The Kirkwood-Buff theory of solutions and the local composition of liquid mixtures

The present paper is devoted to the local composition of liquid mixtures calculated in the framework of the Kirkwood-Buff theory of solutions. A new method is suggested to calculate the excess (or deficit) number of various molecules around a selected (central) molecule in binary and multicomponent liquid mixtures in terms of measurable macroscopic thermodynamic quantities, such as the derivatives of the chemical potentials with respect to concentrations, the isothermal compressibility, and the partial molar volumes. This method accounts for an inaccessible volume due to the presence of a central molecule and is applied to binary and ternary mixtures. For the ideal binary mixture it is shown that because of the difference in the volumes of the pure components there is an excess (or deficit) number of different molecules around a central molecule. The excess (or deficit) becomes zero when the components of the ideal binary mixture have the same volume. The new method is also applied to methanol + water and 2-propanol + water mixtures. In the case of the 2-propanol + water mixture, the new method, in contrast to the other ones, indicates that clusters dominated by 2-propanol disappear at high alcohol mole fractions, in agreement with experimental observations. Finally, it is shown that the application of the new procedure to the ternary mixture water/protein/cosolvent at infinite dilution of the protein led to almost the same results as the methods involving a reference state.     

Hydration of alcohol clusters in 1-propanol-water mixture studied by quasielastic neutron scattering and an interpretation of anomalous excess partial molar volume

Quasielastic neutron scattering measurements have been made for 1-propanol-water mixtures in a range of alcohol concentration from 0.0 to 0.167 in mole fraction at 25 degrees C. Fraction alpha of water molecules hydrated to fractal surface of alcohol clusters in 1-propanol-water mixture was obtained as a function of alcohol concentration. Average hydration number N(ws) of 1-propanol molecule is derived from the value of alpha as a function of alcohol concentration. By extrapolating N(ws) to infinite dilution, we obtain values of 12-13 as hydration number of isolated 1-propanol molecule. A simple interpretation of structural origin of anomalous excess partial molar volume of water is proposed and as a result a simple equation for the excess partial molar volume is deduced in terms of alpha. Calculated values of the excess partial molar volumes of water and 1-propanol and the excess molar volume of the mixture are in good agreement with experimental values.     

Effect of toluene in the dipolar interaction of some aliphatic alcohols

Sound velocity, density and viscosity values have been measured at 303 K in the three binary systems of toluene + methanol, ethanol, 1-propanol. From these data, acoustical parameters such as adiabatic compressibility, free length, free volume and internal pressure have been estimated using the standard relations. The results are interpreted in terms of molecular interaction between the components of the mixtures. Observed excess value in all the mixture indicates that the molecular symmetry existing in the system is highly disturbed by the non-polar toluene molecules and dipole–dipole type interactions exist in the systems.     

Excess compressibility in binary liquid mixtures

Brillouin scattering experiments have been carried out on some mixtures of molecular liquids. From the measurement of the hypersonic velocities we have evaluated the adiabatic compressibility as a function of the volume fraction. We show how the quadratic form of the excess compressibility dependence on the solute volume fraction can be derived by simple statistical effects and does not imply any interaction among the components of the system other than excluded volume effects. This idea is supported by the comparison of the experimental results with a well-established prototype model, consisting of a binary mixture of hard spheres with a nonadditive interaction potential. This naive model turns out to be able to produce a very wide spectrum of structural and thermodynamic features depending on values of its parameters. An attempt has made to understand what kind of structural information can be gained through the analysis of the volume fraction dependence of the compressibility.     

Molecular Interactions in Binary Mixtures of Benzene with 1-Alkanols(C5,C7,C8) at 35℃:An Ultrasonic Study

Densities and ultrasonic speeds have been measured in binary mixtures of benzene with 1‐pentanol, 1‐heptanol and 1‐octanol, and in the pure components, as a function of composition at 35 °C. The isentropic compressibility, intermolecular free length, relative association, acoustic impedance, isothermal compressibility, thermal expansion coefficient, deviations in isentropic compressibility, excess free length, excess volume, deviations in ultrasonic speed, excess acoustic impedance, apparent molar compressibility, apparent molar volume, partial molar volume of 1‐alkanol in benzene have been calculated from the experimental data of densities and ultrasonic speeds. The variation of these parameters with composition indicates weak interaction between the component molecules and this interaction decreases in the order: 1‐pentanol > l‐heptanol> 1‐octanol. Further, theoretical values of ultrasonic speeds were evaluated using free length theory, collision factor theory, Nomoto's relation and Van Dæl‐Vangeel ideal mixing relation. The relative merits of these theories and relations were discussed for these systems.     

