Excess Molar Gibbs Free Energies Research Articles

Study of the intermolecular interaction in hydrophobic deep eutectic solvent of (2-n-octyl-4-isothiazolin-3-one + 1-decanol) from the density, viscosity, thermodynamic, spectroscopic and quantum chemical calculations

Hydrophobic deep eutectic solvents (HDESs) are considered as green solvents and have been developed rapidly in recent years, which are widely used in diverse applications. In this study, we introduce a binary system composed of 2-n-octyl-4-isothiazolin-3-one (OIT) as a novel hydrogen bond acceptor (HBA) and 1-decanol as a hydrogen bond donor (HBD) under atmospheric pressure. The fundamental physicochemical properties, including density and dynamic viscosity, of the binary systems with various mole ratios were measured at temperatures of 293.15 K, 303.15 K, 313.15 K, 323.15 K, and 333.15 K. The excess molar volume (VmE), viscosity deviation (Δη) and excess Gibbs free energy (ΔG∗E) for activation of viscous flow were calculated and fitted according to the Redlich-Kister type polynomial equation. Furthermore, the spectral analysis (FTIR, UV–vis and 1H NMR) confirmed the presence of intermolecular hydrogen bonding in the binary systems. In addition, quantum chemical calculations revealed that there may be multiple modes of hydrogen bond formation between OIT molecule and 1-decanol molecule. However, selecting the most energetically favorable point, the most prominent hydrogen bond was found to be between the amide O atom of OIT and the hydroxyl H atom of 1-decanol.

Density, viscosity, excess properties, and intermolecular interaction of propylene glycol methyl ether + 1,2-propylenediamine binary system

In this work, the systematic measurements of physicochemical properties, viz., density (ρ) and viscosity (η) values of propylene glycol methyl ether (PGME) + 1,2-propylenediamine (1,2-PDA) binary system, including pure substances, over the entire mole fraction range at the temperatures of T/K = (298.15 to 318.15) under atmospheric pressure of P = 100.5 kPa. The fundamental data were used to calculate several excess properties, including excess molar volume (VmE), viscosity deviation (Δη), and excess activation Gibbs free energy (ΔG∗E). Meanwhile, the work further investigated the values of thermal expansion coefficient (αp), partial molar volume (V¯) and apparent molar volume (Vφ), thereby offering a comprehensive understanding on non-ideal behavior of the binary system. Furthermore, the variations in ρ values with various molar ratios and temperatures were evaluated through Jouyban-Acree model and nonlinear least squares method. Simultaneously, Grunberg-Nissan model, Eyring-Margules model, Heric model, and McAllister model, were used to fit the dependence of η values on the molar ratio. Arrhenius equation was employed to fit the temperature dependency of η values. In addition, Redlich-Kister (R-K) equation was utilized to fit the VmE, Δη, and ΔG∗E values of binary system. Based on spectral analyses of Raman, ultra-violet (UV), and 1H Nuclear Magnetic Resonance (NMR) and density functional theory (DFT) calculation, the intermolecular hydrogen bond (IHB) of PGME with 1,2-PDA was discussed in depth.

Viscosity Studies of Binary Liquid Mixture of Methyl Acrylate and Benzene and Substituted Halo Benzenes at 313.15k

Studied the binary liquid mixtures of Methyl Acrylate with Benzene (B), and Substituted Halo Benzene molecules like Chloro Benzene (CB) and Bromo Benzene (BB) at 313.15K. Initially, the density and viscosities of the mixtures are measured and this data is utilized to calculate excess properties like excess molar volume (VE), excess viscosity (ηE), and excess Gibbs free energy (ΔG*E). These excess parameter values are fitted in the Redlich–Kister Polynomial equation and the intermolecular interaction is discussed.

Excess properties, intermolecular interactions, and CO2 absorption property of ethylene glycol + diethylenetriamine binary solutions

In this work, the density (ρ) and viscosity (η) data of ethylene glycol (EG) + diethylenetriamine (DETA) binary solutions at T = 298.15 K–318.15 K and P = 100.5 kPa are reported. The basic physicochemical data of binary solutions were used to investigate their excess molar volume (VmE), viscosity deviation (Δη), and excess viscous flow activation Gibbs free energy (ΔG*E), which revealed that there was strong intermolecular interaction in the EG (1) + DETA (2) binary solutions. The density values, viscosity values, and excess properties of binary solutions were fitted by parametric models, such as Jouyban-Acree model, McAllister four-body model, and Redlich-Kister (R-K) equation. After that, the binary solutions were spectroscopically analyzed to further discuss their intermolecular interaction. Meanwhile, Raman, UV, and 1H NMR spectra jointly demonstrated the intermolecular hydrogen bonding of the binary solutions as the form of –OH···N(H2)–. Finally, CO2 absorption was carried out to investigate the CO2 absorption property of the binary solutions, which provided reference data for CO2 capture.

