are calculated. Experimental results are discussed in terms of the theoretical calculations and size of the probe molecules. © 2001 John Wiley & Sons, Inc. J Appl Polym Sci 80: 1291–1298, 2001

Estimation of Solubility Parameters of Poly(Methyl Methacrylate) and Derivatives by Inverse Gas Chromatography

Abstract Flory – Huggins polymer–solute interaction (χ1 2) parameters have been determined by inverse gas chromatography (i.g.c.) at 453–463 K for alkanes, alcohol, acetates, ketones and O – Xylene in PMMA, PEMA, PIBMA and Pt-BMA to estimate the polymer solubility parameters (δ2) Partial molar free energies of mixing (ΔG1 ∞) and weight fraction activity coefficients of solute probes at infinite dilution (Ω1 ∞) were calculated at temperature range 453–463 K.

Ｃｕ‐Ｚｎ‐Ｘ（Ｘ＝Ｐｂ，Ａｇ，Ａｕ）３元系溶融合金の活量測定

As a fundamental study of new zinc smelting processes in which liquid copper is used to recover zinc in a liquid Cu-Zn alloy, activity measurements in the liquid Cu-Zn-Pb, Cu-Zn Ag and Cu-Zn-Au ternary alloys were conducted at 1, 075 K using an isothermal isopiestic method.Activity of zinc in the Cu-Zn-Pb system forming a wide miscibility gap in the liquid phase represented a very large negative deviation from a Raoultian behavior. The isoactivity lines showed a good agreement with the tie-lines of the miscibility gap. On the other hand, the activities of zinc in the Cu-Zn-Ag and Cu-Zn-Au systems forming electron compounds in the solid phase represented negative deviations from the Raoultin behavior. The deviation in the Cu-Zn-Au system was much larger than that in the Cu-Zn-Ag system, owing to the large difference in the electronegativity factor between the systems.A Redlich-Kister polynomial formula with the first order for expressing the excess molar free energy of mixing as a function of the alloy compositions was applied to the ternary systems, and the constants in the formula were determined by a regression analysis of the obtained data. The vapor pressure over the ternary melts was estimated at 1, 423 K, using the derived constants.

Vaporization study on fission-produced noble metal alloys by mass-spectrometric method

Abstract The vapor pressures over the ϵ-phase of the MoxRuyPdz alloys (x = 0.20-0.45, y = 0.15–0.60, z = 0.20–0.40) were measured by means of mass spectrometry in the temperature range 1536–1791 K. Palladium vapor was observed as the only gaseous species. The chemical activities of palladium in the alloys, determined from the vapor pressures of Pd(g), were compared with those calculated on the basis of the regular solution model using the Kaufman and Bernstein parameters. Applying a least-squares fit to the chemical activity of palladium obtained experimentally in this study, the interaction parameters and the free energy of formation were determined for the regular solution model and the Hillert model. The vapor pressures of Mo(g) and Ru(g) over the Mo-Ru-Pd alloys were calculated using the regular solution model. Thermodynamic quantities such as the partial molar free energy of mixing, the excess partial molar free energy of palladium and the partial molar enthalpy and entropy of Pd(g) over the Mo-Ru-Pd alloys were also calculated from the palladium vapor pressures.

Solubility parameters of gas chromatographic mixed stationary phases

Gas chromatography was used to measure activity coefficients, ϒ ∞, partial molar free energies of mixing, Δ G − ∞ 1, Flory-Huggins interaction parameters, χ ∞, and its enthalpic and entropic contributions, of a number of solutes on five single and fourteen mixed stationary phases at 120°C. Solubility parameters of the stationary phases, δ 2, were deduced by the method of DiPaola-Baranyi and Guillet for the different solute-stationary phase combinations. The polymer-polymer interaction parameter, χ′ 2,3, was also calculated for the various mixed systems.

Thermodynamics of polymer systems

Gas chromatography has been employed to determine partial molar free energies of sorption, ΔC1s, as well as partial molar free energies of mixing, ΔC1∞, of atactic poly(styrene) with linear and branched alkanes (C6-C9), alkenes (C8), cyclohexane and alkylbenzenes (Ph-H to PhC6H13) within the temperature range from 403 to 463 K. The influence of nature and constitution of the solute molecule on sorption and mixing properties in poly(styrene) are discussed in terms of the competing group contributions of the components. Knowledge of this influence may be transduced to understand polymer-polymer compatibility. The cohesive energy density concept has been used to calculate the infinite dilution solubility parameter for the polymer, with the aid of ΔG1∞. From the high temperature range the HILDEBRAND parameter δ2 was extrapolated to 298 K. The value obtained, 9.14, indicates that gas chromatography is an promising alternative to the conventional methods for determination of the solubility parameter for polymers.