同分异构体对苯和丁醇的偶极相互作用的影响

Sound velocity, density, and viscosity values were measured at 303 K in four binary systems of benzene ＋1-, 2-, tert-, or iso-butanol. From these data, acoustical parameters, such as adiabatic compressibility, free length, free volume, and internal pressure were estimated using the standard relations. The results are interpreted in terms of molecular interaction between the components of the mixtures. Observed excess value in all the mixture indicates that the molecular symmetry existing in the system is highly disturbed by the nonpolar benzene molecules. Interaction energy terms of the statistical mixing are also verified for these binary systems and the dipole-dipole interactions are found to be predominantly present and are sharply affected by the isomeric forms of butanol.     

Study of molecular interaction in binary liquid mixtures of ethyl acetoacetate with chloroform and dimethylsulphoxide using excess acoustic parameters and spectroscopic methods

Densities and ultrasonic velocities were measured for binary liquid mixtures of ethyl acetoacetate (EAA) with chloroform (CHCl₃) and dimethylsulphoxide (DMSO) over the entire composition range. These experimental values were used to calculate the adiabatic compressibility (βs), intermolecular free length (L_f), excess molar volume (V^E), excess adiabatic compressibility (β_s^E) and excess intermolecular free length (L_f^E) for the liquid mixtures under consideration. In all the excess parameters, a positive deviation was observed in CHCl₃–EAA binary mixture, whereas a slight negative deviation was found for EAA–DMSO binary liquid mixture. These deviations were explained in terms of molecular interactions between like and unlike molecules and further affirmed by UV–Vis spectroscopic measurements in terms of polar and non-polar environment in the close proximity of solvatochromic dye. Fourier transform infrared spectroscopy (FT-IR) and proton-nuclear magnetic resonance (H¹ NMR) measurements have also been done to explain the molecular interaction in the binary liquid mixtures.     

Effect of Isomerism in the Dipolar Interaction of Benzene with Butanol

Sound velocity, density, and viscosity values were measured at 303 K in four binary systems of benzene + 1-, 2-, tert-, or iso-butanol. From these data, acoustical parameters, such as adiabatic compressibility, free length, free volume, and internal pressure were estimated using the standard relations. The results are interpreted in terms of molecular interaction between the components of the mixtures. Observed excess value in all the mixture indicates that the molecular symmetry existing in the system is highly disturbed by the nonpolar benzene molecules. Interaction energy terms of the statistical mixing are also verified for these binary systems and the dipole-dipole interactions are found to be predominantly present and are sharply affected by the isomeric forms of butanol.     

Excess around a central molecule with application to binary mixtures

It was shown by us (J. Phys. Chem. B, 2006, 110, 12707) that the excess (deficit) of any species i around a central molecule j in a binary mixture is not provided by c(i)G(ij) (where c(i) is the molar concentration of species i in the mixture and G(ij) are the Kirkwood-Buff integrals) as usually considered and that an additional term, involving a volume V(j) which is inaccessible to molecules of species i because of the presence of the central molecule j, must be included. In this paper, the new expression is applied to various binary mixtures and used to establish a simple criterion for preferential solvation in a binary system. First, it is applied to binary Lennard-Jones fluids. The conventional expression for the excess (deficit) in binary mixtures, c(i)G(ij), provides always deficits around any central molecule in such fluids. In contrast, the new expression provides excess for one species and deficit for the other one. In addition, two kinds of binary mixtures involving weak (argon/krypton) and strong (alcohols/water) intermolecular interactions were considered. Again, the conventional expression for the excess (deficit) in a binary mixture, c(i)G(ij), provides always deficits for any central molecule in the argon/krypton mixture, whereas the new expression provides excess for argon (a somewhat smaller molecule) and deficit for krypton. Three alcohol/water binary mixtures (1-propanol/water, tert-butanol/water and methanol/water) with strong intermolecular interactions were considered and compared with the available experimental information regarding the molecular clustering in solutions. We found (for 1-propanol/water and tert-butanol/water) a large excess of alcohols around a central alcohol molecule and a large excess of water around a central water molecule. For both mixtures the maximum of the calculated excess with respect to the concentration corresponds to the maximum in the cluster size found experimentally, and the range of alcohol concentrations in which the calculated excess becomes very small corresponds to the composition range in which no clusters could be identified experimentally.     