Thermodynamic Properties, Activity Coefficients at Infinite Dilution and Cosmo‐SAC Modelling of Deep Eutectic Solvents at Different Temperatures

AbstractA deep understanding of the solute‐ deep eutectic solvent (DESs) interactions is required for an appropriate selection of DESs as absorption media in the extraction of binary mixtures. As a result, these studies are done to evaluate the values of the activity coefficients at infinite dilution ( ), allowing us to define and understand the nature of these intermolecular interactions comprising DES mixtures with volatile organic solvents at different temperatures using gas liquid chromatography technique to determine the for 34 solutes in DESs [zinc chloride+acetic or phosphoric acid] prepared at 1 : 2 molar ratio for the temperature range (313.15–353.15) K. The thermal stability of the prepared DESs was determined by a thermogravimetric analyser. Excess thermodynamic parameters [partial molar excess enthalpies and Gibbs free energies ] were derived from the data. The selectivity and capacity values for the industrial separations were calculated and compared with the literature values of other DESs, ionic liquids, and sulfolane to assess the suitability of the investigated DESs for possible applications as extracting solvents. The selectivity and capacity values are high and therefore, [zinc chloride+acetic or phosphoric acid] can be used as a potential solvent to replace the currently used conventional solvents in the separation of the selected azeotropes. COSMO‐SAC predictions were qualitatively in very good agreement with the experimental data.

Infinite Dilution Activity Coefficients and Gas–Liquid Partition Coefficients of Organic Compounds in Ionic Liquid 1-Butyl-2,3-dimethylimidazolium Thiocyanate: Measurements and LFER Calculations

Infinite dilution activity coefficients (γi∞) of 31 organic solutes (alkanes, cycloalkanes, olefins, aromatics, chlorinated alkanes, alcohols, and other polar organic solutes) in the ionic liquid (IL) 1-butyl-2,3-dimethylimidazole thiocyanate ([BMMIM][SCN]) were determined by gas–liquid chromatographic (GLC) method in the temperature range of 313.15–353.15 K. The infinite dilution partial molar excess enthalpies (H̅iE, ∞), entropies (TrefS̅iE, ∞), and Gibbs free energies (G̅iE, ∞) of the organic solutes at the reference temperature T = 298.15 K and the solubility parameters (δ3) of [BMMIM][SCN] were derived from γi∞. The gas–liquid partition coefficients (KL) of solutes at different temperatures were calculated by referring to the densities of [BMMIM][SCN]. The linear free energy relationship solvation model was used to fit the KL values, and the KL prediction model was obtained. The selectivity (Sij∞) and capacity (kj∞) of n-hexane (i)/benzene (j) and cyclohexane (i)/benzene (j) at infinite dilution at 323.15 K were calculated. The results were compared with the values of ILs with the thiocyanate anion in the literature.

Effect of water or ethanol on the excess properties of deep eutectic solvents (tetrabutylammonium bromide + formic acid/propionic acid)

The density and viscosity of binary mixtures of [tetrabutylammonium bromide + formic acid/propionic acid] with water or ethanol were determined in the entire molar fraction range of 288.15–318.15 K. The influences of temperature, deep eutectic solvents (DESs) composition and molar fraction, as well as different solvents on the excess molar volume, apparent molar volume, partial molar volume, viscosity deviation and excess viscous flow activation Gibbs free energy of the binary mixed system were investigated in detail. The interaction of DESs with solvent molecules in binary system mixtures is discussed. It demonstrated the existence of hydrogen bonding between DESs and solvent molecules, and that the interaction between DESs and ethanol was stronger than DESs-water. By introducing the concepts of relative volume and relative viscosity, the viscosity values of the binary mixed system were predicted by combining the Redlich-Kister equation. This study is expected to provide a theoretical reference for the future application of DESs.

