Kirkwood-Buff theory solutions

In more recent work, Johnston and co-workers (17,18,20,27,32) showed quantitatively that the local fluid density about the solute is greater than the bulk density. In these papers, results were presented for CQ2, C2H4, CF3H, and CF3C1. Local densities were recovered by comparison of the observed spectral shift (or position) to that expected for a homogeneous polarizable dielectric medium. Clustering manifests itself in deviation from the expected linear McRae continuum model (17,18,20,27,32,56,57). These data were subsequently interpreted using an expression derived from Kirkwood-Buff solution theory (20). Detailed theoretical... 

The spectroscopic data may be interpreted using an equation that was derived form Kirkwood-Buff solution theory. The number of solvent molecules in excess of the bulk value, U2 , may be defined in terms of a local volume about the solute Vi2as... 

Ellegaard, M. D., J. Abildskov, and J. P. O Connell. 2011. Solubilities of gases in ionic liquids using a corresponding-states approach to Kirkwood-Buff solution theory. Fluid Phase Equilibria. 302, 93. 

Newman, K. E. 1994. Kirkwood-Buff solution theory—Derivation and applications. Chemical Society Reviews. 23, 31. 

Nichols, J. W., S. G. Moore, and D. R. Wheeler. 2009. Improved implementation of Kirkwood-Buff solution theory in periodic molecular simulations. Physical Review E. 80, 051203. 

In this paper, the system CeFe—CgHg and several other systems such as CeFe—C6H5CH3, CeFg—C-C6H12, CgHe—CeHs-CH3, and CeHe—C-C6H12 will be analyzed and compared on the basis of the Kirkwood—Buff (KB) theory of solutions. 9 The KB theory of solutions allows information about the excess (or deficit) number of molecules, of the same or different kind. 

The Kirkwood-Buff (KB) theory of solution [1] (often called fluctuation theory) was originally developed in 1951. This theory connects the macroscopic properties of solutions, such as the isothermal compressibility, the concentration derivatives of the chemical potentials and the partial molar volumes... 

The Kirkwood—Buff (KB) theory of solution (often called fluctuation theory) employs the grand canonical ensemble to relate macroscopic properties, such as the derivatives of the chemical potentials with respect to concentrations, the isothermal compressibility, and the partial molar volnmes, to microscopic properties in the form of spatial integrals involving the radial distribution function. This theory allows one to obtain information regarding some microscopic characteristics of mnlti-component mixtures from measurable macroscopic thermodynamic quantities. However, despite its attractiveness, the KB theory was rarely used in the first three decades after its publication for two main reasons (1) the lack of precise data (in particular regarding the composition dependence of the chemical potentials) and (2) the difficulty to interpret the results obtained. Only after Ben-Naim indicated how to calculate numerically the Kirkwood—Buff integrals (KBIs) for binary systems was this theory used more frequently. 

The Kirkwood—Buff (KB) theory of solutions relates the local properties of solutions, expressed through the KB integrals, to macroscopic thermodynamic quantities. An important application of this theory is to the excess (or deficit) number of molecules of any type around a central molecule. The calculation of this excess (or deficit) is the matter of our disagreement with the preceding Ben-Naim comment. ... 

In this paper, some recent experimental results regarding the density fluctuations in pure SCF are used to show that the local density enhancement in dilute SCR mixtures is mainly due to the near critical fluctuations in the solvent and an explanation is suggested for the negative partial molar volnme of the solute. This conclusion was also strengthened by a discussion, presented in the following section, based on the Kirkwood—Buff (KB) theory of solution. First, the problem will be examined in the framework of the Kirkwood—Buff theory of solution. Second, nsing experimental results about the near critical fluctuations in pure SCF, it will be shown that the density enhancement in dilnte SCR mixtures is mainly caused by the near critical density fluctuations in pure SCF. 

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. 2001 Elsevier Science B.V. All rights reserved. 

The present paper is concerned with mixtures composed of a highly nonideal solute and a multicomponent ideal solvent. A model-free methodology, based on the Kirkwood—Buff (KB) theory of solutions, was employed. The quaternary mixture was considered as an example, and the full set of expressions for the derivatives of the chemical potentials with respect to the number of particles, the partial molar volumes, and the isothermal compressibility were derived on the basis of the KB theory of solutions. Further, the expressions for the derivatives of the activity coefficients were applied to quaternary mixtures composed of a solute and an ideal ternary solvent. It was shown that the activity coefBcient of a solute at infinite dilution in an ideal ternary solvent can be predicted in terms of the activity coefBcients of the solute at infinite dilution in subsystems (solute + the individual three solvents, or solute + two binaries among the solvent species). The methodology could be extended to a system formed of a solute + a multicomponent ideal mixed solvent. The obtained equations were used to predict the gas solubilities and the solubilities of crystalline nonelectrolytes in multicomponent ideal mixed solvents. Good agreement between the predicted and experimental solubilities was obtained. 

