Gibbs Energy Of Mixing Research Articles

Solution thermodynamics of methocarbamol in some ethanol + water mixtures

Apparent thermodynamic functions, Gibbs energy, enthalpy and entropy of solution and mixing, for methocarbamol in ethanol + water mixtures, were evaluated from solubility data determined at temperatures from 293.15 K to 313.15 K and from calorimetric values of drug fusion. The drug solubility was greatest in the mixtures with 0.70 or 0.80 mass fraction of ethanol and lowest in neat water across all temperatures studied. Non-linear enthalpy-entropy compensation was found for the dissolution processes. Accordingly, solution enthalpy drives the respective processes in almost all the solvent systems analyzed.

Miscibility Behavior and Nanostructure of Monolayers of the Main Phospholipids of Escherichia coli Inner Membrane

We report a thermodynamic study of the effect of calcium on the mixing properties at the air-water interface of two phospholipids that mimic the inner membrane of Escherichia coli: 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphoethanolamine and 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphoglycerol. In this study, pure POPE and POPG monolayers and three mixed monolayers, χ(POPE) = 0.25, 0.5, and 0.75, were analyzed. We show that for χ(POPE) = 0.75, the values of the Gibbs energy of mixing were negative, which implies attractive interactions. We used atomic force microscopy to study the structural properties of Langmuir-Blodgett monolayers that were transferred onto mica substrate at lateral surface pressures of 25 and 30 mN m(-1). The topographic images of pure POPE and POPG monolayers exhibited two domains of differing size and morphology, showing a step height difference within the range expected for liquid-condensed and liquid-expanded phases. The images captured for χ(POPE) = 0.25 were featureless, and for χ(POPE) = 0.5 small microdomains were observed. The composition that mimics quantitatively the proportions found in the inner membrane of E. coli , χ(POPE) = 0.75, showed large liquid condensed domains in the liquid expanded phase. The extension of each domain was quantitatively analyzed. Because calcium is used in the formation of supported bilayers of negatively charged phospholipids, the possible influence of the nanostructure of the apical on the distal monolayer is discussed.

Activity Coefficients of Electrolytes in the NaCl + Na2SO4 + H2O Ternary System from Potential Difference Measurements at (298.15, 303.15, and 308.15) K

Potential difference measurements have been used to obtain the mean ionic activity and osmotic coefficients of NaCl and Na2SO4 in their aqueous solutions. Also, the mean ionic activity coefficients of NaCl in NaCl–Na2SO4–H2O ternary system with sodium as a common ion have been determined from cell potential measurements using: Na-ISE/NaCl (mNaCl); Na2SO4 (mNa2SO4)/Ag/AgCl combined with the reference cell: Na-ISE/NaCl (I = mNaCl + 3mNa2SO4), AgCl(s)/Ag. The measurements were made at ionic strength ratios for Na2SO4, yNa2SO4, of (0.0, 0.2, 0.4, 0.6, 0.8, and 1.0), at constant total ionic strengths, I, of (0.1, 0.5, 1.0, 2.0, 3.0, and 4.0) mol·kg–1 and at temperatures of (298.15, 303.15, and 308.15) K. The experimental mean ionic activity coefficients of NaCl were correlated and analyzed with the Harned rule and Scatchard and Pitzer models. The excess free Gibbs energies of mixing were calculated from the trace activity coefficient data of NaCl and analyzed versus system composition at different temperatures...

Thermodynamic functions of the mixing of acrylic acid solutions in hexane, benzene, and acetonitrile

The saturated vapor pressure over solutions of acrylic acid in hexane, benzene, and acetonitrile was measured tensimetrically over a temperature range of 295 to 355 K. The composition of the equilibrium phases, the activity coefficients of the components, and the thermodynamic functions of mixing (H E , G E , and S E ) of the solutions under study were calculated using the data on temperature dependence. A connection was established between the heat and Gibbs energy of mixing and the physical properties of the solvents.