Ultrasonic and IR study of molecular association process through hydrogen bonding in ternary liquid mixtures

Complex formation in ternary liquid mixtures of heterocyclic compounds, viz. pyridine and quinoline with phenol in benzene has been studied through ultrasonic velocity measurements (at 2 MHz) in the concentration range of 0.010–0.090 at varying temperatures of 35, 45 and 55 °C. The ultrasonic velocity and density data are used to estimate adiabatic compressibility, intermolecular free length, molar sound velocity, molar compressibility and specific acoustic impedance. These acoustical parameters, in turn, are used to study the solute–solute interactions in these systems. The ultrasonic velocity shows a maxima and adiabatic compressibility a corresponding minima as a function of concentration for these mixtures. The results indicate the possible occurrence of complex formation between unlike molecules through intermolecular hydrogen bonding between the nitrogen atom of pyridine and quinoline molecules and the hydrogen atom of phenol molecule. Further, the excess values of adiabatic compressibility and intermolecular free length have also been evaluated and discussed in relation to complex formation. The infrared spectra of both the systems, pyridine–phenol and quinoline–phenol, have been also recorded for various concentrations at room temperature (35 °C) and found to be useful for understanding the presence of N⋯HO bond complexes and the strength of molecular association at specific concentrations.     

Structuring effects and hydration phenomena in poly(ethylene glycol)/water mixtures investigated by brillouin scattering

Aqueous solutions of poly(ethylene glycol) (PEG) of mean molecular mass of 600 g/mol (PEG600) are investigated by Brillouin scattering technique. At high PEG content, a relaxation phenomenon is observed, which is related to a local rearrangement of the polymer structure where the interaction, via hydrogen bonding, with the solvent molecules plays a role. The obtained values of the relaxation times match the literature data very well for a fast relaxation time revealed by dielectric relaxation measurements in very similar mixtures. The calculated concentration behaviors of the excess adiabatic compressibility turns out in good agreement with the previous findings from ultrasonic measurements at 3 MHz. The observed minimum in the adiabatic compressibility is interpreted as the result of the interaction between water and the EO units of the PEG chain, which results in a structure tighter then that typical of bulk water and of pure PEG600. Such a hypothesis is supported by the observation that volume fraction value of about 0.3 coincides with the concentration value at which full hydration of EO units takes place. The observation that at the same concentration, the polymer coils start to overlap each other further supports the idea that the adiabatic compressibility behavior is monitoring the structural evolution of the mixture. However, similar results are obtained for largely different binary mixture which suggests caution in taking this conclusion too literally. In particular, the hypothesis that the occurrence of an extreme in the excess adiabatic compressibility could be simply originated by statistical effects and that further work is required for disentangling entropic contribution from effects of hetero-association and self-aggregation of one or both the components.     

Acoustical study of molecular interactions in polymer solutions through various thermodynamical parameters and Flory's theory at 298.15 K

This study intends to portray the nature of polymer solutions by ultrasonic velocity and density data. Acoustical parameters, such as relaxation strength, relative association, molecular constant, fractional free volume, available volume, Beyer's non-linearity parameter, internal pressure, van der Waals’ constants and molecular radius have been computed for the binary mixtures of PEG400?+?methanol, PEG400?+?ethanol, PPG400?+?ethanol and PPG400?+?2-propanol systems at 298.15?K. Flory's theory has been used for computing ultrasonic velocity, surface tension, thermal expansion coefficient, thermal conductivity, excess heat capacity and excess isothermal compressibility. Isothermal compressibilities of mixtures have been theoretically evaluated using different theories. A new relation has been proposed by us for evaluating excess molar volume using ultrasonic velocity of the mixture which gives fairly good result when compared with the experimental values. Excess molar volume has been calculated using Flory's theory and Prigogine–Flory–Patterson theory. The partial molar volume and its excess value at infinite dilution have also been evaluated.     

