Thermodynamic model regular solution

The solubility parameter 5 of a pure solvent defined initially by Hildebrand and Scott based on a thermodynamic model of regular solution theory is given by Equation 4.4 [13] ... 

The finding that the assumptions of the regular solution approximation do not hold for the mixed micellar systems investigated here suggests a re-examination of how the thermodynamics of mixing enter the nonideal mixed micelle model. 

Figure 10,2 Deviations from Nernst s law in crystal-aqueous solution equilibria, as obtained from application of various thermodynamic models. (A and B) Regular solution (liyama, 1974). (C) Two ideal sites model (Roux, 1971a). (D) Model of local lattice distortion (liyama, 1974). Reprinted from Ottonello (1983), with kind permission of Theophrastus Publishing and Proprietary Co.

The purpose of this paper will be to develop a generalized treatment extending the earlier mixed micelle model (I4) to nonideal mixed surfactant monolayers in micellar systems. In this work, a thermodynamic model for nonionic surfactant mixtures is developed which can also be applied empirically to mixtures containing ionic surfactants. The form of the model is designed to allow for future generalization to multiple components, other interfaces and the treatment of contact angles. The use of the pseudo-phase separation approach and regular solution approximation are dictated by the requirement that the model be sufficiently tractable to be applied in realistic situations of interest. 

Model Development. There is vast opportunity for development of fundamentally based models to describe the thermodynamics of mixed micelle formation. As discussed in Chapter 1, regular solution theory has yielded useful relations to describe monomer—mi cel 1e equilibrium. 

When gas solubility data are lacking or are unavailable at the desired temperature, they can be estimated using available models. The method of Prausnitz and Shair (1961), which is based on regular solution theory and thus has the limitations of that theory. The applicability of regular solution theory is covered in detail by Hildebrand et al. (1970). A more recent model, now widely used, is UNIFAC, which is based on structural contributions of the solute and solvent molecular species. This model is described by Fredenslund et al. (1977) and extensive tabulations of equilibrium data, based on UNIFAC, have been published by Hwang et al. (1992) for aqueous systems where the solute concentrations are low and the solutions depart markedly from thermodynamic equilibrium. 

Here, we only present the simplest thermodynamic expressions used in the CALPHAD method for the major phase classes observed in multicomponent systems namely, disordered miscible and immiscible phases and ordered sublattice phases. The reader is referred to specialized textbooks for further discussion. The Gibbs energies for disordered two-component solid and liquid solution phases are most easily represented by the regular solution model (Eq. 2.10) or one of its variants ... 

This is a model of a strictly regular solution as used by R. Fowler and E. A. Guggenheim, Statistical Thermodynamics, Cambridge University Press, New York, 1949. 

It was found that the humic material ion exchange properties can be explained by a regular solution model similar to that of Truesdell and Christ (16) for clays. The thermodynamic constants for the exchange reactions studied were found to be different for each ionic strength. Changes in the configurations of the organic molecules could cause the observed variations. Other evidence (17,... 

A simple thermodynamical model derived from the theory of regular solutions [26], can account for the main features of both continuous and discontinuous transitions. In this theoretical framework, so-called Slitcher-Drickamer model, the interaction term in equation (2), r( HsX defined as ) hs(J — hs) where y is an interaction parameter which reflects the tendency for molecules of one type to be surrounded by like molecules (y > 0). So, equation (5) becomes ... 

Most of the recent theories of liquid solution behavior have been based on well-defined thermodynamic or statistical mechanical assumptions, so that the parameters that appear can be related to the molecular properties of the species in the mixture, and the resulting models have some predictive ability. Although a detailed study of the more fundamental approaches to liquid solution theory is beyond the scope of this book, we consider two examples here the theory of van Laar, which leads to regular solution theory and the UNIFAC group contribution model, which is based on the UNIQUAC model introduced in the previous section. Both regular solution theory and the UNIFAC model are useful for estimating solution behavior in the absence of experimental data. However, neither one is considered sufficiently accurate for the design of a chemical process. 

The experimental data for the partial solubility of perfluoro-n-heptane in various solvents has been plotted as a function of both mole fraction and volume ftaction in Fig. 11.2-3. It is of interest to notice that these solubility data are almost symmeuic functions of the volume fraction and nonsymmetric functions of the mole fraction. Such behavior has also been found with other thermodynamic mixture properties these observations suggest the use of volume fractions, rather than mole fractions or mass fractions, as the appropriate concentration variables for describing nonideal mixture behavior. Indeed, this is the reason that volume fractions have been used in both the regular solution model and the Wohl expansion of Eq. 94-8 for liquid mixtures. 

If the liquid.mixture is ideal, so that y = 1, we have the case of ideal solubility of a solid in a liquid, and the solubility can be computed from only thermodynamic data and ACp) for the solid species near the melting point. For nonideal solutions, yi must be estimated from either experimental data or a liquid solution model, for example, UNIFAC. Alternatively, the regular solution theory estimate for this activity coefficient is... 

In solid-state thermodynamics, this is referred to as the regular solution model, and is related to the regular solution mode] for liquids of Sec. 9.6 in thatboth assume that 5 and Y are each zero. 

The thermodynamic factor is evaluated for liquid mixtures from activity coefficient models. For a regular solution, for example,... 

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