Solubility Parameter Concepts

It is convenient in practice to use semi-empirical correlations of the mutual solubility of substances and the parameters describing their physical properties. The best known parameter of this type is a solubility parameter reflecting intermolecular interaction. It was introduced in the theory of solutions. The solubility parameter concept is based on enthalpy factors of the interaction between solvent and polymer. It is assumed that the entropy factors are of a similar order of magnitude. 

The solubility parameter, 5, is the square root of the cohesive energy density, CED  

Solubility parameters are measured in (MJ/m )° or (cal/cm )°. The molar cohesive energy is the energy associated with all molecular interactions per mole of material. Expressed in another way it is the excess of the potential energy of a liquid in reference to its ideal vapor at the same temperature. Thus the solubility parameter 8 is an intermolecular interaction parameter for an individual liquid. 

Hildebrand and Scatchard proposed a relationship between the internal energy of mixing and the solubility parameters of a solvent and a solute  

The absence of the volume change presumes that AU is equal to the enthalpy or to heat of mixing which was equated to the right terms of the equation (under the equality of 8 of both components, AU = 0). The Hildebrand-Scatchard approach corresponds to the geometric mean rule.  

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The solubility parameter concept has found widespread use in predicting the compatibility of components used in paints and coatings, and the patent literature contains numerous references to the solubility parameter or solubility parameter ranges in specifying formulations. Its use in predicting adhesion should apply in... 

Hansen [137-139], and later van Krevelen [114] proposed the generalization of the solubility parameter concept to attempt to include the effects of strong dipole interactions and hydrogen bonding interactions. It was proposed that the cohesive energy density be written as the sum of three terms, viz. 

There have been many attempts to divide the overall solubility parameter into components corresponding to the several intermolecular forces. For example, a so-called three-dimensional solubility parameter concept is built on the assumption that the ced is an additive function of contributions from dispersion (d), polar (p), and H-bonding (h) forces. It follows that... 

Molecularly motivated empiricisms, such as the solubility parameter concept, have been valuable in dealing with mixtures of weakly interacting small molecules where surface forces are small. However, they are completely inadequate for mixtures that involve macromolecules, associating entities like surfactants, and rod-like or plate-like species that can form ordered phases. New theories and models are needed to describe and understand these systems. This is an active research area where advances could lead to better understanding of the dynamics of polymers and colloids in solution, the rheological and mechanical properties of these solutions, and, more generally, the fluid mechaiucs of non-Newtonian liquids. 

A number of models have been proposed to describe the solution formation process [505-509], some of which can be extended to Include chromatographic processes and other solvent-dependent phenomena. In terms of chromatographic aiqplications the most useful are the solubility parameter concept, solvatochromic parameters and Snyder s solvent strength and selectivity... 

The solubility parameter concept was established in the 1930s by the work of Hildebrand and Scatchard. The original concept covers regular solutions, i.e., solutions that do not show an excess entropy effect on mixing. The solubility parameter concept offers the following interesting features ... 

The solubility parameter concept relates to compounds rather than to molecules. Because it is a macroscopic approach, it relates to practical data more conveniently than a molecular statistical approach does. 

The above discussion demonstrates that the solubility parameter concept in combination with the gradient oven is a useful tool to select a convenient solvent, which could undergo a phase separation during the crosslinking reaction. 

The solubility parameter concept predicts the heat of mixing liquids and amorphous polymers. It has been experimentally found that generally any nonpolar amorphous polymer will dissolve in a liquid or mixture of liquids having a solubility parameter that generally does not differ by more than 1.8 (cal/cc) /. The Hildebrand (H) is preferred over these complex units, giving as a general difference 1.8 H. 

In GC, the mobile phase acts only as a carrier. In LC, solute undergoes interaction with liquids or mixtures of liquids used as the mobile phase. Selection of the mobile phase is critical. The most useful criteria are the solubility parameter concept, Snyder s selectivity triangle, and solva-tochromic parameters. 

It is known that most mixtures of elastomers and resinous copolymers are rather polydisperse, their incompatibility giving rise to poor interfacial adhesion. Preferably, a resinous monomer or monomers are grafted to the rubber, and they act as a link between the rubber and the resin phases. As Rosen (13) has pointed out, one means of predicting the affinities of polymer pairs from measurable properties is through the use of the solubility parameter, and this has proved useful in this study. The solubility parameter concept was originally derived from the thermody-... 

When the only effects that have to be taken into account are those of cavity formation in the solvent and the dispersion interactions, i.e., when both the solvent and the solute are non-polar, then Hildebrand s solubility parameter concept (Hildebrand and Scott 1950) provides good estimates of the solubility. The mole fraction of a gaseous solute, x2, in a solution in equilibrium at a partial pressure p2 of this gas, can be estimated from the following expression ... 

