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.     

Experimental excess molar volumes of the ternary mixture and comparisonwith several empirical methods

Experimental excess molar volumes for the ternary system {x₁MTBE+x₂1-propanol+(1–x₁–x₂)nonane} and the three involved binary mixtures have been determined at 298.15 K and atmospheric pressure. Excess molar volumes were determined from the densities of the pure liquids and mixtures, using a DMA 4500 Anton Paar densimeter. The ternary mixture shows maximum values around the binary mixture MTBE+nonane and minimum values for the mixture MTBE+propanol. The ternary contribution to the excess molar volume is negative, with the exception of a range located around the rich compositions of 1-propanol. Several empirical equations predicting ternary mixture properties from experimental binary mixtures have been applied.     

Experimental and predicted excess molar volumes of the ternary system.

Summary Experimental excess molar volumes for the ternary system x₁MTBE+x₂1-propanol+(1-x₁-x₂) heptane and the three involved binary mixtures have been determined at 298.15 K and atmospheric pressure. Excess molar volumes were determined from the densities of the pure liquids and mixtures, using a DMA 4500 Anton Paar densimeter. The ternary mixture shows maximum values around the binary mixture MTBE+heptane and minimum values for the mixture MTBE+propanol. The ternary contribution to the excess molar volume is negative, with the exception of a range located around the rich compositions of 1-propanol. Several empirical equations predicting ternary mixture properties from experimental binary mixtures have been applied.     

Analysis of the pressure effect on the local composition in a water-alkanol mixture using Kirkwood-Buff integrals

Kirkwood-Buff integrals are calculated from the thermodynamic data for binary mixtures of water with methanol, ethanol, 1-propanol, and 2-propanol at a temperature of 298.15 K in the pressure range from atmospheric to 100 MPa. The values of local compositions Δn _ij are calculated which characterize the excess (or deficit) of molecules i around the central molecule j. It is found that the pressure affects destructively the homoassociation in all mixtures studied. In a series MeOH < EtOH < 2-PrOH < 1-PrOH an excess of molecules around the similar type molecules increases in the local environment and the pressure effect on the local composition is enhanced.     

Local composition in solvent + polymer or biopolymer systems

The focus of this paper is on the application of the Kirkwood-Buff (KB) fluctuation theory to the analysis of the local composition in systems composed of a low molecular weight solvent and a high molecular weight polymer or protein. A key quantity in the calculation of the local composition is the excess (or deficit) of any species i around a central molecule j in a binary mixture. A new expression derived by the authors (J. Phys. Chem. B 2006, 110, 12707) for the excess (deficit) is used in the present paper. First, the literature regarding the local composition in such systems is reviewed. It is shown that the frequently used Zimm cluster integral provides incorrect results because it is based on an incorrect expression for the excess (or deficit). In the present paper, our new expression is applied to solvent + macromolecule systems to predict the local composition around both a solvent and a macromolecule central molecule. Five systems (toluene + polystyrene, water + collagen, water + serum albumin, water + hydroxypropyl cellulose, and water + Pluronic P105) were selected for this purpose. The results revealed that for water + collagen and water + serum albumin mixtures, the solvent was in deficit around a central solvent molecule and that for the other three mixtures, the opposite was true. In contrast, the solvent was always in excess around the macromolecule for all mixtures investigated. In the dilute range of the solvent, the excesses are due mainly to the different solvent and macromolecule sizes. However, in the dilute range of the macromolecule, the intermolecular interactions between solvent and macromolecule are mainly responsible for the excess. The obtained results shed some light on protein hydration.     

Densities and Viscosities of the Ternary Mixture (Benzene + 1-Propanol + Ethyl Acetate) at 298.15 K

Abstract

Densities and viscosities of the ternary mixture (benzene + 1-propanol + ethyl acetate) and the corresponding binary mixtures (benzene + 1-propanol, benzene + ethyl acetate and 1-propanol + ethyl acetate) have been measured at the temperature 298.15 K. From these measurements excess volumes, V^E , excess viscosities, η^E, and excess Gibbs energies of activation for viscous flow, G*^E , have been determined. The equation of Redlich-Kister has been used for fitting the excess properties of binary mixtures. The excess properties of the ternary system were fitted to Cibulka's equation.     

