Quasichemical theory

For simplicity of notation, we will here discuss the circumstance that the distinguished molecule is present at the lowest concentration. The occupants of the inner shell will be of one type only, solvent of type denoted by w w = H20 for example. Then our discussion can be more economical, though the ideas do have broader relevance. For a distinguished molecule of type a, we will encode the definition of the inner shell by an indicator function ba (k) which is one when the /cth solvent molecule occupies the defined inner shell, and zero otherwise. Then the PDT formula can be recast as 

The right-most term is similar to the familiar PDT formula except that the indicator function combinations forbid binding of solution molecules to the defined inner shell. That last factor is recognized as the Boltzmann factor of the hydration free energy that would result if inner-shell binding were prohibited. The Km are recognizable ratios of equilibrium concentrations - equilibrium constants - that are discussed 

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On the other hand, upon closer examination even the copper-gold solid solutions evince serious discrepancies with the quasichemical theory. There is a composition range where the entropy of solution is larger than that for random mixing (see Fig. 1) where... 

Fig. 3. Schematic diagram for the variation with concentration of the partial molar heat of solution of the liquid noble metals into liquid tin, taken from reference 51. The numbers are the experimental and calculated AHt for the solutes, in cal/g atom, at the two concentrations of 0 and 0.02 mole fraction. Q-C labels the curves calculated by the quasichemical theory in first order B-W labels the curves calculated by the Bragg-Williams, or zeroth-order approximation, which assumes a random...

Asthagiri, D. Pratt, L. R. Ashbaugh, H. S., Absolute hydration free energies ofions, ion-water clusters and quasichemical theory, J. Chem. Phys. 2003,119, 2702-2708... 

A quasichemical theory, using ab initio simulation (rPBE functional) to generate data for the computation of the various contributions to the free energy, yields an estimate for the excess chemical potential of water very close to the experimental value. 

Asthagiri, D. Pratt, L. R. Kress, J. D., Free energy of liquid water on the basis of quasichemical theory and ab initio molecular dynamics, Phys. Rev. E 2003, 68, 041505... 

PREVIOUS APPROACHES FLORY-HUGGINS THEORY AND QUASICHEMICAL THEORY... 

Pratt and co-workers have proposed a quasichemical theory [118-122] in which the solvent is partitioned into inner-shell and outer-shell domains with the outer shell treated by a continuum electrostatic method. The cluster-continuum model, mixed discrete-continuum models, and the quasichemical theory are essentially three different names for the same approach to the problem [123], The quasichemical theory, the cluster-continuum model, other mixed discrete-continuum approaches, and the use of geometry-dependent atomic surface tensions provide different ways to account for the fact that the solvent does not retain its bulk properties right up to the solute-solvent boundary. Experience has shown that deviations from bulk behavior are mainly localized in the first solvation shell. Although these first-solvation-shell effects are sometimes classified into cavitation energy, dispersion, hydrophobic effects, hydrogen bonding, repulsion, and so forth, they clearly must also include the fact that the local dielectric constant (to the extent that such a quantity may even be defined) of the solvent is different near the solute than in the bulk (or near a different kind of solute or near a different part of the same solute). Furthermore... 

A number of directions can be taken to generalize these distributions systematically. Multigaussian models are natural possibilities, and suggest the quasichemical theory taken up later. Here we assume that the distribution P (e i ") in Eq. (4.19) can be expressed as a linear combination of gaussians corresponding to configurational substates of the system. As an example for aqueous solutions, the... 

Lattice theories [37] enable one to consider nonspecific physical forces (e.g., molecular dipole moments, induction effects, and London dispersion forces) and have been applied successfully to model nonideality in a wide range of mixtmes. Guggenheim [43] was the first to develop a quasichemical theory using lattice models. Wilson [44], Renon and Prausnitz [45], Abrams and Prausnitz [46], and Vera et al. [47] modified it for nomandom mixtures. Panayiotou and Vera... 

Phase diagrams of several ternary surfactant-solute-solvent systems predicted using lattice MC simulations and quasichemical theory have been compared and shown to lead to qualitatively similar results. The two diagrams for h t with C solvent are in excellent agreement [25], as this surfactant does not aggregate to form any microstructures. However, similar comparisons for A2/4 [25] and A4/4 [25,36] are not as good, because quasichemical theory cannot account for the formation of micelles. 

The above-mentioned deficiencies of the Flory-Huggins theory can be alleviated, in part, by using the local-composition concept based on Guggenheim s quasichemical theory for the random mixing assumption and replacing lattice theory with an equation-of-state model (Prausnitz et al., 1986). More sophisticated models are available, such as the perturbed hard sphere chain (PHSC) and the statistical associating fluid theory (SAFT) (Caneba and Shi, 2002), but they are too mathematically sophisticated that they are impractical for subsequent computational efforts. 

For the nonrandom correction, the Guggenheim s quasichemical theory is used [1], as proposed in... 

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