Temperature Dependent Microwave Dielectric Characterization of Associated Liquids

The present paper reports static dielectric constants, densities, viscosities, and refractive indices of the binary mixtures of ethanol with DMSO measured at 303 K, 308 K, 313 K. These measured parameters are used to obtain the derived properties, such as the Bruggeman factor, the molar polarization, the excess molar volume, the excess viscosity, the excess static dielectric constant, and the excess molar polarization. The variation in magnitudes of these quantities with composition and temperature is used to discuss the type, strength, and nature of binary interactions. The excess parameters are fitted to the Redlich Kister (R-K) fit equation. The evaluated values of the excess dielectric constant and the excess molar polarization infer that deviations of their mixture values occur from the mole-fraction mixture law. The results confirm that there are dipole-dipole interactions between unlike molecules of ethanol+DMSO mixtures and that 1:1 complexes are formed. The excess static dielectric constant indicates that there is a decrease in the total number of parallel aligned effective dipoles that contribute to the mixture dielectric polarization. It is observed that the excess molar volume becomes more and more positive with the corresponding increase in the temperature. This observation certainly leads to the inference that the intermolecular interaction strength decreases with the temperature.     

Excess Volumes,Isentropic Compressibilities and Viscosities for Binary Mixtures of <Emphasis Type="Italic">tert</Emphasis>-Butylamine with Alkyl Acetates at 303.15 K

The data on excess volume (V ^E), density (ρ), viscosity (η) and speeds of sound (u) for the binary mixtures of tert-butylamine (TBA) + methyl acetate (MA), + ethyl acetate (EA), + butyl acetate (BA) and + isoamyl acetate (IAA) at 303.15 K were measured experimentally over the entire range of composition. Speeds of sound were evaluated using Jacobson’s free length theory (FLT) and Schaaffs’ collision factor theory (CFT). The viscosity data were analyzed on the basis of the corresponding states approach and the Grunberg and Nissan treatment. The experimental results for excess volume, deviation in isentropic compressibility and deviation in viscosity were discussed in terms of molecular interactions between unlike molecules. A Redlich-Kister type equation was used to fit the experimental data on excess volume, deviation in compressibility and deviation in viscosity.     

Effect of Chain Length on the Dipolar Interaction of Morpholine with Primary Alkanols

Sound velocity, density, and viscosity values have been measured at T = 303 K for four binary systems of morpholine + methanol, ethanol, 1-propanol, and 1-butanol. From these data, acoustical parameters, such as adiabatic compressibility, free length, free volume, and internal pressure, have been estimated using the standard relations. The results are interpreted in terms of the molecular interaction between the components of the mixtures. The observed excess values in all the mixtures indicate that the molecular symmetry existing in the system is highly disturbed by the addition of morpholine molecules. The interaction energy terms of the statistical mixing are also verified for these binary systems, and the dipole-dipole interactions are found to be predominant and are greatly affected by the chain length of the primary alkanols.     

Acoustic,excess thermodynamical,molecular interaction and anti-microbial activity studies on binary liquid mixtures of geranyl acetate and benzyl benzoate in the temperature range of 303.15K–318.15K

The binary organic liquid mixture of geranyl acetate + benzyl benzoate was taken at different mole fractions and various temperatures 303.15K, 308.15K, 313.15K and 318.15K and measured their density, ultrasonic sound velocity and viscosity. Data from experiments were used to calculate variations in binary systems at different temperatures regarding excess acoustic parameters. Variations in ultrasonic velocity, intermolecular free length, and adiabatic compressibility were among these. To estimate the coefficients and standard errors for the excess/deviation functions, multi-parametric non-linear regression analysis was used to fit a Redlich-Kister polynomial with the calculated excess/deviation functions. Changes in these properties with temperature and composition have been investigated in the molecular interactions between the molecules of the binary mixtures. FTIR spectra also support the results. Furthermore, liquid mixtures and individual compounds were studied for their antibacterial activity.     