Thermodynamic investigation of the liquid PbS system by using a drop calorimeter

Heat contents of the PbS system were measured by a drop calorimeter in the composition range of sulfur X s = 0 to 0.5 (PbS) and in the temperature range of 560 to 1500 K, and a heat content-temperature-composition ternary diagram was constructed. By using a quantitative thermodynamic analysis method, free energy, heat and entropy of mixing in the liquid PbS binary and PbPbS pseudo-binary systems were derived from the measured heat contents. The obtained partial molar free energies of mixing (activities) are considerably different from those estimated by the use of a regular solution model.

Activities and Other Partial Molar Properties of the Quarternary Molten Salt System MnCl2 ‐ NaCl ‐ KCl ‐ CsCl

The thermodynamic properties of the quarternary molten salt system have been investigated by EMF measurements using a formation cell of the typeIt was found that the partial molar free energies of mixing of in the quarternary solutions are well represented by a previously developed expression given aswhich is valid at constant . In this expression, etc. refer to the corresponding partial molar free energy of in the designated binary system having the same content as the quarternary. The composition parameters and are defined as,

Na<SUB>2</SUB>O-B<SUB>2</SUB>O<SUB>3</SUB>-NiO系融体におけるNiOの活量および溶解度

Activity and solubility of NiO in Na2O-B2O3-NiO melts were determined by use of EMF measurements of the following cell in the temperature range of 1123∼1373 K.(This article is not displayable. Please see full text pdf.) The results obtained are summarized as follows:(1) The activity coefficient (γ°NiO) of NiO in Na2O-B2O3-NiO melts indicates positive deviation from ideality. The values of γ°NiO obtained at 1298 K for the melts with 32.5, 48, and 60 mol%Na2O were 2.5, 6.2, and 3.2, respectively.(2) Solubility of NiO in Na2O-B2O3 melts was determined at the inflexion point on EMF vs NiO content curve and solubility lines of NiO in the Na2O-B2O3-NiO ternary system were estimated.The maximum content of NiO (=11 mol%NiO at 1373 K) was obtained at the composition of nearly 32.5 mol%Na2O.(3) Thermodynamic quantities of mixing of NiO were calculated by using the data of the melts containing 0.9 mol%NiO. Gibbs’s partial molar free energies of mixing of NiO were about −30∼40 kJ/mol at 1173 K and decreased with an increase in temperature and Na2O content.

Thermodynamics of the Fe-Mn-C system from solid state EMF measurements

The partial molar free energy of mixing of Mn, G2M in austenite and in various Mn-C and Fe-Mn-C phase mixtures was measured at temperatures of 690 to 1060°C with solid CaF2 electrolyte galvanic cells. The results for the Fe-Mn system can be represented by {ie2217-01} where T denotes temperature in K and y1 andy2 are the Fe- and Mn-to-metal atom ratios, respectively. The course ofGM2 in its dependence on the carbon atom fraction in the Mn-C system shows a low stability of Mn15C4 and Mn3C with respect to decomposition into neighboring carbides. Partial molar free energies of mixing of Fe and Mn in the metal (austenite or α-Mn(+Fe))-carbide(M3C, M23C6, or e-M4C) phase mixtures are given by {ie2217-02} and {ie2217- 03} {ie2217- 04} whereyi denote thei-to-metal atom ratios(i = 1, 2, 3) in the carbide-saturated metal phase. The partial molar free energy of mixing of carbon, GM 3 in the same two-phase regions was calculated. The results for the austenite-cementite, two-phase, region confirm published gas carburization data but tend to be more negative in value and have a greater curvature in dependence on Mn content. The curvature shows that interaction terms higher than first order must be used to represent GM3 over the composition rangey2 = 0 to 0.545. Evaluation of GM3 over closed paths of integration in the ternary system demonstrates a self-consistency of the phase relations with the emf data. The derived free energy charge for the reaction of mixing of the binary cementite compounds, {ie2217-05} where M denotes the mixture (Fe, Mn), is more negative than that of an ideal solution and itsy2 dependence is asymmetric being more negative in Mn-rich than in Fe-Rich cementite.