Regular solution theory regarding sodium cholate and hexadecyltrimethylammonium bromide or dodecyltrimethylammonium bromide binary mixed micelles

The formation of binary mixed micelles of sodium cholate (SC) – hexadecyltrimethylammonium bromide (HDTAB) and sodium cholate (SC) – dodecyltrimethylammonium bromide (DTAB) is investigated in an aqueous NaCl solution (0.300 mol kg−1). According to the 2D ROESY spectrum, SC steroid skeleton is in contact via its convex surface with the hydrophobic core of the micelle. Existing cross peaks indicate the spatial proximity of the SC carboxylate group and HDTAB or DTAB cationic heads, i.e., there are attractive electrostatic interactions. In the HDTAB-SC 2D ROESY spectrum there are cross peaks that may belong to HDTAB surfactants with hydrocarbon chains that have globular conformations. In both mixed micelles, there are synergistic interactions between structurally different surfactants. Dependence of the molar excess Gibbs free energy (gE) on the mole fraction of the surfactant i (xi) from the binary micellar pseudophase in both HDTAB-SC and DTAB-SC systems is described by the symmetric first-order Margules function. From theoretical considerations, it follows that the first-order Margules function that describes the dependence gE=f(xi) can be obtained if the number of microstates in binary mixed micellar pseudophases approaches the number corresponding to the number of microstates of random mixing of structurally different surfactants (HDTAB-SC), or there exists a compensation of molar excess configurational enthropy (a departure from random mixing of different particles at the atomic level) with molar excess conformational enthropy (DTAB-SC).

Some Thermodynmic Properties of binary Mixtures of Alcohol isomers and Sulfolane at 298.15K

The refractive indices, nD densities , and viscosities h of binary mixtures of sulfolane + n -butanol + sec- butanol + iso- butanol  + tert – butanol + n-propanol and iso- propanol were measured at 298.15K. Form experimental data, excess molar volum VE , excess molar refractivity nD, excess molar viscosityhE and excess molar Gibbs free energy of activation of viscous flow DG*E were calculated. From n-propanol – sulfolane and iso- propanol sulfolane mixtures showed negative nD, n-butanol – sulfolane, sec-butanal – sulfolane, iso-butanol – sulfolane and tert- butanol  sulfolane , DnD was positive over the whole mole fraction rang , while VE, hE and DG*E show a negative deviation. The results obtained for binary mixtures suggest two types of molecular interaction. One is the formation of new stable complexes between the sulfone group of sulfolane and the hydroxyl group of alcohols and the second is related to the participation in destroying the mixture structure and forming a new structure. Excess molar quantities of these binary mixtures were found to be affected directly by the position of hydroxyl group and the steric associated with the methyl group.

Measurements and correlation of activity coefficients at infinite dilution for organic solutes in 1-heptyl-3-methylimidazolium chloride

This work is a continuation of our studies on the determination of activity coefficients at infinite dilution (γi∞) for organic solutes (i) in ionic liquids (ILs) and their use in separation processes. The values of γi∞ for 31 organic solutes including alkanes, cycloalkanes, 1,4-dioxane, aromatic hydrocarbons, cyclohexene, chloromethanes, acetonitrile, acetone, tetrahydrofuran, ethyl acetate and alcohols in the IL 1-heptyl-3-methylimidazolium chloride ([C7MIm]Cl) at six temperatures in range of (313.15–363.15) K were determined by gas-liquid chromatography (GLC). The density of [C7MIm]Cl as a function of temperature at pressure p= 101.33 kPa was measured and the values of gas-liquid partition coefficients (KL) were obtained. The linear relationship between lnγi∞ and 1/T was fitted by the Gibbs-Helmholtz equation. The molar excess thermodynamic functions including the infinite dilution partial molar excess Gibbs free energies (G¯iE,∞), partial molar excess enthalpies (H¯iE,∞) and entropies (TrefS¯iE,∞) at Tref = 298.15 K were calculated. In addition, the solubility parameters (δi) of [C7MIm]Cl were obtained from the regular solution theory combined with Flory “combinatorial” equation. The interaction between the solute and the IL was quantified based on the linear free energy relationship (LFER) model. The infinite dilution selectivity coefficients (Sij∞) of n-hexane (i)/benzene (j) and cyclohexane (i)/benzene (j) were calculated at T = 323.15 K from γi∞ and compared to literature values for [Cl]-based ILs for the same separation problems.

