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.     

Kirkwood-Buff integrals and density fluctuations in aqueous solution of caffeine

The Kirkwood-Buff theory is applied to caffeine aqueous solution. The integrals of radial distribution functions are calculated from the osmotic coefficient, density and sound velocity data at 25°C. The results are discussed in terms of density fluctuations of two components and the correlation between them. It is found that the concentration dependence of Kirkwood-Buff integrals reflects the association tendency of caffeine and its strong influence on the properties of the solvent.     

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.     

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.     

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.     

Hydration patterns and salting effects in sodium chloride solution

The salting effects of 2M sodium chloride electrolyte are studied based on a series of model solutes with properties ranging from hydrophobic to hydrophilic. Generally, hydrophobic solutes will be salted out and hydrophilic solutes will be salted in by NaCl solution. The solvation free energy changes are highly correlated with Kirkwood-Buff integrals. The underlying mechanism resorts to the preferential binding of ions and water to solutes. Our results demonstrate that the salting effect not only depends on the salt's position in Hofmeister series, but also on the solutes' specifics. Taking the hydration free energies of solutes and ions as independent variables, a schematic diagram of salting effects is suggested. The resolved multifaceted salting effects rely on the sensitive balance of the tripartite interaction among solutes, ions, and water.     

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.     

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.     

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.     

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.     

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.     

Equilibrium dialysis data and the relationships between preferential interaction parameters for biological systems in terms of Kirkwood-Buff integrals

Equilibrium dialysis data has provided valuable information concerning the preferential interaction of a cosolvent with a biomolecule in aqueous solutions. Here, we formulate the experimental data in terms of Kirkwood-Buff (KB) theory, resulting in equations that provide a simple physical picture of the dialysis experiment and thereby the interaction of a cosolvent with a biomolecule. These results are then used to establish exact relationships between preferential interaction coefficients, defined in different ensembles and/or using different concentration scales, in terms of KB integrals. It is then argued that the molality based equilibrium dialysis data represent the situation most relevant to computer simulations performed in either open or closed systems.     

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.     

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.     

Application of Kirkwood-Buff theory of liquid mixtures to water-butanol system

The various integrals over the pair correlation functions G_AA' G_WW, and G_AW were calculated for the t-butanol(A)-water(W) system (0 to 8 mole % alcohol) at 25°C by utilizing the thermodynamic quantities, the isothermal compressibility, partial molal volumes, and vapour pressure and by the application of an inverse procedure for Kirkwood-Buff theory of solutions as suggested by Ben-Naim. It is observed that as functions of concentration G_AA', G_AW, and G_WW have extrema in the concentration range studied. The results are interpreted on the basis of structural changes of solvent water. The behavior of G_AA in the concentration range of 0 to 4 % of t-butanol indicates that the strength of hydrophobic interactions decreases with concentration as x_A increases from 0 to 0.04.