The Hildebrand solubility parameter provides a numerical estimate of the degree of interaction between materials and can be a good indication of solubility, particularly for nonpolar materials such as many polymers. Materials with similar values of δ are likely to be miscible.
Definition
The Hildebrand solubility parameter is the square root of the cohesive energy density: The cohesive energy density is the amount of energy needed to completely remove unit volume of molecules from their neighbours to infinite separation. This is equal to the heat of vaporization of the compounddivided by its molar volume in the condensed phase. In order for a material to dissolve, these same interactions need to be overcome, as the molecules are separated from each other and surrounded by the solvent. In 1936 Joel Henry Hildebrand suggested the square root of the cohesive energy density as a numerical value indicating solvency behavior. This later became known as the “Hildebrand solubility parameter”. Materials with similar solubility parameters will be able to interact with each other, resulting in solvation, miscibility or swelling.
Uses and limitations
Its principal utility is that it provides simple predictions of phase equilibrium based on a single parameter that is readily obtained for most materials. These predictions are often useful for nonpolar and slightly polar systems without hydrogen bonding. It has found particular use in predicting solubility and swelling of polymers by solvents. More complicated three-dimensional solubility parameters, such as Hansen solubility parameters, have been proposed for polar molecules. The principal limitation of the solubility parameter approach is that it applies only to associated solutions : it cannot account for negative deviations from Raoult's law that result from effects such as solvation or the formation of electron donor–acceptor complexes. Like any simple predictive theory, it can inspire overconfidence: it is best used for screening with data used to verify the predictions.
Units
The conventional units for the solubility parameter are 1/2, or cal1/2 cm−3/2. The SI units are J1/2 m−3/2, equivalent to the pascal1/2. 1 calorie is equal to 4.184 J. 1 cal1/2 cm−3/2 = 1/2−3/2 = 2.045 103 J1/2 m−3/2 = 2.045 MPa1/2. Given the non-exact nature of the use of δ, it is often sufficient to say that the number in MPa1/2 is twice the number in cal1/2 cm−3/2. Where the units are not given, for example, in older books, it is usually safe to assume the non-SI unit.
Examples
From the table, poly has a solubility parameter of 7.9 cal1/2 cm−3/2. Good solvents are likely to be diethyl ether and hexane. Poly has a solubility parameter of 9.1 cal1/2 cm−3/2, and thus ethyl acetate is likely to be a good solvent. Nylon 6,6 has a solubility parameter of 13.7 cal1/2 cm−3/2, and ethanol is likely to be the best solvent of those tabulated. However, the latter is polar, and thus we should be very cautions about using just the Hildebrand solubility parameter to make predictions.
