Buff Theory Research Articles

A Kirkwood–Buff theoretical approach to Debye–Hückel theory. Interpretation of electrolyte activity coefficients in both dilute and concentrated solutions

A set of equations is developed for the thermodynamic properties of 1:1 electrolytes using as its starting point the non-linearized version of the Poisson–Boltzmann radial distribution function and Kirkwood–Buff theory to forge the connection with the salt chemical potential. It is shown that the Debye–Huckel (DH) limiting law arises not from the linear term in the exponential expansion of the distribution but from the square term. The extended DH equation arises as a direct consequence of the treatment, although the interpretation of the distance of closest approach term is slightly different. By including only two parameters, one representing the distance of closest approach and a constant to represent ion–solvent interactions, excluded-volume effects and/or higher-order ion–ion interactions, the theory is able to model the activity coefficients of aqueous KCl accurately from infinite dilution to 4 mol kg–1. The theory is compared with other approaches.

Application of Kirkwood–Buff theory to free energies of transfer of electrolytes from one solvent to another

Solute n.m.r. may be used to obtain quantitative information concerning the preferential solvation of alkali metal and halide ions in binary solvent mixtures. Using the exact theory due to Kirkwood and Buff one can relate the n.m.r. data to the free energies of transfer of individual ions from one pure solvent to another or to the binary mixture. The results obtained are similar although not identical to less rigorous approaches published earlier. The results obtained, when combined to give data for neutral combinations of ions, may be compared with thermodynamically measured free energies of transfer.

Interpretation of free energies of transfer and solute partial molar volumes in mixed solvents using Kirkwood–Buff theory

Using the Kirkwood–Buff theory for partial molar volumes in ternary mixtures and the Hall formulation of the same theory for free energies of transfer, we have demonstrated how one may obtain separately the two solute–solvent Kirkwood–Buff radial distribution function integrals for an infinitely dilute solute in a binary solvent mixture. As an example, the parameters are calculated for NaCl in MeOH–H2O.

Application of Kirkwood–Buff theory to enthalpies of transfer and expansibilities of solutes in binary solvent mixtures

Using Kirkwood–Buff theory for a dilute solute in a binary solvent mixture, the variable-temperature thermodynamic properties, enthalpies of transfer and solute expansibilities may be interpreted in terms of the temperature dependence of the solute–solvent component radial distribution function integrals. The treatment is applied to the alkali-metal chlorides in methanol–water mixtures.

The statistical mechanical theory of concentration fluctuations in mixtures

A general theory of concentration fluctuations in mixtures is derived. The resulting expressions, which include the Kirkwood–Buff theory as a particular case, relate different partial molar properties to a single combination of molecule number fluctuations within differently defined subsystems. The formalism, therefore, gives rise to a common definition for partial molar energies, volumes, enthalpies, and entropies in terms of molecule number fluctuations exclusively. Likewise, a second function of molecule number fluctuations describes both the mixture’s isobaric specific heat as well as its isothermal compressibility. The partial molar energy and enthalpy definitions, moreover, suggest new methods for the study of mixture properties via computer simulations.

The status of transition-state theory in non-ideal solutions and application of Kirkwood–Buff theory to the transition state

The status of the equilibrium hypothesis in transition-state theory is examined. For non-ideal systems weaknesses in previous versions are identified and an attempt is made to overcome them by providing an alternative treatment based on arguments developed previously by the author. It is proposed that medium effects on the equilibrium concentration of activated complexes, C[graphic omitted], can be treated formally using the Kirkwood–Buff theory of solutions. The resultant expressions apply to rates when the parameters other than C[graphic omitted] in the rate equations are insensitive to changes in the transition-state environment.

Application of the Kirkwood–Buff theory to the problem of hydrophobic interactions

Two possible applications of the Kirkwood–Buff (KB) theory of solutions to the problem of hydrophobic interactions (HI) are presented. The first involves the inversion of the KB theory and was published some years ago. Its main result, as far as HI is concerned, is the possibility of evaluating the integral Gss for solute–solute interactions using experimental thermodynamical data. The second application is based on the exact relation [eqn (12)] which may be approximately factorized into two terms [eqn (17)], one depending on the excluded volumes of the solutes and the other depending only on properties of the solvent. This relation enables one to estimate the strength of the HI and its dependence on the temperature and pressure. A preliminary set of results is presented.

Inversion of the Kirkwood–Buff theory of solutions: Application to the water–ethanol system

A general procedure is outlined whereby experimental data such as partial molar volumes, isothermal compressibilities, and partial vapor pressures may be processed to obtain information on the extent of the affinity between two species in a mixture of two (or more) components. A particular example of the water–ethanol system is processed in this manner to obtain the quantities Gαβ which are integrals over the pair correlation functions between two species α and β. This information is relevant to several topics of interest in the field of aqueous solutions, such as the solvation of solutes, hydrophobic interactions, and structural changes in the solvent brought by the addition of solutes to water. More generally it may be used to characterize the properties of various mixtures on a molecular level.

Thermodynamics of solutions of interacting aggregates by methods similar to surface thermodynamics. Part 1.—General equations for multi-component systems

The general results obtained previously when methods similar to those of surface thermodynamics were used to provide an alternative derivation of part of the Kirkwood—Buff theory of solutions are applied to solutions of interacting multicomponent charged aggregates. General and exact expressions which account for aggregation explicitly are derived and are compared with the corresponding equations for small systems in a solvent given by T. L. Hill. It is shown how the theory can be used to discuss conformation changes in macromolecules. A general interpretation in molecular terms of the behaviour of the micelle point in multi-component solutions is also given. Finally, expressions are presented for the interpretation of light scattering data.