Noura Dawass

1.2. I NVERSION OF THE K IRKWOOD –B UFF THEORY 1 7 where the isothermal compressibility κ T and partial molar volumes v α and v β are obtained from experiments. The term ³ ∂µ α ∂ N β ´ T , P , N α can be obtained using second derivatives of the Gibbs excess energy, or experimental vapor pressure data [13] . In Refs. [33] and [34] , equations for KBIs in terms of thermodynamic properties were derived for ternary mixtures. Ben-Naim [14] introduced the inversion procedure in 1977 and applied it to a mixture of water and ethanol. For water (W) and solute (S) systems, it was shown that KBIs obtained from experimental data are useful for studying several local phenomena: (1) the quantity G ∞ WS = G ∞ SW indicates the affinity between the solvent and the solute; (2) KBIs of water, G ∞ WW , reflect the water-water affinity, which can be used to study the changes in the molecular structure of water when adding solutes; and (3) KBIs of solutes, G ∞ SS , are of particular interest for studying hydrophobic interactions. Following the work of Ben-Naim [14] , the inversion of the KB theory was applied to study various types of binary and ternary mixtures at the molecular level [19, 35– 43] . For instance, Patil [39] computed KBIs of water-butanol mix- tures from experimental data of partial molar volumes, isothermal compresibil- ities, and vapor pressures. KBIs of the considered system were used to study lo- cal structure at various concentrations. Similarly, Matteoli et al. [38] used par- tial molar volumes and isothermal compresibilities of mixtures of water and dif- ferent organic co-solvents to find KBIs. The KBIs obtained from the inversion procedure were taken as a measure of the net attraction or repulsion, indicat- ing the level of hydrophobicity of these mixtures. More recently, Kobayashi et al. [44] used KBIs to study properties of residual water in ionic liquids. The au- thors found that the values of KBIs computed using molecular simulation agree with KBIs obtained from experimental data. However, the inversion of the KB theory requires the partial derivatives, ³ ∂µ α ∂ N β ´ T , P , N α , which are difficult to accu- rately obtain from experimental data [45] . Matteoli et al. [38] demonstrated how the accuracy of KBIs obtained from experimental data is very sensitive to uncer- tainties in partial derivatives of the chemical potential. Alternatively, KBIs can be obtained from local fluctuations in number of molecules measured by small an- gle scattering experiments [46] , such as SANS and SAXS [46– 51] . Perera et al. [52] examined a number of water-alcohol mixtures using KBIs and demonstrated that both methods are reliable and should provide similar values of KBIs. Perera et al. [52] pointed out possible sources of errors leading to inaccurate KBIs when using experimental data. For instance, the largest differences between the two methods were observed at the range where the values of the term ³ ∂µ α ∂ N β ´ T , P , N α in