Hildebrand solubility theory

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

Because the entropy of formation in Hildebrand theory is ideal, this approach should be restricted to those systems in which there are no structure effects due to solute-solvent and solvent-solvent interactions. The implication of this is that the solute should be non-ionic and not have functional groups which can interact with the solvent. According to Equation (4.8), the maximum solubility occurs when the Hildebrand parameter of the solvent is equal to the Hildebrand parameter of the solute. That is, when plotting the solubility versus the Hildebrand parameter, the solubility exhibits a maximum when the solubility parameter of the solvent is equal to the solubility parameter of the solute. 

Even though Hildebrand theory should not apply to solvent systems having considerable solvent-solvent or solute-solvent interactions, the solubility of compounds in co-solvent systems have been found to correlate with the Hildebrand parameter and dielectric constant of the solvent mixture. Often the solubility exhibits a maximum when plotting the solubility versus either the mixed solvent Hildebrand parameter or the solvent dielectric constant. When comparing different solvent systems of similar solvents, such as a series of alcohols and water, the maximum solubility occurs at approximately the same dielectric constant or Hildebrand parameter. This does not mean that the solubilities exhibit the same maximum solubility. 

Several studies attempted to relate the partition coefficient P of a solute in a liquid chromatographic or a gas chromatographic system with the composition of the two phases, one of which has a varying composition [19-23]. Tijssen et al. [24] and Schoenmakers [25] derived a relation between the partition coefficient and a binary mobile phase in reversed-phase HPLC from the solubility parameter theory of Hildebrand et al. [26]. Similarly, a relation can be derived for liquid-liquid extraction with extraction liquids composed of three components ... 

One approach that was considered is based upon the solubility parameter theory of Hildebrand and Scott (36, 37). This approach attempts to determine the best solvent for cleaning resins as a function of the known resin contaminants. Hildebrand and Scott (36, 37) developed the solubility parameter (6) to describe the property of solvents ... 

The solubility parameter theory (Eq. 4), first proposed by Hildebrand [21], was combined with the Flory-Huggins theory [43] to produce yet another means for determination of x-... 

In spite of widespread applications, the exact mechanism of retention in reversed-phase chromatography is still controversial. Various theoretical models of retention for RPC were suggested, such as the model using the Hildebrand solubility parameter theory [32,51-53], or the model supported by the concept of molecular connectivity [54], models based on the solvophobic theory [55,56) or on the molecular statistical theory [57j. Unfortunately, sophisticated models introduce a number of physicochemical constants, which are often not known or are difficult and time-consuming to determine, so that such models are not very suitable for rapid prediction of retention data. 

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... 

For the description of such interactions as well as of polymer swelling, models based on the Flory-Huggins Theory (Flory, 1953 Mulder, 1991) and UNIQUAC are often applied for mixtures in general and, for binary mixtures, also the Solubility Parameter Theory if the feed components are hydrophobic (Hildebrand and Scott,... 

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

Hildebrand and his co-workers have produced accurate gas solubilities for a great variety of systems over a lengthy period, and many of their measurements are tabulated in the comprehensive review of Battino and Clever. They have, however, persisted in the use of solubility parameter theory to correlate and interpret their measurements and in much of this work systems containing fluorocarbons either as the gaseous solute or as the liquid solvent appear to behave anomalously when compared with most other mixtures composed of non-polar molecules. 

On the other hand, the quality of the solvent or the solubility of the polymer in a solvent is determined by the solubility parameter ( ) and the Flory-Huggins polymer-solvent interaction parameter (j). Solvating potential of a solvent can be written by using Hildebrand theory [34, 63, 64]. 

Of presently available methods for the prediction of solvent physical properties, the solubility parameter theory by Hildebrand may still supply one of the most accurate and eompre-hensive results. However, the solubility parameter used there has no purely molecular character. Many other methods are more or less of empirical character. 

Solubility parameter theory (Hildebrand ) is not separately considered below but is still widely used in industry. It has led to the construction of comprehensive tables that provide an easy means of estimating thermodynamic quantities of rather limited reliability. Harris and Seymour have edited a collection of papers in several of which solubility parameter theory is used and these offer more details. 

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 second part of the study of Singh and Schweizer" described in Section V.C was to investigate the validity of a solubility parameter approach to polymer blend miscibility. Solubility parameter, or Hildebrand, theory is potentially extremely useful from a practical viewpoint... 

Applying the solubility parameter theory first introduced by Hildebrand, X-,- was expressed as ... 

Solubility parameter theory was advanced first by Hildebrand and Scott. Small developed a method for calculating the parameters from the contributions of groups within the molecule. Bunell, Hansen, and Crowley et al. were especially successful in utilizing the concept for the formulation of solvent-based... 

If we express the heat of mixing in terms of the Hildebrand solubility parameter theory, the B parameter is (see Eq. 3.17) ... 

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. 

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] ... 

Various models of SFE have been published, which aim at understanding the kinetics of the processes. For many dynamic extractions of compounds from solid matrices, e.g. for additives in polymers, the analytes are present in small amounts in the matrix and during extraction their concentration in the SCF is well below the solubility limit. The rate of extraction is then not determined principally by solubility, but by the rate of mass transfer out of the matrix. Supercritical gas extraction usually falls very clearly into the class of purely diffusional operations. Gere et al. [285] have reported the physico-chemical principles that are the foundation of theory and practice of SCF analytical techniques. The authors stress in particular the use of intrinsic solubility parameters (such as the Hildebrand solubility parameter 5), in relation to the solubility of analytes in SCFs and optimisation of SFE conditions. 

Hildebrand, J., and Scott, R. (1949). Solubility of Non-Electrolytes, 3rd ed. Reinhold, New York. The classic book on solution theory. 

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