Binary mixture (1:1) of Triton X100 and Propranolol hydrochloride in an aqueous solution of NaCl: Whether mixed micelles are formed, possible clarification in 1H DOSY NMR experiment

Micellisation of the binary mixture (1:1) of non-ionic surfactant Triton X100 and surface-active drug Propranolol hydrochloride is examined in an aqueous solution of NaCl (0.3 molkg−1) in the temperature interval T = (273.15–313.15) K with steps of 5 K. Propranolol hydrochloride has two critical micellar concentrations (cmc) if the solution contains NaCl (0.3 molkg−1), while its binary mixture with Triton X100 (1:1) has one critical micellar concentration. The interaction coefficient (β) between structurally different micellar building units is β > 0, which means that there are antagonistic interactions in the binary mixed micelle, i.e., the molar excess Gibbs free energy is higher than zero, which probably originates from the increase in the degree of hydrophobic hydration when incorporating the naphthalene ring (part of Propranolol hydrochloride) into the Triton X100 micelle. The change of the molar Gibbs free energy of mixing is lower than zero. Thus the driving force for the formation of the binary mixed micelle originates from the entropy of mixing structurally different particles. The Diffusion-Ordered SpectroscopY (DOSY) experiment makes it possible to determine, based on the change (reduction) of the self-diffusion coefficient (D) of a surfactant concerning the D value in the monomeric state, whether the observed surfactant (whose concentration in the solution must be lower than its monocomponent cmc values) with another surfactant particle (from a binary mixture of surfactants) forms a binary mixed micelle. DOSY experiment was performed in an aqueous solution without NaCl. If the total concentration of the examined binary mixture is higher than its critical micellar concentration, it decreases the self-diffusion coefficient of both components, suggesting the formation of the binary mixed micelle. The self-diffusion coefficient of Triton X100 is significantly lower than that of propranolol hydrochloride, indicating that non-ionic surfactant dominates in the binary mixed micelle.

Symmetry (Asymmetry) of the Molar Excess Gibbs Free Energy Function of the Binary Mixed Micelles of Bile Acid Anion and Classical Cationic Surfactant: Influence of Sterically Shielded and Sterically Unshielded Polar Groups of the Steroid Skeleton

Binary mixtures of surfactants build a binary mixed micelle in which the ratio of surfactants usually differs from the initial ratio of surfactants in their binary mixture. The thermodynamic stabilization of the binary mixed micellar pseudophase about the hypothetical ideal state (intermolecular interactions between the different particles and the conformational states of the particles are identical to those of monocomponent states) is described by the molar excess Gibbs free energy (gE). The dependence of gE on the molar fraction of surfactant i (xi) from the binary mixed micelle can be described by a symmetric function (symmetry is described to the line parallel to the y-axis and passes through xi = 0.5) or by an asymmetric function. Theoretical analysis (canonical partition function, conformational analysis) examines how the presence of different polar functional groups, some of which are sterically shielded from the steroid skeleton of bile salts (surfactant), affect the symmetry of the function gE of the binary mixed micelle of the cholic acid anion (bile salts) and classic cationic surfactant (hydrophobic tail and polar head). Suppose the steroid skeleton of the bile salt contains non-sterically shielded polar groups (or the temperature is relatively high). In that case, gE is a symmetric function. At the same time, if the steroid skeleton also contains sterically shielded polar groups, then the gE function is asymmetric.

Thermodynamics of trimethyltetradecylammonium bromide – Sodium deoxycholate binary mixed micelle formation in aqueous solution: Regular solution theory with mutual compensation of excess configurational and excess conformational entropy

A binary mixture of trimethyl(tetradecyl)ammonium bromide = TB-SD = sodium deoxycholate surfactants forms non-ideal binary mixed micelles that have molar excess Gibbs free energy described with the Margules function of the first order. Strong synergistic interactions exist between TB and SD particles (interaction coefficient with a magnitude of 10). Based on the temperature dependence of interaction coefficient and temperature dependence of TB and SD micellar molar fractions product logarithm, it follows that the molar excess entropy is zero. Therefore, although the surfactants TB and SD are structurally very different, their binary mixed micelles can still be described with regular solution theory (random mixing of TB and SD). However, the 2D ROESY spectrum indicates that the binary micellar pseudophase is not random in terms of the spatial distribution of TB and SD particles. Namely, intermolecular interactions between deoxycholic acid anions are missing in the binary mixed micelle. This results in the appearance of excess configuration entropy. However, a zero value of the total molar excess entropy and the existence of the first order Margules function for the molar excess Gibbs free energy means that the molar excess configurational entropy is compensated with the molar excess conformational entropy and that there are correlation effects between the excess configurational enthalpy and entropy as well as between the excess conformational enthalpy and entropy.

