Scatchard Hildebrand theory

Regular solutions, the solubility parameter and Scatchard-Hildebrand theory... 

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... 

Another formal shortcoming of Scatchard-Hildebrand theory, or any of its variants, is its requirement that the interacting molecules be of essentially the same size and shape. This disallows an accounting for any non-randomness of the pack-... 

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). 

TABLE 1.9 Solubility of Napthalene in Various Solvents by UNIFAC and Scatchard-Hildebrand Theory... 

The groups contribution methods can also be used to calculate solubility in binary (solute-solvent) systems. A comparison of solubilities calculated employing the UNIFAC method with experimental values and values obtained from the Scatchard-Hildebrand theory is given in Table 1.9. 

Finding an appropriate mixed solvent system should not be done on a strictly trial and error basis. It should be examined systematically based on the binary solubility behavior of the solute in solvents of interest. It is important to remember that the mixed solvent system with the solute present must be miscible at the conditions of interest. The observed maximum in the solubility of solutes in mixtures is predicted by Scatchard-Hildebrand theory. Looking at Eq. (1.50) we see that when the solubility parameter of the solvent is the same as that of the subcooled liquid solute, the activity coefficient will be 1. This is the minimum value of the activity coefficient possible employing this relation. When the activity coefficient is equal to 1, the solubility of the solute is at a maximum. This then tells us that by picking two solvents with solubility parameters that are greater than and less than the solubility parameter of the solute, we can prepare a solvent mixture in which the solubility will be a maximum. As an example, let us look at the solute anthracene. Its solubility parameter is 9.9 (cal/cm ). Looking at Table 1.8, which lists solubility parameters for a number of common solvents, we see that ethanol and toluene have solubility parameters that bracket the value of anthracene. If we define a mean solubility parameter by the relation... 

Browarzik et al calculated asphaltenes flocculation at high pressures for methane + crude oil - - 2,2,4-trimethylpentane [i-octane] using continuous thermodynamics where 2,2,4-trimethylpentane acts as a precipitant. The asphaltene flocculation was considered to be a liquid -b liquid equilibrium. Browarzik et al applied the van der Waals equation of state. The polydispersity of the crude oil was considered to be described by the solubility parameter of the Scatchard-Hildebrand theory. Within this distribution the asphaltenes represent the species with the highest solubility parameters. The calculated results were compared to experimental data. For oils with a very low content of asphaltenes the model describes the experimental flocculation data reasonably well. However, on contrary to the experimental results, the model predicts the asphaltenes to show a higher flocculation tendency with increasing asphaltenes content of the crude oil. Based on these comparisons further work was undertaken by Browarzik et al and the associates formed... 

Stepanova and Velikovskii (1970) stated that deviation from ideal behavior is connected with fugacity and activity. A paper on the prediction of vapor-liquid equilibrium for polar-nonpolar binary systems by Finch and Van Winkle is mentioned here because of the terminology and the principles involved. The 12 systems examined comprised systems such as ethylbenzene-hexylene glycol, n-octane-cellosolve, toluene-phenol, and n-heptane-toluene. It was pointed out that whereas the Scatchard-Hildebrand theory has had some success in predicting the vapor-liquid equilibria for nonpolar binary systems, it has proved to be unsatisfactory in the quantitative prediction of such equilibria for polar-polar systems and for polar-nonpolar systems. 

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