Free energies of mixing in the liquid iron-cobalt orthosilicates at 1450°c

Measurements have been made of the equilibrium between liquid iron-cobalt orthosilicates and solid iron-cobalt alloys. It is shown that the integral free energies of mixing of the oxide components and the integral and partial molar free energies of mixing of the pseudobinary (orthosilicate) components can be derived from a knowledge of the metallic activities in such exchange equilibria. The thermodynamic properties are presented for 1450°C. It is found that the integral free energy of mixing shows a maximum deviation of −2.1 (±0.3) kJ per mole of MO • 1/2 SiO2 from ideal silicate mixing.

The thermodynamic properties of cobalt-palladium solid solutions

The thermodynamic activities of cobalt in palladium, relative to pure f.c.c. ferromagnetic cobalt, have been determined from e.m.f. measurements on solid-electrolyte oxygen concentration cells over the temperature range 800–1100°C. The activity of cobalt in palladium exhibits positive departures from ideal solution behavior in cobalt-rich alloys and negative departures in palladium-rich alloys. The activities of palladium, deduced from the experimental data, indicate negative departures from ideality at all compositions. Cobalt-palladium alloys were of particular interest because their unusually high Curie temperatures permitted compositions up to 40 at. % palladium to be studied in the ferromagnetic state. The experimental data were of sufficient precision that the ferromagnetic-paramagnetic transition could be detected in alloys containing nominally 20 and 30 at. % palladium. The relative integral molar excess entropies, determined from the changes in the partial molar free energies of mixing as a function of temperature, are positive for all the compositions studied. The heats of mixing are endothermic for cobalt-rich compositions and exothermic for palladium-rich compositions. An extrapolation of the experimental values of the partial molar free energies of cobalt to lower temperatures, suggests the presence of a miscibility gap below 600°C at high cobalt concentrations.

Hydrolytic polymerization of caprolactam. II. Vapor–liquid equilibria

AbstractThe system water–caprolactam–polymer at equilibrium is regarded as a solution consisting of two solvents (water and caprolactam) and one solute (polymer). The activities of water and caprolactam in equilibrium at 270°C in the range of 2–10 wt‐% total water content have been determined by vapor‐pressure measurements. Water shows large negative deviations from Raoult's law, as a consequence of the different size of water and polymer molecules. The partial molar free energies of mixing are compared with the expressions derived from the Flory‐Huggins theory of polymer solutions; the results are not conclusive, but seem to indicate a qualitative agreement with the theory. The increase in vapor pressure during polymerization in sealed systems and the water dependence of the polycondensation equilibrium are discussed and explained in terms of water activity changes.

Free energy and electrical resistivity of molten alloys

Abstract The free energies of mixing for molten indium-antimony, cadmium-antimony, indium-bismuth, lead-bismuth and tin-bismuth were calculated from the variation of electrical resistivity with composition employing the model of Takeuchi and Endo. Resistivities measured in this laboratory with an electrodeless technique for In-Sb alloys, together with published values for Cd-Sb, In-Bi, Pb-Bi and Sn-Bi alloys were used in the calculations. Evaluation of the resistivity data gave the composition dependence of the derivatives of the chemical potentials of the constituents and the integral molar free energies of mixing. No assumptions regarding ideal entropy were made to obtain these free energy values although a statistically random mixture of ions is presumed in the scattering model. Conclusions drawn from a comparison between the calculated free energy values and published thermodynamic data for these systems are discussed in terms of departures from regularity and the variations in the effective free elec...

Thermodynamic functions for the liquid systems argon + carbon monoxide, oxygen + nitrogen, and carbon monoxide + nitrogen

Measurements have been made of the total vapour pressure as a function of composition for argon + carbon monoxide at 83.82°K, for oxygen + nitrogen at 63.14°K, and for carbon monoxide + nitrogen at 68.09°K. These measurements have been used to evaluate GE, the excess molar free energy of mixing. By combining these values of GE for oxygen + nitrogen and carbon monoxide + nitrogen with values previously determined at 83.82°K, estimates have been made for these two mixtures of the heat of mixing HE and of TSE, where SE is the excess entropy of mixing. The experimental values of GE, HE, and TSE are compared with those calculated from statistical theories of solutions.

Prediction of Critical Mixtures. Use of Mathematical Representations for Molar Free Energy of Mixing

Prediction of Critical Mixtures. Use of Mathematical Representations for Molar Free Energy of Mixing