Interaction between Triton X100 and Brij 58 in their binary mixed micelles: Micellization in aqueous solution and aqueous solution of Poloxamer 188 at the range of temperature T = (273.15–323.15) K

The micellization of the binary mixture of surfactants Triton X100 – Brij 58 in an aqueous solution (with and without Poloxamer 188) was investigated using a spectrofluorimetric method with pyrene as a probe molecule. There are synergistic interactions between the micellar building units in the binary mixed micelles Triton X100 – Brij 58, which increase with increasing temperature. The analyzed binary mixed micelles possess molar excess entropy. The molar excess Gibbs free energy is a first-order Margules function from the surfactant (Triton X100 or Brij 58) molar fraction in the binary mixed micelles Triton X100 – Brij 58. Poloxamer 188, in the temperature range T = (273.15–323.15) K, does not form micelles. Poloxamer 188 in an aqueous surfactant solution (0.01 w/w) reduces the thermodynamic stabilization of the binary mixed micelle Triton X100 – Brij 58 concerning the state of the same binary mixed micelle when this polymer is not present in an aqueous solution. In the presence of Poloxamer 188, the thermodynamic destabilization of the binary mixed micelle Triton X100 – Brij 58 increases with increasing temperature.

Understanding the physical and thermodynamic properties of monoethanolamine‐ionic liquids for solvent screening in CO2 capture process

AbstractThe physical properties such as density, surface tension, and viscosity of monoethanolamine (MEA)‐ionic liquids (ILs) solvent mixtures were studied experimentally in this work. The ILs namely, tetrabutylammonium acetate TBAAc, tetrabutylammonium bromide TBABr, and tetrabutylammonium hydroxide TBAOH were used. All the above parameters were measured at atmospheric pressure and various temperatures from 283 to 313 K with a 10 K interval. From the measured experimental data, thermodynamic properties such as thermal expansion, excess molar volume, viscosity deviation, and excess Gibbs free energy were also calculated. The physical and thermodynamic properties are more important to understand the solvent behavior during solvent screening in solvent‐based CO2 capture process. The 30 wt% solvent mixture composition was prepared as 28, 25, and 20 wt% MEA mixed with 2, 5, and 10 wt% ILs. Furthermore, a single empirical model was developed from the measured experimental data and the results are correlated. A good agreement was obtained between correlated and experimental data.

Influence of hydrogen bond donor on zinc chloride in separation of binary mixtures: Activity coefficients at infinite dilution

Deep eutectic solvents are solvents similar to the ionic liquids (ILs) but less expensive and simple to prepare than ILs. The activity coefficients at infinite dilution of solutes in the deep eutectic solvents (DESs) plays an important role in designing of the separation processes. Gas liquid chromatography technique (GLC) was used to determine activity coefficients at infinite dilution for 34 polar and non-polar organic solutes: solutes include alkanes, alkenes, alcohols, ketones, thiophene, heterocyclics, cycloalkanes, acetonitrile, tetrahydrofuran, cycloalkenes, aromatic hydrocarbon and water in two zinc chloride based DESs [zinc chloride + acetic acid] (1:4) and [zinc chloride + phosphoric acid] (1:2.5) at temperatures (313.15, 323.15, 333.15, 343.15, 353.15) K. Excess thermodynamic parameters [partial molar excess enthalpies ΔG1E,∞,entropies(TrefΔS1E,∞) and Gibbs free energies (ΔG1E,∞)] were derived from activity coefficient at infinite dilution data. The selectivity and capacity values for separation of benzene/ethanol, cyclohexane/ethanol, n-octane/acetonitrile, ethylbenzene/butan-1-ol, n-heptane/butan-1-ol at T = 323.15 K were calculated and compared to literature values for DESs, ionic liquids (ILs), and sulfolane to assess the suitability of the DESs for possible use as an entrainers. Both DESs [zinc chloride + acetic acid] (1:4) and [zinc chloride + phosphoric acid] (1:2.5) have high selectivity values as compared to studied ionic liquids as well as conventional solvents in the literature for difficult separation system of benzene/ethanol, cyclohexane/ethanol, ethylbenzene/butanol and heptane/butanol which indicate that these DESs are an extraction solvent and has separation ability for difficult separation system of benzene/ethanol, cyclohexane/ethanol, ethylbenzene/butan-1-ol and n-heptane/butan-1-ol.

