A critique of some recent suggestions to correct the Kirkwood-Buff integrals

This article is a thorough critique of some recent publications by Matteoli, Lepori, Ruckenstein and others who suggested a correction to the Kirkwood-Buff integrals to obtain "better" information on the molecular interactions. It is shown that the suggested "corrected" Kirkwood-Buff integrals are, in fact, less informative than the original integrals. A detailed and critical examination of the arguments that led to the suggested correction reveals some serious flaws. Therefore, it is argued that the corrected Kirkwood-Buff integrals should be "recorrected" to restore their original definition and meaning.     

A fluctuation theory analysis of the salting-out effect

An analysis of the salting-out, or Sechenow, effect is given in terms of Kirkwood-Buff, or fluctuation, integrals. The analysis is formally exact but cannot easily be applied in its original form. When the solute that is being salted out is sparingly soluble, simplifications arise and the theory can be used to compute one of the Kirkwood-Buff integrals which is otherwise difficult to obtain.     

Kirkwood-Buff integrals of aqueous alcohol binary mixtures

The Kirkwood-Buff integrals of some binary aqueous alcohol mixtures are computed from the available vapor pressure measurements and compared with previous results as well as small angle neutron scattering experiments. The emphasis of the present report is on accuracy of the results that can be achieved by these two different types of measurements. This seems to be needed, mainly in view of the discrepancies between the various published results, as shown herein. It is argued that agreement in peak positions is more important than that in magnitude. In general, very good agreement is obtained by both methods, and sources of disagreements are discussed. The issue of the computer simulations of aqueous systems and the problematics related to correlations, microheterogeneity, and consequently the Kirkwood-Buff integrals are equally discussed herein.     

Structure of aqueous solutions of ionic liquid 1-butyl-3-methylimidazolium tetrafluoroborate by small-angle neutron scattering

The structure of aqueous solutions of a prototype ionic liquid, the short alkyl chain 1-butyl-3-methylimidazolium tetrafluoroborate ([C4mim][BF4]) has been investigated by small-angle neutron scattering. Concentration fluctuations and Kirkwood-Buff integrals have been calculated, and the results are in good agreement with corresponding data calculated herein from vapor pressure measurements. The large concentration fluctuations and Kirkwood-Buff integral values indicate that the system is in the vicinity of phase separation, which is known to occur some 20 K below room temperature, at a salt mole fraction of around 0.075.     

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.     

The Kirkwood-Buff integrals for one-component liquids

The Kirkwood-Buff integrals (KBIs) for one-component systems are calculated from either the pair correlation functions or from experimental macroscopic quantities. As in the case of mixtures, the KBIs provide important information on the local densities around a molecule. In the low density limit (rho-->0) one can extract from the KBI some information on the strength of the intermolecular forces. No such information may be extracted from the KBIs at higher densities. We used experimental data on densities and isothermal compressibilities to calculate the KBIs for various liquids ranging from inert molecules, to hydrocarbons, alcohols, and liquid water.     

Aqueous tert-butanol mixtures: a model for molecular-emulsions

By analogy with micro-emulsion, we introduce the molecular-emulsion picture to describe particular aqueous mixtures. The analogy is set by introducing the equivalent of the Teubner-Strey structure factor, the latter which is traditionally used to describe the structure of micro-emulsions. The main difference resides in the fact that the size of the oil and water domains are not in the micrometer, but in the nanometer scale. This implies that the molecular size and the molecular geometry cannot be neglected anymore. The introduction of this analogy is used to settle the problem of properly describing with computer simulations highly micro-heterogeneous aqueous mixtures. In particular, the issue of whether or not the Kirkwood-Buff integrals represent solely concentration fluctuations is settled by showing the contribution of the micro-heterogeneity to these integrals through the presence of an associated pre-peak in the structure factors. Both the Optimized Potentials for Liquid State (OPLS) and Transferable Potential for Phase Equilibria-United Atoms (TraPPE-UA) force fields for tert-butanol turn out to be remarkably good in describing the structure of the corresponding aqueous mixtures, when the above-mentioned analogy with micro-emulsion is introduced to correct for the computational artifacts in the Kirkwood-Buff integrals.     

