Regular solution/solubility parameter theory

Actually, perfluorocarbons behave in many ways quite differently from hydrocarbons, as already established in the literature. For example, then-behaviour in the context of thermodynamic models differs significantly from all other compounds, including hydrocarbons (Figure 3.12). Moreover, in the context of the regular solution/solubility parameter theory (see below), solutions containing fluorocarbons show deviations not shared by other mixtures of non-polar compounds, which constitutes the main area of applicability of regular solution/ solubility parameter theory (Prausnitz, Lichtenthaler and de Azevedo, 1999). 

If the mutual solubilities of the solvents A and B are small, and the systems are dilute in C, the ratio ni can be estimated from the activity coefficients at infinite dilution. The infinite dilution activity coefficients of many organic systems have been correlated in terms of stmctural contributions (24), a method recommended by others (5). In the more general case of nondilute systems where there is significant mutual solubiUty between the two solvents, regular solution theory must be appHed. Several methods of correlation and prediction have been reviewed (23). The universal quasichemical (UNIQUAC) equation has been recommended (25), which uses binary parameters to predict multicomponent equihbria (see Eengineering, chemical DATA correlation). 

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

We encountered the quantity AE ap/V in Eq. (8-35) it is the cohesive energy density. The square root of this quantity plays an important role in regular solution theory, and Hildebrand named it the solubility parameter, 8. 

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 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] ... 

Fig. 4. 23 Application of the regular solution theory for correlation of distribution constants for ZnA2 and CuA2 with solvent properties (solubility parameters) the numbers refer to the solvents listed in Table 4.10. (From Ref. 22.)...

One of the approaches to calculating the solubility of compounds was developed by Hildebrand. In his approach, a regular solution involves no entropy change when a small amount of one of its components is transferred to it from an ideal solution of the same composition when the total volume remains the same. In other words, a regular solution can have a non-ideal enthalpy of formation but must have an ideal entropy of formation. In this theory, a quantity called the Hildebrand parameter is defined as ... 

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... 

The solubility parameter is therefore a measure of the energy density holding the molecules in the liquid state. Note that regular solution theory can only predict positive AH. Thus, with this approach, prediction of solubility involves matching the solute and solvent solubility parameters as closely as possible to minimize AH. As a very rough mle of thumb 61 — 62 must be less than 2 (f/cm3)1 /2 for solubility. 

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... 

According to the regular solution theory, polymers are as a rule soluble in solvents if their solubility parameters are similar to those of the corresponding solvent. The upper limit for good solubility is defined to he a difference (AS) of 6 units between solubility parameters ... 

Regular solution theory, the solubility parameter, and the three-dimensional solubility parameters are commonly used in the paints and coatings industry to predict the miscibility of pigments and solvents in polymers. In some applications quantitative predictions have been obtained. Generally, however, the results are only qualitative since entropic effects are not considered, and it is clear that entropic effects are extremely important in polymer solutions. Because of their limited usefulness, a method using solubility parameters is not given in this Handbook. Nevertheless, this approach is still of some use since solubility parameters are reported for a number of groups that are not treated by the more sophisticated models. 

A thermodynamic method, more fitting to this chapter, has been proposed by Nauman et al. They claim a process for the separation of a physically mixed solid polymers by selective dissolution. They rely on the different polymer solubility characteristics. Tables of this property have been reported and are based on regular solution theory and Hildebrand solubility parameters. The core of the Nauman invention is to find suitable solvents to dissolve particular polymers under defined temperature and pressure conditions. A mixture of polymers is first added to one solvent, at a given temperature, in order to dissolve a particular polymer. The remaining polymer mixture is then treated at a higher temperature with the same solvent or with a different solvent. For clarity, two examples are taken from the patent."... 

Regular solution theory characterises nonpolar solvents in terms of solubility parameter, 6y which is defined as... 

Other molecular properties have been also proposed to model the hydrophobic interactions. The parachor, which is related to the surface tension of a compound (139, 140) represents mainly the intermolecular interactions in a liquid. The Hildebrand-Scott solubility parameter, 6, (141) is related to intermolecular van der Waals forces and the closely related molar attraction constant, F, is obtained by multiplying 6 by the molar volume (142). The partition coefficient between two solvents can be obtained from the solubility parameters and the molar volumes of the solute and the solvents (193). This relationship is based on regular solution theory (194) and the assumption that the partial molar volumes of the solute is not different from its molar volume. Recently this has been criticized and a new derivation was proposed (195) in which the partial molar volumes are taken into account. The molar refractivity, MR, is related to dispersion forces and can be obtained as a sum of the partial molar refractivi-ties assigned to atoms and bonds (140, 143). These parameters have been compared (144) to establish their relative applicability to correlations with biological activity. The conclusion was that logP and molecular refractivity were the best parameters. Parameters obtained from high pressure liquid chromatography (144,... 

