Buff Theory Research Articles

Improvement of the reference interaction site model theory for calculating the partial molar volume of amino acids and polypeptides

We propose a simple, efficient bridge correction of the one-dimensional reference interaction site model (1D-RISM) theory. By combining the modified RISM method with the Kirkwood–Buff theory, the partial molar volume (PMV) is calculated for the 20 amino acids and for oligopeptides of glutamic acids in extended and α-helix conformations. The bridge correction drastically improves agreement between the calculated values and the experimental data.

Preferential Interactions of Cosolvents with Hydrophobic Solutes

The variation in solute excess chemical potential has been determined for a range of nonpolar solutes (He, Ne, Ar, CH4) in a series of cosolvent solutions (sodium chloride, urea, guanidinium chloride, 2,2,2-trifluoroethanol) as a function of cosolvent concentration using computer simulations. The data are analyzed using a combination of Kirkwood−Buff theory and the concept of preferential interactions. The results demonstrate that one can accurately reproduce the excess chemical potential changes with a knowledge of the appropriate radial distribution functions over 2−3 solvation shells. The simulations indicate that cosolvent effects are not limited to direct binding of the cosolvent to the solute, although the total and direct binding are linearly related. In addition, it is observed that the effects of changes in water association can be neglected for cases in which the preferential interaction parameter, |ν| < 1.

Hydrophobic self-assembling in dilute aqueous solutions of alcohols and hydrocarbons

Microheterogeneities, such as local compositions which differ from the average ones, are typical features of aqueous solutions of organic substances. A method for computing the sizes of microheterogeneities at infinite dilution (correlation volumes) is proposed, which is based on a combination between the Kirkwood–Buff theory of solution, an expression for the local concentration, ab initio quantum chemical calculations of the interaction energies and available thermodynamic data. The correlation volumes are calculated for aqueous solutions of methanol, ethanol, propanol and isopropanol. The results obtained for propanol and isopropanol could be compared with the sizes determined via small-angle X-ray scattering and good agreement between the calculated and experimental values found. In addition, the mutual affinity of solute molecules (their self-assembling), which is one of the important characteristics of hydrophobic interactions in aqueous solutions, was evaluated for a number of infinitely dilute aqueous solutions of alcohols and hydrocarbons. The calculations provided an additional argument that the hydrophobic self-assembling of hydrocarbons is mainly a result of the preference of the water molecules to interact among themselves via hydrogen bonding than a result of the interactions between hydrocarbon molecules.

Inversion of the Kirkwood–Buff theory of solutions: application to binary systems

Kirkwood–Buff (K–B) integrals play an important role in characterizing the properties and interactions of various liquid mixtures. However, there exists no method to calculate directly the K–B integrals from the easily available experimental data of ultrasonic velocity and density. An attempt has been made to evaluate the same using these initial parameters. A statistical mechanical theory advanced by Arakawa et al. has been used here, in combination with a semi-empirical formula to compute K–B parameters in the whole concentration range for six binary systems at atmospheric pressure and at 298.15 K.

Effect of a third component on the interactions in a binary mixture determined from the fluctuation theory of solutions

The Kirkwood–Buff (KB) theory of solution is applied to a ternary mixture by deriving explicit expressions for the various Kirkwood–Buff integrals (KBIs) and the corresponding excesses of the number of molecules around central ones. However, the ideal solution should be considered non-aggregated, and the above expressions for the excesses provide non-zero values for such a case. For this reason, in order to obtain information about clustering one must subtract from the traditional excesses those which correspond to a reference state, thus ensuring that for an ideal mixture the excesses are zero. The expressions derived for the latter excesses have been applied to the investigation of the N, N-dimethylformamide–methanol–water mixture, to conclude that: (i) in the vicinity of the water molecules there are excesses of water and N, N-dimethylformamide molecules and a deficit of methanol molecules; (ii) in the vicinity of the methanol molecules there are excesses of methanol and N, N-dimethylformamide molecules and a deficit of water molecules; (iii) in the vicinity of the N, N-dimethylformamide molecules there are excesses of methanol and water molecules and a deficit of N, N-dimethylformamide molecules; (iiii) the excesses of N, N-dimethylformamide around water and methanol molecules and those around N, N-dimethylformamide are weakly dependent on the concentration of the third component in a large range of concentrations of the latter, and these results are compatible with the existence of N, N-dimethylformamide–water and N, N-dimethylformamide–alcohol complexes.