Thermodynamic Properties of Alkanediols+Acetates at 298.15 K

In this work we present experimental values of the density, refractive index, speed of sound, isentropic compressibility and liquid-liquid equilibria of the binary mixtures (methyl acetate, ethyl acetate, propyl acetate, and butyl acetate) with (1,2-ethanediol, 1,2-propanediol, or 1,3-propanediol) at 298.15 K and atmospheric pressure, as a function of mole fraction. From the experimental values, the corresponding excess and deviation values were computed (excess molar volumes, changes of refractive index on mixing, and changes of isentropic compressibility), variable-degree polynomials being fitted to the results. The validity of different estimation methods for predicting the experimental values of physical properties was tested. The limiting partial excess molar volume of the components in each binary mixture was determined by means of predetermined Redlich-Kister parameters. Group contribution method (UNIFAC-Dortmund) was applied in order to compare their capability in predicting the experimental equilibria values. This revised version was published online in July 2006 with corrections to the Cover Date.     

Excess molar volumes and deviation in viscosities of binary liquid mixtures of acrylic esters with hexane-1-ol at 303.15 and 313.15 K

Densities and viscosities for the four binary liquid mixtures of methyl acrylate, ethyl acrylate, butyl acrylate and methyl methacrylate with hexane-1-ol at temperatures 303.15 and 313.15 K and at atmospheric pressure were measured over the entire composition range. These values were used to calculate excess molar volumes and deviation in viscosities which were fitted to Redlich–Kister polynomial equation. Recently proposed Jouyban Acree model was also used to correlate the experimental values of density and viscosity. The mixture viscosities were correlated by several semi-empirical approaches like Hind, Choudhary–Katti, Grunberg–Nissan, Tamura and Kurata, McAllister three and four body model equations. A graphical representation of excess molar volumes and deviation in isentropic compressibility shows positive nature whereas deviation in viscosity shows negative nature at both temperatures for all four binary liquid mixtures. Positive values of excess molar volumes show that volume expansion is taking place causing rupture of H-bonds in self associated alcohols. The results were discussed in terms of molecular interactions prevailing in the mixtures.     

Correlated Volume Fluctuations in Binary Liquid Mixtures from Isothermal Compressions at 298.15 K

New fluctuation‐related properties are introduced based on the link between the mean‐squared fluctuation of the volume and the isothermal compressibility of binary liquid mixtures by applying the methods of chemical thermodynamics. Some weaknesses have been pointed out in previous similar attempts by other authors. A different result is obtained when Pfeiffer and Heremans′ model for correlated volume fluctuations is worked out in terms of the PTN ensemble (i.e. at constant pressure and temperature). An expression is derived for estimating adjusted correlation coefficients in pairwise volume fluctuations from the knowledge of excess molar isothermal compressions, and it is shown that this expression predicts bounding values for the latter property in real mixtures. Ultrasound speeds in 31 aqueous mixtures of 2‐(ethylamino)ethanol are reported at 298.15 K. The adjusted correlation coefficients for volume fluctuations are graphically depicted at several compositions of two nonaqueous mixtures and eleven aqueous amphiphile mixtures at 298.15 K. This procedure is shown to be an effective means of monitoring interactions between unlike molecules in binary liquid mixtures. A surprisingly high limiting adjusted correlation coefficient is found for water in neat amino alcohols and alcohols possessing a tertiary functional group.     

Modeling of the molar mass distribution of six-arm star-branched poly-epsilon-caprolactam using size-exclusion chromatography

This paper presents a modeling-based approach to the prediction of the molar mass distribution of the various species in a star-branched polycondensation mixture. The interpretation of experimental SEC data of the mixture of linear, cyclic and star-branched molecules is not straightforward, because of the different sizes of those molecules (having the same molecular mass). Therefore we have opted to use SEC analysis with only a concentration detector and fit the experimental data to the theoretical mass distribution, corrected for the volume of the various molecules. This allows the relative fraction and the distribution of the various species in the mixture (linear, cyclic and star-branched) to be determined. To demonstrate this, the six-arm star-branched poly-epsilon-caprolactam based on the six-functional coupling molecule, hexa(6-caproic acid) melamine has been analyzed. Five polymer mixtures with different initial concentration of coupling molecule have been synthesized. As the initial concentration of coupling molecule increased, we found that the weight fraction of star-branched molecules increased, while the weight fraction of linear and cyclic molecules decreased. We also found that the weight-average molar mass and the arm length decrease as the initial fraction of the coupling molecule increases.