Modeling nonionic aqueous solutions: the acetone-water mixture

Several combinations of existing classical water and acetone models are studied by molecular dynamic simulations in order to sort out which models can reproduce available experimental data: enthalpies, pressure, densities, diffusion coefficients, and Kirkwood-Buff integrals. It turns out that all these properties, but the last, are rather well reproduced by all models, and with little numerical effort. By contrast, trials to measure by simulations the Kirkwood-Buff integrals lead to very long simulation times, thus revealing unexpected divergent behavior between the different models, such as phase separation, for example, and ultimately leading to a failure of any models combinations to reproduce these properties according to the experimental tendencies. It is argued herein that these deficiencies provide, in fact, an insightful picture of the microscopic structure of the solution, particularly into the relation between the hydrogen-bond network and the concentration fluctuations, as well as the role played by the solute in their spatial organization.     

Thermodynamics of Mixtures Containing Organic Carbonates. Part XV. Application of the Kirkwood-Buff Theory to the Study of Interactions in Liquid Mixtures Containing Dialkyl Carbonates and Alkanes,Benzene, CCl4 or 1-Alkanols

Binary liquid mixtures containing a dialkyl carbonate (dimethyl or diethyl carbonate) and organic solvents such as alkanes, benzene, CCl₄, or 1-alkanols were studied within the framework of the Kirkwood-Buff formalism. The Kirkwood-Buff integrals, linear coefficients of preferential solvation and local mole fractions were calculated. Results were interpreted assuming that the mixtures with alkanes or 1-alkanols are not random mixtures, which can be ascribed to the existence of strong dipolar interactions between like molecules. Systems containing benzene or CCl₄ are both random and more ordered because of the charge transfer or dipole/induced dipole interactions between the polar group of the solute (O–CO–O) and the polarizable solvent molecules. The effect of increasing temperature was also examined.     

On the evaluation of the Kirkwood-Buff integrals of aqueous acetone mixtures

The Kirkwood-Buff integrals of acetone-water mixtures are determined using two experimental techniques: small-angle neutron scattering and vapor pressure measurements, in order to test the precision and reliability that can be achieved. The data are then compared with those previously reported by different authors, which tend to show considerable variation between them. The various possible sources of inaccuracies are pointed out, both from experimental origins and from the numerical treatment of the data. Comparison with recent simulation results allows to critically compare different models and provide some information about the microstructure of the aqueous mixture.     

Solution structure and Kirkwood-Buff theory: Informativity and sensitivity to specific interactions

A comparative significance of the contribution from density and excess Gibbs energy into Kirkwood-Buff integrals G _ij has been considered exemplified by H₂O-sulfolane, H₂O-THF and model mixtures. It is shown that some salient features of the volume properties which are generally thought to be the sign of strongly hydrophobic behavior of solutes, do not clearly manifest themselves in the concentration dependences of these integrals. Literature data for G _ij have been analyzed and the structural information inherent to G _ij is assessed. Contributions from the first and the following solvation spheres to G _ij have been evaluated from the distribution functions of model mixtures computed by the Born-Green equation and it is shown that with no new chemical bonds, the contribution from the first solvation sphere does not govern the whole of G _ij and, consequently, G _ij as calculated from the thermodynamic properties contain no direct information as far as the details of short-range interactions are concerned.     

Local and global properties of mixtures in one-dimensional systems. Part I. Mixtures of two simple components

Two sets of quantities are calculated for two-component mixtures in one dimension. One consists of the traditional excess thermodynamic quantities which provide global information on the mixtures. The second, referred to as local properties, consists of the Kirkwood-Buff integrals, local composition, solvation, and preferential solvation quantities. In this part, we discuss simple particles interacting via either square-well potential or hard rod potential. It is shown that a host of new information can be obtained from the local properties of the mixtures which supplements the information conveyed by the global properties.     

On the theory of solute solubility in mixed solvents

A series of equations are developed for the study of the effects of cosolvents on the solubility of a solute in mixed solutions where the solute displays a finite solubility. The equations differ depending on the scale used for the solute (and cosolvent) concentrations. The expressions use Kirkwood-Buff integrals to relate the changes in solubility to changes in the local solution composition around the solute and can be applied to study any type of ternary system including electrolyte cosolvents. The expressions provided here differ from previous approaches because of the use of a semi-open ensemble and the extension to finite solute solubilities.     

