Solubility Scatchard-Hildebrand theory

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

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... 

A better estimate of all attractive forces surrounding a molecule was found in the use of the solubility parameter [32,33], Hancock et al. [34] has reviewed the use of solubility parameters in pharmaceutical dosage form design. The solubility parameter is used as a measure ofthe internal pressures ofthe solvent and solute in nonideal solutions. Cosolvents that are more polar have larger solubility parameters. The square root ofthe cohesive energy density, that is, the square root of the energy of vaporization per unit volume of substance, is known as the solubility parameter and was developed from Hildebrand s Regular Solution Theory in the Scatchard-Hildebrand... 

Generally, the activity coefficients are < 1 when polar interactions are important, with a resulting increase in solubility of compounds compared with the ideal solubility. The opposite is often true in nonpolar systems where dispersion forces are important, with the activity coefficients being > 1. A variety of methods are used to calculate activity coefficients of solid solutes in solution. A frequently used method is that of Scatchard-Hildebrand, which is also known as regular solution theory (Prausnitz et al. 1999). 

Equation 8.3 is based on the Scatchard-Hildebrand Regular solution theory that considers interaction due only to dispersion forces. This was extended to include hydrogen bonding and polar forces through a 3D solubility parameter by Hansen. In this form. Equation 8.3 becomes... 

If the interactions are confined to van der Waals ones and the solution conforms to the restrictions of regular solution theory (Hildebrand and Scott (1950)) then the well known Scatchard-Hildebrand solubility parameter expression can be applied ... 

For nonpolar systems the activity coefficient can be estimated using the Hildebrand-Scatchard theory of regular solutions. To calculate the activity coefficient of a dissolved solute using regular solution theory, solubility parameters must be available for the components. For ntany materials these paraiiteters can be calculate and/or are available in standard engineering references. 

When X values are determined for a given polymer or other nonvolatile component of a polymer system, and for a series of vapors for which solubility parameter values are known, the IGC method provides a unique approach to determining the solubility parameter, dr, for the polymer phase. The method is based on the principle that the Flory-Hu ins interaction parameter, x> can be related to dr by combining the Hildebrand-Scatchard solution theory with the Flory-Huggins theory [21] ... 

As early as 1916 Hildebrand pointed out that the order of solubility of a given solute in a series of solvents is determined by the internal pressures of the solvents. Later Scatchard (1931) introduced the concept of "cohesive energy density" into Hildebrand s theories, identifying this quantity with the cohesive energy per unit volume. Finally Hildebrand (1936) gave a comprehensive treatment of this concept and proposed the square root of the cohesive energy density as a parameter identifying the behaviour of specific solvents. In 1949 he proposed the term solubility parameter and the symbol S. 

The Hildebrand-Scatchard Solubility Parameter Theory. —According to this theory the interaction parameter is given by... 

The solubility parameter defined by eqn (5.39) is not identical to that conventionally measured by swelling, solubility or surface tension data, since in the first case the solute is at infinite dilution in the polymer, while in the other cases its concentration is high. Because it is possible that at high dilutions the behaviour as a regular solution, inherent to the development of the Hildebrand-Scatchard theory, is more rigorously obeyed, 8" may be more meaningful than 8j. 

The theory of solubility parameters was developed by Scatchard in 1931 and further refined by Hildebrand (5). Originally, the concept of solubility parameters was developed to describe the enthalpy of mixing of simple liquids. Afterwards it has been extended to polymers. 

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