The present paper is devoted to the extension of the theory developed by the authors for the solubility of proteins to the solubility of gases. Because this theory is based on the Kirkwood-Buff fluctuation theory of solutions, the next section summarizes the expressions which are involved. This is followed by a summary of the derivation of an equation for the solubility of proteins and finally its extension to the solubility of gases. 

The application of the Kirkwood-Buff fluctuation theory of solutions to the activity coefficients in ternary and multicomponent solutions... 

The main difficulty in predicting the solid solubility in a mixed solvent consists in calculating the activity coefficient of a solute in a ternary mixture In this paper, the Kirkwood-Buff (KB) theory of solutions (or fluctuation theory) (Kirkwood and Buff, 1951) is employed to analyze the solid (particularly drug) solubility in mixed (mainly aqueous) solvents. The analysis is based on results obtained previously regarding the composition derivatives of the activity coefficients in ternary solutions (Ruckenstein and Shulgin, 2001). These equations were successfully applied to gas solubilities in mixed solvents (Ruckenstein and Shulgin, 2002 Shulgin and Ruckenstein, 2002). 

An analysis of the cosolvent concentration dependence of the osmotic second virial coefficient (OSVC) in water—protein—cosolvent mixtures is developed. The Kirkwood—Buff fluctuation theory for ternary mixtures is used as the main theoretical tool. On its basis, the OSVC is expressed in terms of the thermodynamic properties of infinitely dilute (with respect to the protein) water—protein—cosolvent mixtures. These properties can be divided into two groups (1) those of infinitely dilute protein solutions (such as the partial molar volume of a protein at infinite dilution and the derivatives of the protein activity coefficient with respect to the protein and water molar fractions) and (2) those of the protein-free water—cosolvent mixture (such as its concentrations, the isothermal compressibility, the partial molar volumes, and the derivative of the water activity coefficient with respect to the water molar fraction). Expressions are derived for the OSVC of ideal mixtures and for a mixture in which only the binary mixed solvent is ideal. The latter expression contains three contributions (1) one due to the protein—solvent interactions which is connected to the preferential binding parameter, (2) another one due to protein/protein interactions (B p ), and (3) a third one representing an ideal mixture contribution The cosolvent composition dependencies of these three contributions... 

The Kirkwood-Buff (KB) theory is the most important theory of solutions. This chapter is therefore central to the entire book. We devote this chapter to derive the main results of this theory. We start with some general historical comments. Then we derive the main results, almost exactly as Kirkwood and Buff did, only more slowly and in more detail, adding occasionally a comment of clarification that was missing in the original publication. We first derive the results for any multicomponent system, and thereafter specialize to the case of two-components system. In section 4, we present the inversion of the KB theory, which has turned a potentially useful theory into an actually useful, general and powerful tool for investigating solutions on a molecular level. Three-component systems and some comments on the application of the KB theory to electrolyte solutions are discussed in the last sections. 

There are basically two main developments in the molecular theory of solutions in the sense of route —IV one based on the inversion of the Kirkwood-Buff (KB) theory the second is the introduction of a new measure to study solvation properties. Both of these use measurable macroscopic, or global quantities to probe into the microscopic, or the local properties of the system. The types of properties probed by these tools are local densities, local composition, local change of order, or structure (of water and aqueous solutions) and many more. These form the core of properties discussed in this book. Both use exact and rigorous tools of statistical mechanics to define and to calculate local properties that are not directly accessible to measurements, from measurable macroscopic quantities. 

Third, to specify the spatial difference in the degree of preferential exclusion, we define and analyze the preferential exclusion parameters of ectoine for two solutes with the aid of the Kirkwood-Buff (KB) theory [36,37] (Section 8.2.3). To obtain the spatial profiles of the preferential exclusion parameter, we modified the calculation procedure of the KB integral from that in the original KB theory so as to enable systematic discussion of the dependence of the KB integral on the... 

Ruckenstein and Shulgin (2002) used the Kirkwood-Buff fluctuation theory to obtain an expression for the salting out (of gases, but applicable to any non-electrolyte solute) in electrolyte solutions. The resulting expression can be re-written as ... 