Thermodynamic properties of strong electrolyte solutions from correlation functions

General relations are presented to relate the fluctuation thermodynamic properties of multicomponent electrolyte solutions (concentration derivatives of the chemical potential, partial molar volume, and compressibility) to integrals of the total correlation function (Kirkwood-Buff solution theory) and of the nondivergent portion of the direct correlation function. Detailed expressions are given for the single-salt, single-solvent system. It appears that the direct correlation function expressions may be of more practical use in developing correlations for solution properties because, unlike the total correlation functions, terms exist which distinguish between cation and anion interactions with water and with other ions.     

A new force field for atomistic simulations of aqueous tertiary butanol solutions

We present a new tert-butanol force field parametrized to reproduce the mixture thermodynamics of tert-butanol/water over a wide range of solution compositions at room temperature and atmospheric pressure. The experimental Kirkwood-Buff integrals, which quantify preferential solvation of solution components by the same species or by the other components, were used as target values to be reproduced. Water was modeled using the simple point charge model. In the range of alcohol mole fractions between 0.02 and 0.98, our optimized model satisfactorily reproduces alcohol-alcohol, water-water, and alcohol-water aggregation behavior. As a consequence, the solution activity derivatives are reproduced as well. A comparison has been made with solution activities obtained by free energy calculations (i.e., thermodynamic integration). It clearly shows that the Kirkwood-Buff based approach performs superior in predicting solution activities of liquid mixtures. The new tert-butanol model has been used to examine the solution structure and hydrophobic interactions in aqueous tert-butanol at the various mixture compositions. A comparison is made with structural data obtained by neutron diffraction.     

Thermodynamic studies of molecular interactions in aqueous alpha-cyclodextrin solutions: application of McMillan-Mayer and Kirkwood-Buff theories

Osmotic vapor pressure and density measurements were made for aqueous alpha-cyclodextrin (alpha-CD) solutions in the temperature range between 293.15 and 313.15 K. The experimental osmotic coefficient data were used to determine the corresponding activity coefficients and the excess Gibbs free energy of solutions. Further, the activity data obtained at different temperatures along with the enthalpies of dissolution (reported in the literature) were processed to obtain the excess enthalpy and excess entropy values for the solution process. The partial molar entropies of water and of alpha-cyclodextrin were calculated at different temperatures and also at different concentrations of alpha-CD. Using the partial molar volume data at infinite dilution, the solute-solvent cluster integrals were evaluated which yielded information about solute-solvent interactions. The application of McMillan-Mayer theory of solutions was made to obtain osmotic second and third virial coefficients which were decomposed into attractive and repulsive contributions to solute-solute interactions. The second and third osmotic virial coefficients are positive and show minimum at 303.15 K. The Kirkwood-Buff (KB) integrals G(ij), defined by the equation G(ij) = f(infinity)0 (g(ij)- 1)4pir(2) dr, have been evaluated using the experimental osmotic coefficient (and hence activity coefficient) and partial molar volume data. The limiting values of KB integrals, G(ij)(0) are compared with molecular interaction parameters (solute-solute i.e., osmotic second virial coefficient) obtained using McMillan-Mayer theory of solutions. We found an excellent agreement between the two approaches.     

Fluctuations and micro-heterogeneity in aqueous mixtures

The problem as to why water-water density correlations are systematically overestimated in computer simulation of aqueous mixtures is examined through an extensive molecular dynamics study of mixtures of the extended single point charge water model with a fully miscible weaker version of it, obtained by scaling down the site partial charges by a factor 2/3, thereby eliminating solute-solvent size differences. The study reveals that enhanced water correlations is a genuine physical effect, and are not an artifact of the simulations or the models, as previously suggested in the context of realistic aqueous mixtures. Rather, they correspond to the existence of strongly correlated water domains, for "weak-water" mole fraction x > 0.4, that modulate the spatial decay of the density correlations. These domains produce a prepeak in the structure factor, suggesting that simple aqueous mixture might behave just like micro-emulsions. The overestimated long range water correlations result from incorrect predictions of the asymptote of these correlations, which themselves arise from size limitations of the simulation box. However, by requiring consistency between thermodynamical and structural expressions of the concentration fluctuations, a method to predict the proper decay of the correlation function is obtained herein, inspired by the formal analogy with micro-emulsions. This study provides a new insight for the large values of the experimental Kirkwood-Buff integrals for many aqueous mixtures: these mixtures are in a Lifshitz-type regime, where concentration fluctuations compete with water domain formation.