Thermodynamic properties calculation in Ni-Cr-Co liquid alloys using FactSage

The thermodynamic properties of liquid binary and ternary alloys in Ni-Cr-Co system, obtained by FactSage thermodynamic calculations, are presented. Thermodynamic calculations for three binary systems – Ni-Cr, Ni-Co and Cr-Co and ternary Ni-Cr-Co system, involved thermodynamic determination of activities, coefficient of activities, partial and integral values for enthalpies and Gibbs energies of mixing and excess energies at four different temperatures: 2,000 K, 2,173 K, 2,200 K and 2,273 K, as well as calculation of phase diagrams for the investigated binary systems.

Thermodynamic properties of Al-Y system melts

The thermochemical properties of Al-Y melts were determined by isoperibolic calorimetry. It was established that the minimal value of integral mixing enthalpies is equal to −40.8 + 0.4 kJ/mol at 1770 K and xY = 0.41. The thermodynamic properties of liquid alloys were modeled by the developed procedure using the coordinates of a liquidus line in the phase diagram of the Al-Y system, and by the theory of ideal associated solutions. The component activities exhibit high negative deviations from the Raoult law. The Gibbs energies of mixing of Al-Y melts have a minimum of −30.6 kJ/mol at xY = 0.48.

Thermodynamic mixing properties of liquids in the system Na 2O-SiO 2

Enthalpies of fusion have been measured by differential scanning calorimetry for a Na 2O-SiO 2 system at 50, 66.6, and 74.4 mol% SiO 2. Enthalpies of mixing of liquids obtained from different calorimetry techniques are critically evaluated. The data on calorimetric enthalpy, activity of Na 2O, cristobalite liquidus, and immiscibility gap are used to determine the enthalpy and entropy of mixing of sodium–silicate liquids are determined as a function of composition by the least squares method. The derived mixing properties are based only on the experimental data and are independent of any assumption about the structure and chemical species in liquids. The enthalpy of mixing has a minimum value of −120 kJ/mol at 35–40 mol% SiO 2 and is convex upward around 80–90 mol% SiO 2. The entropy of mixing have a maximum value of + 6 J/K-mol at 75 mol% SiO 2, and it decreases with the SiO 2 content to −5 J/K-mol at 40 mol% SiO 2. This decrease in entropy can be accounted for by ideal mixing of Q 4, Q 3, and Q 0 + 1 + 2 (= Q 0 + Q 1 + Q 2) species in the liquids and is responsible for the negative temperature dependence of the partial molar Gibbs energy of mixing of Na 2O, observed in activity measurements. Comparison of the present results with previous values suggests that a quasi-chemical model and the Adam–Gibbs model overestimate the configurational entropy of mixing of liquids.

Thermodynamics of aqueous solutions containing poly (N-isopropylacrylamide) and vitamin C

Using vitamin C as a model drug we focus our attention to the experimental and theoretical investigation of swelling equilibria of ternary system made from water, cross-linked poly (N-isopropylacrylamide) and vitamin C. This contribution aims to the prediction of the amount of drug uptake by the hydrogel using a thermodynamic model and independent experimental information, like the demixing behavior of linear polymer in water and in aqueous vitamin C solutions as well as the solubility of vitamin C in water. As theoretical approach a combination of the Koningsveld–Kleintjens model for the Gibbs energy of mixing and the affine network theory for the elasticity of the gel is applied. The model shows an excellent performance in the prediction of the degree of swelling as function of vitamin C concentration and in the amount of drug in the hydrogel. Only for the calculation of the temperature dependency two parameters must be refitted slightly in order to achieve quantitative agreement with the experimental data. From the experimental point of view some hysteresis effects, growing with increasing vitamin C concentration are found, especially in the transformation range.