Deep eutectic solvent as a possible entrainer for industrial separation problems: Pre-screening tool for solvent selection

Deep eutectic solvents, as a new type of nature-welcoming solvents, have shown a great interest in different areas of science and in solvent extraction for industrial separation processes. In this present study, the infinite dilution activity coefficients γ13∞, have been measured for 31 volatile organic solvents (alkanes, alkenes, alkynes, aromatics, cycloalkanes, cycloalkenes, alcohols, ketones, and thiophene) in the deep eutectic solvent (1-ethyl-1-methylpyrrolidinium bromide + glycerol) prepared at (1:2 molar ratio) measured at temperature ranging from T = (313.15 to 343.15) K and at atmospheric pressure using gas liquid chromatography coupled with thermal conductivity detector (GC-TCD). The values of the partial molar excess enthalpies (ΔH1E,∞), entropies (TrefΔS1E,∞), and Gibbs free energy (ΔG1E,∞) at infinite dilution were calculated from the experimental data of γ13∞ attained over the temperature range mentioned above. Selectivities and capacities for two separation problems (cyclohexane/benzene and acetone/ethanol) were calculated fromγ13∞ and compared to the other investigated DESs, ILs as well as the currently used traditional solvents found from the literature. Furthermore, the selectivity and capacity results proved that the examined DES cannot be utilized in separation of (acetone/ethanol) but can be utilized for cyclohexane/benzene separation.

VOLUMETRIC AND VISCOMETRIC DETERMINATION OF BINARY LIQUID MIXTURES OF 2-ETHOXYETHANOL AND AMYL ACETATE AT TEMPERATURES OF (298.15 AND 303.15) K

Densities and viscosities have been determined at temperatures of (298.15 and 303.15) K for binary liquid mixtures of 2-ethoxyethanol with amyl acetate over the entire range of solvent composition. From the experimentally determined values, excess molar volume, VE, excess viscosity, ηE and excess Gibbs free energy of activation of viscous flow, G*E have been calculated. These calculated excess thermodynamic functions were fitted to Redlich-Kister polynomial equation to obtain the fitting coefficients and standard deviations. The values of excess molar volume, VE were negative and that of the excess viscosities, ηE were found to be positive, while excess Gibbs free energy of activation of viscous flow, ΔG*E were negative over the whole range of solvent composition for the binary systems at the studied temperatures. The behavior of these excess functions with composition of the mixtures have been discussed in respect of molecular interactions between the components of liquid systems. The mixture viscosities were correlated using empirical relations like Grunberg-Nissan, Frenkel, Hind, Wijk and Kendall-Monroe model equations. Comparison of these interaction parameters have been engaged to explain the intermolecular interactions between the alkoxy alcohol and the ester.

The density, viscosity, speed of sound, excess properties of binary mixtures of linear polydimethylsiloxane and various alkanes at temperatures in the range (288.15–328.15) K

This article describes the binary system composed of linear polydimethylsiloxane (PDMS) and diesel fuel main components n-decane, n-dodecane, n-tridecane and n-tetradecane at atmospheric pressure, and the density, viscosity and speed of sound were measured at 288.15 K, 298.15 K, 308.15 K, 318.15 K and 328.15 K, respectively. Their excess molar volume (VmE), excess viscosity (ηE), excess molar Gibbs free energy (ΔGEm), molar isobaric thermal expansion (EP,m) and excess molar isentropic compressibility (κEs,m) were calculated. The influence of the intermolecular force, steric hindrance, molecular stacking and other factors on the excessive properties of the binary system solution was discussed. The results indicate that with an increase in carbon chain length, the excess molar volume, excess viscosity, molar isobaric thermal expansion and excess molar isentropic compressibility increased and excess molar Gibbs free energy decreased, which probably ascribe to the increase in steric effect and the stronger interactions between homo-molecular than those of hetero-molecular interactions between PDMS and long-chain alkane molecules.