Characterization and preferential solvation of the hexane/hexan-1-ol/methylbenzoate ternary solvent

The thermophysical properties of the hexane/hexan-1-ol/methylbenzoate ternary system and its binary constituents were studied at 298.15 K over the whole composition range. The excess and mixing properties calculated from the experimental values combined with the mixture activity coefficients deduced from the UNIFAC group contribution method were used to calculate the integrals of the Kirkwood-Buff fluctuation theory for the ternary system and the binary constituents. Also the local composition and the excess or deficit number of molecules around a central molecule have been determined. The volumetric properties for the ternary system and its binary constituents were correlated and predicted successfully with several cubic equations of state combined with two simple mixing rules. The structural and intermolecular interactions of the mixtures were analyzed on the basis of the measured and derived properties.     

Excess volumes,isentropic compressions,and isobaric heat capacities for methanol mixed with other alkanols at 25°C

Excess volumes, excess isentropic compressions and excess isobaric heat capacities for binary liquid mixtures of methanol with ethanol, 1-propanol and 1-butanol have been determined at 25° C. These thermodynamic functions are smaller than those for alkanol + water mixtures and are correlated with the difference in the alkyl chain length in two of the alkanol molecules. The behavior of the component molecules in solution is found to be similar to that in the pure liquid. The excess isentropic compressions of methanol + 1-butanol show an S-shaped concentration dependence with a positive lobe in the methanol rich range and a negative lobe in the methanol poor range, which resembles that of the excess Gibbs energy reported by Polak et al.     

Excess molar volumes for ternary mixture (N,N-dimethylformamide+1-propanol+water) at the temperature 298.15 K

The results of excess molar volumes for ternary mixture N,N-dimethylformamide (DMF)+1-propanol+water and for binary constituents, DMF+water, DMF+1-propanol and 1-propanol+water at 298.15 K are reported. Several empirical expressions were used to predict and correlate the ternary excess molar volumes from experimental results on the constituent binaries. A pseudo-binary mixture approach (PBMA) was used to analyze the system studied. The partial molar volumes of 1-propanol at infinite dilution in [f_mDMF+(1−f_m)water] mixed solvents at their several fixed composition f_m were evaluated and correlated with the composition f_m.     

UV-visible spectroscopic study of solvation in ternary solvent mixtures: ketocyanine dye in methanol + acetone + water and methanol + acetone + benzene

Solvation characteristics of a ketocyanine dye have been studied in completely miscible ternary solvent mixtures, namely, methanol + acetone + water and methanol + acetone + benzene, by monitoring the solvatochromic absorption band of the dye. The maximum energy of absorption (E) of the solute in a ternary solvent mixture differs significantly from the mole fraction average of the E values in the component solvents. Results in the corresponding binary solvent mixtures also show a deviation of the E value from the mole fraction averaged E values. The results have been explained in terms of preferential solvation using a two phase model of solvation. The excess or deficit over the bulk composition of a solvent component in the vicinity of the solute molecule in a ternary solvent mixture has been estimated using the knowledge of solvation in the corresponding binary mixtures.     

Thermodynamic Properties of Multicomponent Liquid Mixtures

Considering a ternary liquid mixture to be made up of three binary mixtures, by means of cell model using Sutherland type potential function for pair interaction between molecules, a statistical theory for binary liquid mixtures has been extended for ternary systems. In the light of above extension, excess volume ( V E ), excess energy ( E E ) and excess entropy ( TS E ) have been computed for three binary (benzene + cyclohexane, benzene + chlorobenzene and cyclohexane + chlorobenzene) and the resultant ternary system (benzene + cyclohexane + chlorobenzene) at 298.15 K. All the above mentioned excess properties have been computed from the data of ultrasonic velocity and density only.     