Phase- and interfacial behavior of hyperbranched polymer solutions

Macromolecular architecture of hyperbranched polymers is receiving increasing interest as the search for new tailor-made polymeric materials with strictly specified properties. The liquid–liquid equilibrium of binary solutions of hyperbranched polyesters of second generation (Boltorn H20) in water or in propan-1-ol is investigated experimentally and theoretically. For the theoretical description of the experimental phase diagram a corrected version of the lattice-cluster theory (LCT) is applied, where water occupies one lattice site and has no special structure. In contrast, propan-1-ol is considered as a chain having three segments. The LCT allows the incorporation of the architecture of the polymer and the solvent directly in the thermodynamic quantities, like Gibbs energy of mixing. However, the LCT neglected the self- and cross-association occurring in the mixture made from a polar solvent and a hyperbranched polymer with several functional groups. In order to study the influence of this association interaction on the phase behavior a modified version of the Wertheim theory is combined with the LCT. The developed model shows a good performance for the calculation of the demixing curve in comparison with experimental data, especially in the diluted concentration range. Additionally, the interfacial properties (interfacial tension, concentration profile) between the demixed phases are predicted applying LCT and LCT in combination with the Wertheim theory in the special version of the density gradient theory. This situation allows the investigation of the influence of association forces on interfacial properties.

Thermodynamic features of mixing of chitosan with polyvinyl alcohol and polyethylene oxide

Chitosan-polyvinyl alcohol and chitosan-polyethylene oxide systems were examined by water vapor sorption method. Based on the experimental data, the Gibbs energy, entropy, and enthalpy of the polymer mixing were calculated.

Calorimetric study of melts in the system KCl–K 2TaF 7

Enthalpy increment measurements on melts in the system KCl–K 2TaF 7 were carried out by drop calorimetry at temperatures between 298 and 1053, 1093 and 1133 K and selected compositions. The heat capacities of melted mixtures and enthalpies of mixing were determined using the experimental data. Calorimetric experiments showed nonideality of the melts in several properties. The molar relative enthalpy and molar heat capacity of melts exhibited small negative divergence from additivity. The molar enthalpy of mixing of melts showed exothermic deviation from ideality which increased with increasing temperature. The thermal effect at mixing was assigned predominantly to addition and substitution reactions producing heteroligand complex anions TaF 6Cl 2−. The nonideality was also confirmed by evaluating of activities considering Margules type model for excess Gibbs energy of mixing.

Interactions of Meibomian gland secretion with polar lipids in Langmuir monolayers

The surface interactions of Meibomian gland secretion (MGS) with polar lipid (PL), Egg Sphingomyelin (SM) or Dipalmitoylphosphatidylcholine (DPPC), are studied in mixed pseudo-binary films formed at the air/water interface of Langmuir surface balance. The behavior of the mixed films during slow quasi-equilibrium compression and during fast dynamic compression–decompression is registered by measurements of surface pressure and surface potential, and by monitoring film morphology with Brewster Angle Microscopy (BAM). Quasi-equilibrium compression isotherms are used to calculate the excess Gibbs and Helmholtz energy of mixing between MGS and PLs and thus to evaluate the interactions between the lipid compounds at the interface. The effects of PLs on the mixed film's elastic moduli of area compressibility, morphology and capability to attain high surface pressures are also examined. PLs interact with MGS with different strength and in different manner: MGS–SM interaction is weak and might lead to interfacial disaggregation of the thick meibium domains when SM is in excess, while MGS–DPPC interaction is strong and results in the formation of thick lipid aggregates. Both PLs increase the mixed films reciprocal compressibility and capability to achieve higher surface pressures. The results demonstrate that in vitro studies of the surface interactions between MGS and PLs might be beneficial in the selection of PLs for artificial tear formulations and for examination on molecular scale of the possible role of PLs at the ocular surface.

Thermodynamic analysis of the solubility of ketoprofen in some propylene glycol + water cosolvent mixtures

By using the van’t Hoff and Gibbs equations the thermodynamic functions Gibbs energy, enthalpy, and entropy of solution, mixing, and solvation for ketoprofen in propylene glycol + water (PG + W) cosolvent mixtures, were evaluated from solubility data determined at several temperatures. The solubility was greater in pure PG and lower in W at all temperatures studied. By means of enthalpy–entropy compensation analysis, non-linear Δ H soln ° vs. Δ G soln ° plot with negative slope from pure water up to 0.50 in mass fraction of PG and positive beyond this PG proportion was obtained. Accordingly to this result, it follows that the driving mechanism for solubility of KTP in water-rich mixtures is the entropy, probably due to water-structure loosing around the drug non-polar moieties by PG, whereas, over 0.50 in mass fraction of PG the driving mechanism is the enthalpy probably due to KTP solvation increase by cosolvent molecules. On the other hand the Jouyban–Acree model was challenged in front to experimental KTP solubility values finding a predictive power within 30% of deviation.