Entrainer effect in supercritical mixtures

The objective of this paper is to propose a predictive method for the estimation of the change in the solubility of a solid in a supercritical solvent when another solute (entrainer) or a cosolvent is added to the system. To achieve this goal, the solubility equations were coupled with the Kirkwood–Buff (KB) theory of dilute ternary solutions. In this manner, the solubility of a solid in a supercritical fluid (SCF) in the presence of an entrainer or a cosolvent could be expressed in terms of only binary data. The obtained predictive method was applied to six ternary SCF–solute–cosolute and two SCF–solute–cosolvent systems. In the former case, the agreement with experiment was very good, whereas in the latter, the agreement was only satisfactory, because the data were not for the very dilute systems for which the present approach is valid.

Properties of 2,2,2-trifluoroethanol and water mixtures

2,2,2-trifluoroethanol (TFE) is a commonly used cosolvent in experimental studies of peptides and proteins. Although concentration-dependent TFE effects have been well studied experimentally, the exact mechanism by which TFE affects the solubility and stability of peptides is still unclear. Here we report molecular dynamics simulations of TFE/water mixtures of different composition in an attempt to improve our atomic level understanding of the properties of TFE/water mixtures. The trends in most properties—densities, diffusion constants, dielectric constants, and enthalpies of mixing—were well reproduced, although quantitative agreement with experiment was poor. Other thermodynamic properties of the solutions—partial molar volumes, derivatives of activity coefficients, and isothermal compressibilities—were also determined using the Kirkwood–Buff theory of mixtures. The Kirkwood–Buff analysis indicated significant aggregation of TFE molecules in the mixtures, especially at low mole fractions, in agreement with experiment. However, the aggregation of TFE molecules was exaggerated using the current TFE and water models. The results suggest that the combination of simulation data and Kirkwood–Buff theory provides a powerful tool for the investigation of the thermodynamic properties of hydrogen bonding mixtures.

On Density Microheterogeneities in Dilute Supercritical Solutions

The dilute supercritical mixtures were examined in the framework of the Kirkwood−Buff theory of solutions. Various expressions were employed for the excess number of aggregated molecules of solvent around individual solute molecules to conclude that at infinite dilution the above mentioned excess is zero. This suggested that the density enhancement observed when small amounts of a solute were added to a solvent near the critical point of the latter may not be caused by the aggregation of the solvent molecules around individual solute molecules as usually considered. Further, comparing experimental results, it was shown that the density enhancement caused by the near critical fluctuations in a pure solvent are almost the same, in a wide range of pressures, as those in dilute supercritical mixtures near the critical point of the solvent.

Preferential solvation of N-methylformamide, N,N-dimethylformamide and N-methylacetamide by water and alcohols in the binary and ternary mixtures

Using the Kirkwood–Buff theory of solutions, the preferential solvation of the N-methylacetamide molecule has been investigated in the binary and ternary mixtures containing N-methylacetamide (NMA), aliphatic alcohol and water. The results are compared with those obtained previously for N-methylformamide (NMF) and N,N-dimethylformamide (DMF). The thermodynamic investigations, based on the Kirkwood–Buff theory of solutions, lead to the unexpected conclusion that both NMA and DMF are solvated in the investigated binary and ternary mixtures in a very similar manner, but solvation of NMF differs from other amides. For all the investigated amides, the local mole fractions differ only slightly from the bulk ones—the deviations are only a few per cent or less. Moreover, for the {amide+methanol} binary mixtures, where amide=NMF, DMF and NMA, molecular dynamics calculations at xamide=0.518 were performed. From the obtained molecule–molecule radial distribution functions (rdf) and atom–atom rdf, it was possible to estimate the local mole fractions around the amide molecule, the orientation effects of molecules within the solvation shell, and a possibility of the formation of complexes. The general picture obtained from analysis of the molecular dynamics results is consistent with the deductions derived from thermodynamic data.

Aggregation in Binary Solutions Containing Hexafluorobenzene

Some information about the aggregation in aromatic fluorocarbon−aromatic hydrocarbon systems was obtained on the basis of the Kirkwood−Buff theory of solution. The Kirkwood−Buff integrals and the excess (or deficit) number of molecules aggregated around a central one were calculated for the following systems: hexafluorobenzene−benzene, hexafluorobenzene−toluene, hexafluorobenzene−cyclohexane, benzene−toluene, and benzene−cyclohexane. It was found that the composition dependence of the excess (or deficit) number of molecules aggregated around a central one for the systems hexafluorobenzene−benzene and hexafluorobenzene−toluene has a nontypical character since it changes sign for a mole fraction of about 0.4 for the former and 0.2 for the latter. It was found that such compositions correspond to extrema in the activity coefficients and inflection points in the excess Gibbs energy. The excess (or deficit) number of molecules aggregated around a central one in the systems investigated allowed us to conclude ...