Excess volumes of ternary mixtures of N,N-dimethylformamide-diethyl ketone-1-alkanols at 303.15K

Volume changes on mixing of ternary liquid mixtures of N,N-dimethylformamide and diethyl ketone with 1-alkanols have been measured as a function of composition at 303.15 K. The alkanols include 1-propanol, 1-butanol, 1-pentanol and 1-hexanol. The measured V^E values are negative in the mixtures of N,N-dimethylformamide, diethyl ketone and 1-propanol, or 1-butanol. The V^E data exhibits an inversion in sign in the mixture containing 1-pentanol and positive excess volumes are observed in the mixture containing 1-hexanol. The measured data are compared with predicted values based upon empirical relations. The excess volume for the binary mixture of N,N-dimethylformamide with diethyl ketone has been measured over the entire range of composition at 303.15 K. The V^E values are negative for the binary mixture.     

Structures of alkyl benzoate binary mixtures. A Kirkwood-Buff fluctuation theory study using UNIFAC

The structure of the alkyl benzoate + n-alkane, and + alkan-1-ol binary mixtures were analyzed according to the Kirkwood-Buff fluctuation theory on the basis of both the mixture properties measured over a wide temperature range and the activity coefficients calculated with the modified UNIFAC (Dortmund) model as well. Application of this model reveals that both the microheterogeneous structure and the clustering effects are strongly dependent on the chain length of the n-alkane and alkan-1-ol cosolvents. Knowledge of the local composition around each type of molecule is drawn from the Kirkwood-Buff integrals and the excess (or deficit) molecules aggregated around a central one. The rather high values of the integrals evaluated for some of these systems provide first-hand evidence for phase splitting. The conclusions drawn support previous analyses and confirm the adequacy of the methodology put forward for studying liquid mixtures at microscopic level; easily measurable experimental properties can advantageously be used with the fluctuation theory.     

Excess molar volume measurements of ternary mixtures [2-propanol+ethyl acetate+n-hexane] and their binary constituents at 298.15, 308.15 and 313.15 K

The excess molar volume of the ternary mixture [2-propanol?+?ethyl acetate?+?n-hexane], and its binary constituents; [2-propanol?+?ethyl acetate], [2-propanol?+?n-hexane] and [ethyl acetate?+?n-hexane] were evaluated by the mixtures density measurements over the whole concentration range at three temperatures 298.15, 308.15 and 313.15?K. The excess molar volumes data were fitted to the Redlich–Kister (RK) type equation and the parameters of this equation have been calculated and presented for the studied mixtures.     

Refractive Index of Liquid Mixtures: Theory and Experiment

An innovative approach is presented to interpret the refractive index of binary liquid mixtures. The concept of refractive index “before mixing” is introduced and shown to be given by the volume‐fraction mixing rule of the pure‐component refractive indices (Arago–Biot formula). The refractive index of thermodynamically ideal liquid mixtures is demonstrated to be given by the volume‐fraction mixing rule of the pure‐component squared refractive indices (Newton formula). This theoretical formulation entails a positive change of refractive index upon ideal mixing, which is interpreted in terms of dissimilar London dispersion forces centred in the dissimilar molecules making up the mixture. For real liquid mixtures, the refractive index of mixing and the excess refractive index are introduced in a thermodynamic manner. Examples of mixtures are cited for which excess refractive indices and excess molar volumes show all of the four possible sign combinations, a fact that jeopardises the finding of a general equation linking these two excess properties. Refractive indices of 69 mixtures of water with the amphiphile (R,S)‐1‐propoxypropan‐2‐ol are reported at five temperatures in the range 283–303 K. The ideal and real refractive properties of this binary system are discussed. Pear‐shaped plots of excess refractive indices against excess molar volumes show that extreme positive values of excess refractive index occur at a substantially lower mole fraction of the amphiphile than extreme negative values of excess molar volume. Analysis of these plots provides insights into the mixing schemes that occur in different composition segments. A nearly linear variation is found when Balankina’s ratios between excess and ideal values of refractive indices are plotted against ratios between excess and ideal values of molar volumes. It is concluded that, when coupled with volumetric properties, the new thermodynamic functions defined for the analysis of refractive indices of liquid mixtures give important complementary information on the mixing process over the whole composition range.     