Thermodynamic investigation of mixed monolayers of trans-dehydrocrotonin and phospholipids

The thermodynamic behavior of mixed floating monolayers of zwitterionic phospholipids and trans-dehydrocrotonin (t-DCTN) at different molar fractions ( x) of the diterpene has been investigated by measuring the surface pressure and surface potential Langmuir isotherms. Excess Gibbs energies of mixing have been calculated for different compositions of the floating monolayer at varying surface pressure values. Spreading of pure t-DCTN molecules at the air–water interface resulted in a compressed-type isotherm. For the t-DCTN/DBPC and t-DCTN/DOPC binary systems, the maximum stability was obtained at x t-DCTN = 0.375 and 0.500 at a surface pressure of 15 mN/m, with a minimum ΔG M value equal to −1.7 kJ/mol. The analyses of the obtained thermodynamic parameters such as excess areas, excess free energies and free energy of mixing confirmed the miscibility of the phospholipids and t-DCTN in the binary systems. In these mixed monolayers, the phospholipid molecules seemed to exhibit higher long-range orientation order for intermediary values of t-DCTN molar fractions. As a whole, the above observations suggest that the t-DCTN molecules exert a condensing effect on the monolayers when mixed with the phospholipids.

A Determination of the Hansen Solubility Parameters of Hexanitrostilbene (HNS)

AbstractThe temperature‐dependent solubility of hexanitrostilbene (HNS) [CAS# 20062‐22‐0] was determined in ten solvents and solvent blends using the Tyndall effect. Thermodynamic modeling of the data yielded Flory interaction parameters, the molar enthalpy of mixing, the molar entropy of mixing, and the molar Gibbs energy of mixing. All solutions exhibited endothermic enthalpies and positive entropies of mixing. The presence of water in some of the solvent blends made dissolution increasingly endothermic and disfavored solubility. The solubilities of HNS at 25 °C were used to determine the three‐component Hansen solubility parameters (HSP) (δD=18.6, δP=13.5, δH=6.1 MPa1/2) and the radius of the solubility sphere (R0=5.8 MPa1/2). The HSP determined for HNS using group‐additivity (δD=21.0, δP=13.3, and δH=8.6 MPa1/2) also correctly predicted the optimum solvents for this explosive.

Calculation of the liquid–liquid equilibrium of aqueous solutions of hyperbranched polymers

The liquid–liquid equilibrium of aqueous solutions of hyperbranched polyesters of generation 2, 3 and 4 is described by the lattice-cluster theory. The gist of this approach is the incorporation of the architecture of the polymer directly into the thermodynamic quantities, like Gibbs energy of mixing. The very important geometric parameters describing the polymer architecture are calculated in a new way that seems to be more realistic than older ones. The phase-equilibrium calculations include the binodal curve, the spinodal curve and the critical point neglecting the polydispersity of the polymer samples. Without any additional adjustable parameter these corrections lead to a shift of the cloud-point curve towards higher polymer concentration, as observed in experiments. However, the agreement of the calculated and the experimental values is not quantitative. A possible reason for that may be the disregarding of association effects.

Solution Thermodynamics of Ketoprofen in Ethanol + Water Cosolvent Mixtures

Ketoprofen (KTP) is an anti-inflammatory drug widely used in therapeutics. By using the van’t Hoff and Gibbs equations, the thermodynamic functions Gibbs energy, enthalpy, and entropy of solution and mixing for KTP in ethanol (EtOH) + water cosolvent mixtures were evaluated from solubility data determined at several temperatures. The solubility was greater in pure EtOH and lower in water at all temperatures studied. This behavior shows the cosolvent effect present in this system. By means of enthalpy−entropy compensation analysis, a nonlinear ΔsolnH0 vs ΔsolnG0 plot with negative slope from pure water up to 0.6 in mass fraction of EtOH and positive beyond this EtOH proportion was obtained. Accordingly to this result, it follows that the dominant mechanism for solubility of KTP in water-rich mixtures is the entropy, probably due to water-structure loosening around the drug nonpolar moieties by EtOH, whereas over 0.6 in mass fraction of EtOH, the dominant mechanism is the enthalpy probably due to the KTP so...

