Of regular solutions

Guggenheim [5] extended his treatment to the case of regular solutions, that is, solutions for which... 

A theory of regular solutions leading to predictions of solution thermodynamic behavior entirely in terms of pure component properties was developed first by van Laar and later greatly improved by Scatchard [109] and Hildebrand [110,1 11 ]. It is Scatchard-Hildebrand theory that will be briefly outlined here. Its point of departure is the statement that It is next assumed that the volume... 

Strictly speaking Eq. (8-51) should be applied only to reacting systems whose molecular properties are consistent with the assumptions of regular solution theory. This essentially restricts the approach to the reactions of nonpolar species in nonpolar solvents. Even in these systems, which we recall do not exhibit a marked solvent dependence, correlations with tend to be poor. - pp Nevertheless, the solubility parameter and its partitioning into dispersion, polar, and H-bonding components provide some insight into solvent behavior that is different from the information given by other properties such as those in Tables 8-2 and 8-3. 

The Scatchard-Hildebrand theory of regular solutions is most attractive because of its simplicity, and it is of special interest here because it has been applied to hydrocarbon mixtures at high pressures (PI 3), leading to the correlation of Chao and Seader (Cl). 

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 theory of regular solutions applied to mixtures of aromatic sulfonate and polydispersed ethoxylated alkylphenols provides an understanding of how the adsorption and micellization properties of such systems in equilibrium in a porous medium, evolve as a function of their composition. Improvement of the adjustment with the experimental results presented would make necessary to take also in account the molar interactions of surfactants adsorbed simultaneously onto the solid surface. 

The extension of the cell model to multicomponent systems of spherical molecules of similar size, carried out initially by Prigogine and Garikian1 in 1950 and subsequently continued by several authors,2-5 was an important step in the development of the statistical theory of mixtures. Not only could the excess free energy be calculated from this model in terms of molecular interactions, but also all other excess properties such as enthalpy, entropy, and volume could be calculated, a goal which had not been reached before by the theories of regular solutions developed by Hildebrand and Scott8 and Guggenheim.7... 

It is notified in the work [15], that the swelling of some coal does not agree with the thesis of regular solutions theory that is why, it is not allowed to calculate the parameter for them. Authors explain this fact by the presence of oxygen atoms in the investigated coal. But also the molecular weight of separate sections (clusters) between the points of crossing for methylated or acetylated samples of this coal is equal only to 300 - 600 in accordance with the calculations (that is unreal). 

Statistical thermodynamic analyis of regular solutions, with solvent and solute molecules of the same size, indicate that the free energy of mixing per mole of solution is given by... 

SOL.5. 1. Prigogine et R. Defay, Tension superficieUe dynamique des solutions regulieres (Dynamic surface tension of regular solutions), J. Chim. Phys. 46, 367-372 (1949). 

SOL.13.1. Prigogine and R. Defay, Surface tension of regular solutions, Trans. Faraday Soc. 46, 199-204 (1950). 

The solubility of a gas is an integral part for the prediction of the permeation properties. Various models for the prediction of the solubility of gases in elastomeric polymers have been evaluated (57). Only a few models have been found to be suitable for predictive calculations. For this reason, a new model has been developed. This model is based on the entropic free volume activity coefficient model in combination with Hildebrand solubility parameters, which is commonly used for the theory of regular solutions. It has been demonstrated that mostly good results are obtained. An exception... 

C contains the formation entropy and r is the coordination number of the vacancy. Thus, AJf j/r is the enthalpy per V-A bond in the sense of the thermodynamics of regular solutions [H. Schmalzried, A. Navrotsky (1975)]. For random A-B distributions, the probability of the configuration (/ a b) in the nearest neighbor shell of the vacancy V is... 

The factors that cause solutions of iodine to deviate from die behavior of regular solutions are illustrated in Fig. 3. in which values of the left hand member of Eq. (7) are plotted against those of the right for iodine solutions at 25°C ai is tire activity of solidiodine Xy denotes measured solubility Vy is the extrapolated molal volume of liquid iodine. 59 cra3 i is the volume fraction of the solvent, 1.0 62 = 14.1 1 is the solubility parameter of the solvent. Illustrative values of xi and 6] are given in accompanying table. 

Others have studied the volumetric changes occurring in mixed micelles of anionic-anionic and nonionic-nonionic surfactants as a determinant of intermolecular interactions and a measure of the thermodynamic ideality of mixing. In particular, Funasaki et al. (1986) have studied the volumetric behavior of mixed micelles of ionic and nonionic surfactants and analyzed their results in terms of regular solution theory. They found that in water, anionic surfactants such as SDS bind to PEG,... 

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. 

Since the Flory interaction parameter, x> was derived by considering only interaction energies between the molecules, it should not contain any entropic contributions and Equation (2D-9) should yield the correct value for the Flory-/ parameter. Unfortunately, x contains not only enthalpic contributions from interaction energies, but also entropic contributions. The solubility parameter includes only interaction energies and by the definition of regular solutions does not include any excess entropy contributions. Blanks and Prausnitz (1964) point out that the Flory / parameter is best calculated from... 

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