Use of a solvatochromic probe for study of solvation in ternary solvent mixture

Solvation characteristics of 2,6-diphenyl-4-(2,4,6-triphenyl-1-pyridino)phenolate in completely miscible ternary solvent mixtures (viz., methanol + acetone + water, methanol + acetone + benzene, and methanol + chloroform + benzene) have been studied by using an electronic spectroscopic procedure. The transition energy (E) corresponding to the charge-transfer band maximum of the solute in a ternary solvent mixture differs significantly from the average E-values in the component solvents weighted by the mole fraction of the solvents. A two-phase model of solvation has been invoked to explain the results. The excess or deficit of solvent components in the local region of the solute molecule over that in the bulk has been estimated using the knowledge of solvation in binary solvent mixtures.     

Volumetric and acoustic properties of the ternary system (1-butanol+1,4-dioxane+cyclohexane)

Densities and speeds of sound for the ternary system 1-butanol+1,4-dioxane+cyclohexane have been measured at the temperatures of 298.15 and 313.15 K. Excess molar volumes and excess isentropic compressibilities have been calculated from experimental data and fitted by the Redlich-Kister equation for ternary mixtures. The ERAS model has been used to calculate excess molar volumes of the ternary mixture from parameters obtained from the constituent binary mixtures.     

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.     

Densities and excess molar volumes of the binary system N-methyldiethanolamine + (2-aminoethyl)ethanolamine and its ternary aqueous mixtures from 283.15 to 363.15 K

Experimental density data of the binary mixtures of N-methyldiethanolamine + (2-aminoethyl)ethanolamine and the ternary mixtures of N-methyldiethanolamine + (2-aminoethyl)ethanolamine + water were reported at atmospheric pressure over the entire composition range at temperatures from 283.15 to 363.15 K. Density measurements were performed using an Anton Paar digital vibrating U-tube densimeter. Excess molar volumes were calculated from the experimental data and correlated as the Redlich-Kister equation for the binary mixtures, and as the Nagata-Tamura equation for the ternary mixtures. Several empirical models were applied to predict the excess molar volumes of ternary mixtures from the corresponding binary mixture values. It indicates that the best agreement with the experimental data was achieved by the Redlich-Kister, Kohler, and Jacob-Fitzner models.     

Local composition in the vicinity of a protein molecule in an aqueous mixed solvent

This paper is focused on the composition of a cosolvent in the vicinity of a protein surface (local composition) and its dependence on various factors. First, the Kirkwood-Buff theory of solution is used to obtain analytical expressions that connect the excess or deficit number of cosolvent and water molecules in the vicinity of a protein surface with experimentally measurable quantities such as the bulk concentration of the mixed solvent, the preferential binding parameter, and the molar volumes of water and cosolvent. Using these expressions, relations between the preferential binding parameter (at a molal concentration scale) and the above excesses (or deficits) are established. In addition, the obtained expressions are used to examine the effect of the nonideality of the water + cosolvent mixtures and of the molar volume of the cosolvent on the excess (or deficit) number of cosolvent molecules in the vicinity of the protein surface. It is shown that at least for the mixed solvents considered (water + urea and water + glucose) the nonideality of the mixed solvent is not an important factor in the local compositions around a protein molecule and that the main contribution is provided by the nonidealities of the protein-water and protein-cosolvent mixtures. Special attention is paid to urea as cosolvent, because urea is one of only a few compounds with a concentration at the protein surface larger than its concentration in the bulk. The composition dependence of the excess of urea around a protein molecule is calculated for the water + lysozyme + urea mixture at pH = 7.0 and 2.0. At pH = 7.0, the excess of urea becomes almost composition independent at high urea concentrations. Such independence could be explained by assuming that urea totally replaces water in some areas of the protein surface, whereas on the remaining areas of the protein surface both water and urea are present with concentration comparable to those in the bulk. The Schellman exchange model was used to relate the preferential binding parameter in water + lysozyme + urea mixtures to the urea concentration.