As we saw above (eqn.3.34), the solubility parameter concept provides a very simple rule for approximating the polarity of a mixture. For a binary mobile phase containing water (W) and methanol (Me) the sum of the two volume fractions should equal 1, hence... 

While solubility parameter concepts and equations are designed for liquid solvents, they have been shown to be applicable to dense gases or SFs [25,26]. The solubility parameter 8 for a dense gas can be estimated by [25]... 

For these reasons a more refined treatment of the solubility parameter concept is often necessary, especially for interactions between polymers and solvents. Nevertheless, the solubility parameters of polymers and solvents are important quantities in all phenomena involving interactions between polymers and solvents. 

Unfortunately, values of <5d, <5p and cannot be determined directly. There are, in principle, two ways for a more intricate use of the solubility parameter concept ... 

The Flory-Huggins theory has been modified and improved and other models for polymer solution behavior have been presented. Many of these theories are more satisfying intellectually than the solubility parameter model but the latter is still the simplest model for predictive uses. The following discussion will therefore focus mainly on solubility parameter concepts. 

Also, the original Hildebrand approach has been refined to take into account the contribution of polar groups and hydrogen bsolubility parameters. These mndifications of the Flory-Huggins theory and of the solubility parameter concept have made these methods an even more useful tool in the description of solutions, especially of mixtures containing polymer compounds. A comprehensive treatment of these extensions of Flory-Huggins and Hildebrand s theories, as well as the new equation of state approach of Flory (1965), bns re ntly been published (Shinoda, 1978 Olahisi et al 1979). 

A practical eluotropic series of solvents, based on the expended solubility parameter concept, was reported. This series was defined based on partial specific solubility parameter (5 ) that is equal to the sum of Keeson (5q) and acid-base (2 a b)> which represents the contribution to interaction forces introduced to characterize the solute, the mobile, and the stationary phase in liquid-solid chromatography. Exactly the same two interaction forces define e° and, consequently, there should exist a direct relation between e° and s = o+2 a b- Unfortunately, the general correlation for all the solvents on alumina is poor (r =0.75). 

Tortorello, A., and Kinsella, M. A., Solubility parameter concept in the design of polymers for high performance coatings. I. J. Coat. Technol. 55(696), 99-38 (1983a). 

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... 

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). 

The presence of a higher aromatic content In the gasoline resulted In Increased swell and hence Increased deterioration of tensile properties of elastomers exposed to the gasoline and Its mixtures. Addition of benzene to Increase the aromatic content resulted In slightly more detrimental effects on nitrile elastomers than the addition of toluene. The data on all elastomers can be explained In terms of the solubility parameter concept. 

Indolene mixtures have been adequately explained In terms of the solubility parameter concept [2]. It was found that with the exception of the fluorocarbon elastomer the overall solubility parameter of elastomers was equal to that of the methanol/Indolene mixture In which maximum swell of the elastomer was measured. 

Ethanol has an overall solubility parameter (4] of 13.0 (cal/cc). The contributions of the London dispersion (nonpolar) forces, polar forces and hydrogen bonding forces to the overall solubility parameter are 6 =7,5, 6 =4.3 and jj=10.9 (cal/cc) respectively. The overall solubility parameter of ethanol Is slightly lower In value than the solubility parameter of methanol mainly due to smaller contributions by the polar forces. The 6p for ethanol ts 4.3 as compared to 6.0 (cal/cc) for methanol. The swell behavior of most elastomers In ethanol resembles that In methanol. In order to examine tdiether or not the swell data In ethanol obtained for the various polymers (Table III) can be explained In terms of the solubility parameter concept we compared established solubility parameters of the elastomers with those calculated from maximum swell data. The solubility parameters of nine of the elastomers Investigated have been reported In the literature [3-6] and are shown in column 2 of Table VII. The next column of the Table Is generated from the present data and lists the concentrations of ethanol In the... 

BurreU, H., Solubility parameters for film formers, Off. Dig., 27(369), 726-758, 1972 BurreU, H., A solvent formulating chart. Off. Dig., 29(394), 1159-1173, 1957 Burrell, H., The use of the solubility parameter concept in the United States, VI Federation d Associations de Techniciens des Industries des Peintures, Vemis, Emawc et Encres d Imprimerie de VEurope Continentale, Congress Book, 1962, 21-30. Hansen, C.M., The three dimensional solubility parameter-key to paint component affinities 1, J. Paint TechnoL, 39(505), 104-117, 1967. 

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