From accurate data of activities (a), partial molar volumes (V̄), and compressibility (K) of binary aqueous mixtures, the so-called Kirkwood–Buff integrals Gij defined by Gij=∫∞0 [ gij(r) −1] 4πr2 dr=f(a,V̄,K), (i=1,2; j=1,2), have been calculated in the whole concentration range. Fourteen water(1)-organic cosolvent(2) systems [methanol, ethanol, 1-propanol, 1-butanol, 2-methyl-2-propanol, acetonitrile, acetone, dimethylsulfoxide, tetrahydrofuran, piperidine, pyridine, 1,4-dioxane, 2-aminoethanol, 2-(dimethylamino)ethanol] have been studied at 25 °C, and two (methanol and ethanol) also at different temperatures. The Gij functions show these features in relation to the molecular structures of component 2: (1) when this component presents a large nonpolar moiety, extrema are exhibited by Gij’s at certain concentrations the more marked the larger the nonpolar portion; (2) when component two is bifunctional, Gij trend is monotonic with concentration; (3) in the temperature range 0–90 °C, G22 increases and G12 decreases with increasing T in the water-rich concentration region. By interpreting the Gij quantities as a measure of the net attraction (or repulsion) among i and j molecules and as an indication of the tendency of molecules j to cluster around a molecule i, the present results also suggested that: (a) the hydrophobic interaction (attraction) more and more increases with increasing the size of the nonpolar moiety of component two, this increase being most marked at mole fraction x2≂0.2–0.3; (b) hydrophilic groups remarkably reduce the attraction among hydrocarbon-like chains according to the sequence: OH≊NH2>NH≊O≊SO>CO >CN≊Nar; (c) the hydrophobic interaction increases with increasing temperature, in contrast to the common belief that such a phenomenon is induced by the peculiar structural features of water, and that these features fade out as temperature increases.

It is shown that a reference state is necessary for the correct interpretation of the Kirkwood−Buff integrals, G ij , of liquid mixtures in terms of interactions between the components and for their use in the calculation of the local composition. This state is identified with the symmetrical ideal system, and its G ij 's are taken as zero-level. The equations for calculating the G ij of the reference mixtures are derived and discussed, and those for calculating local composition and preferential solvation are reformulated with respect to the reference system. The mixtures of compounds with large size mismatch and/or small deviations from Raoult's law are those for which the new equations should be applied in order to get correct indications on the interactions that take place and influence the preferential solvation. A comparison with Flory−Huggins athermal mixtures (G E = −TSE) as reference systems is also made, allowing one to estimate the relative weights of the contributions to G ij and preferential solvation due to the excluded volume and to the entropy effect both originated by the size mismatch of the components. Seventeen binary mixtures chosen to cover a wide range of deviation from Raoult's law and of the ratio and difference of the component molar volumes are examined; they comprise mixtures of apolar or low-polarity substances (rare gases, hydrocarbons, halocarbons), athermal mixtures, as well as systems involving strongly polar or associating compounds such as water, alcohols, glycols, dimethylformamide. For most mixtures, the present new treatment provides either different or new information, in regard to preferential solvation and molecular interactions, with respect to the usual way of examining G ij data.

A simple expression for the radial distribution function ͑RDF͒ 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 ⑀ AA /⑀ BB 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.

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