Range and Energy of Interaction at Infinite Dilution in Aqueous Solutions of Alcohols and Hydrocarbons

Infinitely dilute hydrocarbon/water and alcohol/water systems were examined, with the objective to gather information about the size of the volume which is affected by the presence of a solute molecule and the interaction energy parameter between solute and solvent. First, an expression for the local composition at infinite dilution was obtained on the basis of the Kirkwood−Buff theory of solution. Second, equations for the activity coefficients at infinite dilution were derived using a modified Flory−Huggins equation for the excess free energy. In this modified expression, the molar fractions in the volume fractions were replaced by the local compositions provided by the first step. Finally, an additional expression for the local molar fraction was selected, which was coupled with that obtained on the basis of the Kirkwood−Buff approach. Experimental data regarding the activity coefficient at infinite dilution combined with the above equations allowed to obtain the values of the correlation volume (volum...

Kirkwood–Buff Thermodynamics Derived from Grand Canonical Molecular Dynamics and DRISM Calculations

The grand canonical ensemble techniques—both Monte Carlo and molecular dynamics—have become very popular in recent years, but no direct link between the number fluctuation results from these simulation methods and a Kirkwood–Buff theory has been established. In this article we look at Kirkwood–Buff integrals computed using thermodynamic averages derived from grand canonical ensemble molecular dynamics simulations and compare them to similar quantities derived from the dielectrically consistent reference interaction site model many-body theory. These calculations will be carried out for three different water models, SPC, SPC/E, and TIP3P.

Kirkwood−Buff Integrals in Aqueous Alcohol Systems: Aggregation, Correlation Volume, and Local Composition

The Kirkwood−Buff theory of solution was used to investigate the formation of clusters in aqueous alcohol solutions. The correlation volume (volume in which the composition differs from the bulk one) was calculated for the systems 1-propanol−water and tert-butyl alcohol−water and compared with the sizes of clusters determined by various physical techniques. The calculations indicated that two types of clusters, alcohol- and water-rich clusters, are present in the solutions. Their sizes, which depend on composition in a similar way, exhibit maxima in the water-rich region. The calculated values are in a satisfactory agreement with experiment. The composition inside the clusters (the local composition) was calculated as a function of the correlation volume for dilute aqueous methanol, ethanol, propanols, and tert-butyl alcohol solutions. The results were compared with the local compositions provided by the Wilson and NRTL equations.

On the calculation of thermodynamic properties of electrolyte solutions from Kirkwood–Buff theory

Earlier workers discussed a methodological difficulty of using Kirkwood–Buff theory for ionic solutions, arising from the non-invertibility of the matrix ∂ρ/∂μ for ionic species. We point out that there exists no such difficulty if the method of generalized inverse is used. It is found that the problem of non-uniqueness of the generalized inverse does not affect the thermodynamic properties, and is related to our inability to split the chemical potential of salt into that of its constituent ions, uniquely.

Solvation of amide group by water and alcohols investigated using the Kirkwood–Buff theory of solutions

The Kirkwood–Buff theory of solutions has been used to investigate the preferential solvation of N-methylformamide by water and alcohol. Binary mixtures (N-methylformamide–A), where A = water, methanol or ethanol and ternary mixtures (N-methylformamide–alcohol–water), were studied at 313.15 K. The results are compared with those obtained previously for analogous mixtures containing N,N-dimethylformamide at the same temperature. It was found that the differences between the local mole fractions of water or alcohol in the immediate vicinity of the amide molecule and the bulk ones can be mainly explained by the differences in molecular sizes, the deviations are only a few per cent. From the calculation of the entropy change resulting from the orientation effects it follows that for amide–alcohol mixtures, for the investigated amides, this entropy change is positive, increasing systematically in the order: methanol<ethanol<propanol. For the N,N-dimethylformamide–water mixture the orientational entropy is strongly negative, and for N-methylformamide–water this value is expected also to be strongly negative. For ternary mixtures containing amide, alcohol and water, preferential hydration is weak and it is observed in the alcohol-rich region only. Both the amides are solvated in the mixture in a very similar manner, which means that replacing a methyl group by hydrogen and exposing the lone electron pair on the nitrogen atom to interactions with water or alcohol molecules shows insignificant influence on the local mole fractions of the components around the amide molecule and on the solvation process.