A number of methods based on regular solution theory also are available. Only pure-component parameters are needed to make estimates, so they may be applied when UNIFAC group-interaction parameters are not available. The Hansen solubility parameter model divides the Hildebrand solubility parameter into three parts to obtain parameters 8d, 5p, and 5 accounting for nonpolar (dispersion), polar, and hydrogenbonding effects [Hansen,/. Paint Technot, 39, pp. 104-117 (1967)]) An activity coefficient may be estimated by using an equation of the form... 

The method of DiPaola-Baranyi and Guillet is an extension of the work of Bristow and Watson [21] who calculated solubility parameters for a series of network polymers from swelling equilibria. The basis is that the solubility parameters of solvent, 61, and polymer, 2) are introduced in the form of Regular Solution theory [19] to account for enthalpic effects ... 

In the above considerations, the hydrophobic portions of both the membrane polymer and the small molecules that enter the membrane are expected to interact in the hydrophobic microphases in the membrane. It therefore becomes useful to find a numerical measure of the miscibility of these hydrophobic portions of molecules. In the case of complete molecules, both small and polymeric, the solubility parameter concept has been useful in the past. This concept is related to the enthalpy change which occurs on mixing in regular solution theory as developed by Hildebrand and coworkers (10) and as used for polymer solution theory by Flory (11). The Hildebrand solubility parameter is a measure of the attraction between molecules of the same kind, including dispersion forces, polar forces, and hydrogen bonding... 

In the liquid phase, the simplest option is an ideal liquid, with an activity coefficient equal to 1.0. That choice leads to Raoult s law, which may suffice for similar chemicals. Other models include regular solution theory using solubility parameters (although not in Aspen Plus), NRTL, Electrolyte NRTL, UNIFAC, UNIQUAC, Van Laar, and Wilson. Characteristics of the models are ... 

Fortunately, most organic solvents are nonpolar and therefore their intermolecular forces are weak London or dispersion forces. Hildebrand used the term "regular solutions" to describe solutions of nonelectrolytes and their nonpolar solvents. Additional theories on the solubility of polymers were developed by Flory ( ) and Huggins O). Probably the most important publications leading to the practical use of solubility theories by polymer scientists were those published by Burrell in 1955 ( ) and 1966 ( ). Modifications in the Hildebrand solubility parameter concept for regular solutions to account for larger intermolecular forces were made by Liebermann ( ), Crowley (.7), Hansen and Beerbower ( ) and Nelson et al. (9). 

Snyder has discussed liquid solvent characterization on several occasions (29,30,38,39). One of the very interesting points is that when several solvents have essentially the same solvent power as described by the Hildebrand solubility parameter (40), those solvents often do not dissolve a particular solute to the same extent. This is attributed to the fact that the Hildebrand solubility parameter does not, and cannot by regular solution theory. 

Traditionally, solubility parameters are given in (cal/cm ) = Hild(ebrands), in honor of the founder of the regular solution theory, Joel Hildebrand. Now, they are more commonly listed in (MPa) (= 1 (J/cm ) ). The solubility parameters were originally defined in conjunction with the regular solution theory, as discussed in Section 16.3.3.1. 

The heat of mixing term can be obtained from various theories. One valid possibility for nonpolar systems is the regular solution theory, introduced by Joel Hildebrand, which employs the concept of the solubility parameter. For a binary solvent(l)-polymer(2) system, the heat of mixing is given according to the regular solution theory ... 

Accurate results with the FH model can only be obtained if equations like 16.38 or 16.39 are used for estimating the FH parameter. Still, for some practical cases, a reasonable value of the FH parameter can be obtained, by combining the FH and regular solutions theories, using the solubility parameters of the compounds via the equation ... 

Barton"" " provides empirical methods based on solubility parameters for ternary solvent systems. All these methods provide only a qualitative idea on miscibility. The combination of regular solution theory and solubility parameters has been employed for predicting the partition coefficients of organic compounds between water and polystyrene and between alcohols and polyolefins. The results are useful to a first approximation. 

As a result, the cohesive energy is the enthalpy of evaporation plus the change in enthalpy to expand from the vapor pressure to the ideal gas state (which is usually neglected in liquids at ordinary temperatures and low pressures, see also Section 4.2.1) minus RT. The cohesive energy concept is used to derive regular solution theory and also the solubility parameters (see Section 5.3). 

Since the solubility parameters of all the components are similar, regular solution theory predicts essentially ideal solution behavior, even though, for example, the water-aromatic hydrocarbon mixtures are highly nonideal. This is an example of how bad the regular solution theory predictions can be when used for mixtures for which it is not appropriate. 

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