A new activity model for Fe\u2013Mg\u2013Al biotites: I\u2014Derivation and calibration of mixing parameters

A new activity model for Fe–Mg–Al biotites is formulated, which extends that of Mg–Al biotites (Dachs and Benisek, Contrib Mineral Petrol 174:76, 2019) to the K2O–FeO–MgO–Al2O3–SiO2–H2O (KFMASH) system. It has the two composition variables XMg = Mg/(Mg + Fe2+) and octahedral Al, and Fe–Mg and Mg–Al ordering variables resulting in five linearly independent endmembers: annite (Ann, K[Fe]M1[Fe]2M2[Al0.5Si0.5]2T1[Si]2T2O10(OH)2, phlogopite (Phl, K[Mg]M1[Mg]2M2[Al0.5Si0.5]2T1[Si]2T2O10(OH)2, ordered Fe–Mg biotite (Obi, K[Fe]M1[Mg]2M2[Al0.5Si0.5]2T1[Si]2T2O10(OH)2, ordered eastonite (Eas, K[Al]M1[Mg]2M2[Al]2T1[Si]2T2O10(OH)2, and disordered eastonite (Easd, K[Al1/3Mg2/3]M1[Al1/3Mg2/3]2M2[Al]2T1[Si]2T2O10(OH)2. The methods applied to parameterize the mixing properties of the model were: calorimetry, analysis of existing phase-equilibrium data, line-broadening in powder absorption infrared (IR) spectra, and density functional theory (DFT) calculations. For the calorimetric study, various biotite compositions along the annite–phlogopite, annite–siderophyllite (Sid, K[Al]M1[Fe]2M2[Al]2T1[Si]2T2O10(OH)2), and annite–eastonite joins were synthesized hydrothermally at 700 °C, 4 kbar and logfO2 of around − 20.2, close to the redox conditions of the wüstite–magnetite oxygen buffer at that P–T conditions. The samples were characterised by X-ray powder diffraction (XRPD), energy-dispersive scanning electron microprobe analysis, powder absorption IR spectroscopy, and optical microscopy. The samples were studied further using relaxation calorimetry to measure their heat capacities (Cp) at temperatures from 2 to 300 K. The measured Cp/T was then integrated to get the calorimetric (vibrational) entropies of the samples at 298.15 K. These show linear behaviour when plotted as a function of composition for all three binaries. Excess entropies of mixing are thus zero for the important biotite joins. Excess volumes of mixing are also zero within error for the three binaries Phl-Ann, Ann-Sid, and Ann-Eas. KFMASH biotite, therefore, has excess enthalpies which are independent of pressure and temperature (WGij = WHij). A least-squares procedure was applied in the thermodynamic analysis of published experimental data on the Fe–Mg exchange between biotite and olivine, combined with phase-equilibrium data for phlogopite + quartz stability and experimental data for the Al-saturation level of biotite in the assemblage biotite–sillimanite–sanidine–quartz–H2O to constrain enthalpic mixing parameters and to derive enthalpy of formation values for biotite endmembers. For Fe–Mg mixing in biotite, the most important binary, this gave best-fit asymmetric Margules enthalpy parameters of WHAnnPhl = 14.3 ± 3.4 kJ/mol and WHPhlAnn = −8.8 ± 8.0 kJ/mol (3-cation basis). The resulting asymmetric molar excess Gibbs free energy (Gex) departs only slightly from ideality and is negative at Fe-rich and positive at Mg-rich compositions. Near-ideal activity–composition relationships are thus indicated for the Ann–Phl binary. The presently used low value of − 2 kJ/mol for the enthalpy change of the reaction 2/3 Phl + 1/3 Ann = Obi is generally confirmed by DFT calculations that gave − 2 ± 3 kJ/mol for this ∆HFe–Mg order, indicating that Fe–Mg ordering in biotite is weak. The large enthalpy change of ∆HMg-Al disorder = 34.5 kJ/mol for the disordering of Mg and Al on the M sites in Eas (Dachs and Benisek 2019) is reconfirmed by additional DFT calculations. In combination with WHPhlEas = 10 kJ/mol, which is the preferred value of this study describing mixing along the Phl–Eas join, Mg–Al disordering over the M sites of biotite is predicted to be only significant at high temperatures > 1000 °C. In contrast, it plays no role in metamorphic P–T settings.