Molecular Probing of Polymeric Microstructure and Nonrandom Partitioning of Solvents Absorbed in Polymers by Inverse Gas Chromatography

The microscopic structure of amorphous polymers was studied by using different molecular probes in finite dilution inverse gas chromatography (FDIGC) experiments. This molecular probe technique allows one to study nonrandom partitioning of solvent molecules and spatial correlation of polymer chain segments in a bulk. A novel approach was developed to determine cluster integrals as defined in the Kirkwood−Buff theory of mixtures. Solvent self-cluster integrals, a combination of cluster integrals expressing preferential solvation, and the values of the mean cluster size were determined for different polymer systems as a function of the volume fraction of the probe in the bulk of the polymers. Polymers with different polarities [a substituted poly(thionylphosphazene), a saturated polyester poly(diethylene glycol−succinic acid), and an essentially apolar poly(dimethylsiloxane)] were used as model materials. The microstructure and the solvent−polymer interaction are discussed in detail for each system. The results obtained allowed us to gain novel insight into the polymeric microstructure and short-range order, thus giving credibility to our approach to study microstructure by cluster integrals from inverse gas chromatography (IGC) data.

Volumetric properties of aqueous solutions of ethylene glycol oligomers at 25 °C

Densities have been measured of aqueous solutions of ethylene glycol oligomers at 25 °C. Expressions for the limiting partial molar volumes were obtained: V2=V02+V22X2. Both V02 and V22 were found to be linear functions of the ethoxy group (—CH2—O—CH2—) number. The Kirkwood–Buff theory was used to interpret the V2 behaviour.

A simple expression for radial distribution functions of pure fluids and mixtures

A simple expression for the radial distribution function (RDF) of pure fluids and mixtures is presented. It satisfies the limiting conditions of zero density and infinite distance imposed by statistical thermodynamics. The equation contains seven adjustable parameters; they have been fitted to extensive literature data of RDF’s for a Lennard-Jones fluid at different values of temperature and density. These in turn have been expressed as functions of reduced temperature and density, thus allowing a complete parametrization with respect to these variables using 21 parameters altogether with fairly good accuracy. The values of the reduced pressure and internal energy calculated by numerical integration of the completely parametrized equation compare fairly with literature molecular dynamics simulation results. The capability of the expression to fit to RDF’s of mixtures has been checked against some of the extensive RDF simulation data of binary mixtures of Lennard-Jones fluids with different diameters available in the literature. Data pertaining to different molar fractions as well as to different εAA/εBB ratios have been considered, and the agreement between calculated and simulation curves has resulted satisfactory. The proposed expression can be used to calculate by integration related quantities such as compressibility, internal energy, pressure and, using the Kirkwood–Buff theory, the chemical potentials and partial molar volumes of the components of mixtures for which RDF data are available.

On the calculation of single ionic activity coefficients by Kirkwood—Buff theory: comments

An expression derived recently describing the dependence of single ionic activity coefficients on solution composition is compared with earlier work. The condition that must be met for the two approaches to be compatible is derived and shown to apply to a solution in which the ions associate to form a series of charged complex species whose distribution functions conform to Debye—Hückel theory.

Thermodynamics of the transition state and the application to interfacial reactions

According to transition-state theory, when the equilibrium hypothesis is valid, activated complexes formed from reactants may be treated thermodynamically in the same way as other species present in very small amounts. Inclusion of these complexes in the Gibbs–Duhem equation for the solution enables an expression to be derived for the dependence of the equilibrium concentration of activated complexes on the solution composition. When the transmission coefficient of the reaction is insensitive to the reaction environment this expression leads directly to the effect of solution composition on the reaction rate. For bulk solutions, this approach is entirely equivalent to that published recently based on the Kirkwood–Buff theory of solutions. For reactions at interfaces the Gibbs adsorption equation plays the same role as the Gibbs–Duhem equation for reactions in bulk and similar arguments apply. These arguments are used to obtain a general expression for the transfer coefficient β in the Butler–Volmer equation of electrode kinetics and for the dependence of β on solution composition. A similar treatment can also be applied to the effects on reaction rates of macromolecules which interact with reactants. Finally, the situation in which adsorbed material is not in equilibrium with that in the bulk solution immediately adjacent to the interface is considered and general guidelines for dealing with this type of situation are forwarded.