Garcia, B., S. Aparicio, R. Alcalde, and J. M. Leal. 2003. Preferential solvation in ternary solutions containing methylbenzoate. A Kirkwood-Buff fluctuation theory study. Journal of Physical Chemistry B. 107, 13478. 

Many, if not most, processes of interest occnr in solutions. It is therefore somewhat unfortunate that our understanding of solutions and their properties remains rather limited. There are essentially two theories of solutions that can be considered exact. These are the McMillan-Mayer theory of solutions and Fluctuation Solution Theory (FST), or the Kirkwood-Buff (KB) theory of solutions. The former has practical issues, which limit most applications to solutes at low concentrations. The latter has no such issues. Nevertheless, the general acceptance and appreciation of FST remains limited. It is the intention of this book to outline and promote the considerable advantages of using FST/KB theory to study a wide range of solution properties. 

While linking structure and thermodynamics based on the virial expression is not straightforward, this link can in fact be established using an alternative desciiptiOTi based on Kirkwood-Buff (KB) theory [76], Whereas the virial route requires information on the effective potential, the KB description does not make any assumption on the nature of the potentials, is exact, and its central quantities can be interpreted in terms of local solution structure. To this end, we consider the derivatives of the salt activity with respect to the density at constant pressure p and temperature T. For the systems shown in Fig. 5 these derivatives show the same order as the osmotic coefficients/salt activities for the different ions [70]. Hence, the microscopic mechanism explaining the order among the derivatives of the salt activity for the different ions also explains the Hofmeister series for the activities obtained by integration of the derivatives. Based on this, the relation between... 

The Kirkwood-Buff (KB) theory of solutions provides new relations between thermodynamic quantities and molecular distribution functions. Moreover, these relations are very general and indeed enjoy all of the advantages that we listed in connection with the compressibility equation (section 5.8). Because of its importance, we shall recapitulate the main features of these relations that make them powerful ... 

The Kirkwood-Buff theory of solutions (Kirkwook and Buff, 1951) doesn t depend on special assumptions about the nature of the intermolecular interactions... 

In the next section we shall present a simplified expansion theorem of osmotic pressure which was first obtained by McMillan and Mayer. This cluster expansion theory will be further extended in Section 3 to distribution functions, and medn results of Kirkwood and Buff will be recovered. A new and simple derivation of the cluster expansion of the pair distribution function is also given. Section 4 presents a new expression for the chemical potential of solvents in dilute solutions. Section 5 shows how the general solution theory may be applied to compact macromolecules. Finally, Section 6 deals with the second osmotic virial coefficient of flexible macromolecules and is followaJ in Sa tion 7 by concluding remarks. 

The Kirkwood-Buff theory of solutions and the local composition of liquid mixtures. 

Chapter 1 is devoted to the application of the Kirkwood-Buff theory of solutions to the investigation of the structures of binary and multicomponent mixtures. The analysis involves the quantity, which represents the excess (or deficit) number of molecules of species i around a central molecule of species j compared with a hypothetical mixture in which molecules of species i are distributed randomly around a central molecule of species j. 

Many models are available for describing the thermodynamic behavior of solutions. " However, so far no one could satisfactorily simulate the solution behavior over the whole concentration range and provide the correct pressure and temperature dependencies. This generated interest in the thermodynamically rigorous theories of Kirkwood—Buff and McMillan—Mayer. In the present paper, the emphasis is on the application of the Kirkwood—Buff theory to the aqueous solutions of alcohols, because it is the only one which can describe the thermodynamic properties of a solution over the entire concentration range. The key quantities in the Kirkwood-Buff theory of solution are the so-called Kirkwood-Buff integrals (KBIs) defined as... 

The aqueous systems of methanol, ethanol, propanols, and butanols were examined in the framework of the Kirkwood-Buff theory of solution. The Kirkwood—Buff integrals were calculated using thermodynamic equations, in which the derivatives (9 nyi/dxi)pj were expressed in terms of (9 nP/dXi)r, which... 

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 fert-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 terf-butyl alcohol solutions. The results were compared with the local compositions provided by the Wilson and NRTL equations. 

The clustering in aqueous solutions of alcohols was examined by combining the Kirkwood—Buff theory of solution with the Wilson and the NRTL equations. The correlation volumes were calculated for the aqueous systems of 1-PrOH and f-BuOH. Two type of clusters, alcohol- and water-rich, were found with similar dependencies of size on composition. Satisfactory agreement was found between the calculated cluster sizes and those provided by the SAXS, SANS, and LS experiments. 

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