A monolayer study on phase behavior and morphology of binary mixtures of sulfatides with DPPC and DPPE

Sulfatides are important constituents of brain myelin membranes and it is thought to be involved in lateral domain formation in biological membranes. In this work, the interaction of mixed systems of sulfatide with 1,2-dipalmitoyl-sn-glycero-3-phosphocholine (DPPC) and 1, 2-dipalmitoyl- sn-glycero-3-phosphoethanolamine (DPPE), two of the major components in biological membranes, was investigated using the monolayer technique at the air–water interface. Based on the regular solution theory, the miscibility of the two binary systems in the mixed monolayer was evaluated in terms of mean surface area per molecule ( A m), excess molecular area (Δ A (ex)), surface excess Gibbs energy (Δ G (ex)), interaction parameter ( ω) as well as activity coefficients ( f 1 and f 2) of formed films. Thermodynamic analysis indicates in the two binary systems with negative deviations from the ideal behavior. Accordingly, the values of the Gibbs energy of mixing, sulfatide-DPPC form stable mixtures at X sul = 0.4 ( X sul is molar ratio of sulfatide in binary mixture) for all the selected pressures. As for sulfatide/DPPE system, at π = 5 and 30 mN m −1, the minimum for the Gibbs energy of mixing was found at X sul = 0.6 and 0.2 respectively. But the minimum appeared at X sul = 0.4 for other surface pressures. The activity coefficients ( f 1 and f 2) of mixed monolayers were evaluated which show a marked dependence on the mole faction of sulfatide X sul. AFM images could support the above findings as well as interpretation.

Tuning the Interaction Parameter for the Soave−Redlich−Kwong Equation of State Using the Critical End Points

In the petroleum industry, to solve problems such as the design of the catalytic cracking of heavy oil, correct knowledge of the phase behavior is essential. As a benchmark where the number of degrees of freedom for binary mixtures is zero, the critical end points can represent the type of phase behavior of the binary mixtures according to van Konynenburg and Scott’s classification scheme (van Konynenburg, P. H. and Scott, R. L.Philos. Trans. R. Soc. London A 1980, 298, 495−540). Calculating the phase behavior of binary mixtures using interaction parameters evaluated by other methods can cause wrong determinations of the type of phase behavior. The critical end points were employed to fit the interaction parameters for binary mixtures in the critical state at high pressure. The molar Gibbs energy of mixing was evaluated to locate the ranges of values for the interaction parameters where exploration for the critical end point would not fail. The phase behavior at the critical end point is rather complex. B...

Langmuir Monolayers of a Hydrogenated/Fluorinated Catanionic Surfactant: From the Macroscopic to the Nanoscopic Size Scale

Langmuir monolayers of the hydrogenated/fluorinated catanionic surfactant cetyltrimethylammonium perfluorooctanoate at the air/water interface are studied at room temperature. Excess Gibbs energies of mixing, DeltaG(E), as well as transition areas and pressures, were obtained from the surface pressure-area isotherm. The DeltaG(E) curve indicates that tail-tail interactions are more important than head-head interactions at low pressures and vice versa. Atomic force microscopy and molecular dynamics simulations allowed a fine characterization of the monolayer structure as a function of the area per molecule at mesoscopic and nanoscopic size scales, respectively. A combined analysis of the techniques allow us to conclude that electrostatic interactions between the ionic head groups are dominant in the monolayer while hydrophobic parts are of secondary importance. Overall, results obtained from the different techniques complement to each other, giving a comprehensive characterization of the monolayer.