Solubility Parameters: Theory and Application

John Burke
The Oakland Museum of California
August 1984

Part 4 - Component polarities

As was mentioned above, there are inconsistencies in Fig.1 that are difficult to explain in terms of single component Hildebrand parameters. The graph shows chloroform and ethylene dichloride (with Hildebrand values of 18.7 and 20.2 respectively) swelling a linseed oil film considerably more than methyl ethyl ketone(MEK) and acetone. And yet the Hildebrand values for MEK and acetone are 19.3 and 19.7, both between the values for the two high swelling solvents. Theoretically, liquids with similar cohesive energy densities should have similar solubility characteristics, and yet the observed behavior in this instance does not bear this out. The reason for this is the differences in kinds of polar contributions that give rise to the total cohesive energy densities in each case.

It was mentioned that van der Waals forces result from the additive effects of several different types of component polarities. The inconsistencies in Fig.1 are due to the fact that, while the sum total cohesive energy densities are similar in the four solvents in question, the addends that make up those individual totals are different. These slight disparities in polar contributions result in considerable differences in solubility behavior. If these component differences are taken into account, quantified, and included in solubility theory, the prediction of solubility behavior can become more accurate. To do this, different types of polar contributions must be examined, and differentiated.

The following section is an introduction to the three types of polar interactions that are most commonly used in solubility theories: dispersion forces, polar forces, and hydrogen bonding forces. In some systems, the Hildebrand parameter is used in conjunction with only one or two of these forces (i.e. Hildebrand value and hydrogen bonding value), while more recent developments subdivide the Hildebrand parameter into all three forces, or derivatives of them. The concepts discussed provide an excellent foundation for understanding the inner workings of the practical systems introduced later. It should be stressed, however, that it is possible to use these practical systems without a thorough understanding of the molecular dynamics on which they are based.


Strong electromagnetic forces are present in every atom and molecule. At the center of a molecule is a positively charged atomic nucleus, while the outer surface is covered by a dispersed cloud of negatively charged electrons. These positive and negative charges balance out, and the molecule as a whole is neutral. If, for reasons we will investigate, the distribution of the electron cloud is uneven (maybe thicker in one place and thinner in another), small local charge imbalances are created: the parts of the molecule with a greater electron density will be negatively charged, and the electron deficient parts will be positively charged. The molecule as a whole, while still neutral, will have the properties of a small magnet, with equal but opposite poles, called dipoles.

A single molecule, because of its structure, can have several dipoles at once, some strong and some weak, some which cancel out, and some which reinforce each other. The resulting sum of all the dipoles is what is known as the dipole moment of the molecule. Molecules that have permanent dipole moments are said to be polar, while molecules in which all the dipoles cancel out (zero dipole moment) are said to be nonpolar.

This molecular polarity is at the heart of intermolecular attractions (imagine a pile of small magnets sticking together). The strength with which the molecules cling together, and therefore the cohesive energy density and the solubility parameter, is directly related to the strength of the molecular dipoles. But since the overall polarity of a molecule is often the combined result of several contributing polar structures, it is not enough to know the dipole moment of a molecule. The component polarities must be considered as well. Molecules like to be with other molecules of their own electromagnetic kind, both in terms of polar strength and in terms of polar composition.


Nonpolar liquids, such as the aliphatic hydrocarbons, have weak intermolecular attractions but no dipole moment. Magnets without poles; how can this be? The source of their electromagnetic interactions can be described by quantum mechanics, and is a function of the random movement of the electron cloud surrounding every molecule. From instant to instant, random changes in electron cloud distribution cause polar fluctuations that shift about the molecular surface. Although no permanent polar configuration is formed, numerous temporary dipoles are created constantly, move about, and disappear.

When two molecules are in proximity, the random polarities in each molecule tend to induce corresponding polarities in one another, causing the molecules to fluctuate together. This allows the electrons of one molecule to be temporarily attracted to the nucleus of the other, and vise versa, resulting in a play of attractions between the molecules. These induced attractions are called London dispersion forces, or induced dipole-induced dipole forces.

The degree of "polarity" that these temporary dipoles confer on a molecule is related to surface area: the larger the molecule, the greater the number of temporary dipoles, and the greater the intermolecular attractions. Molecules with straight chains have more surface area, and thus greater dispersion forces, than branched-chain molecules of the same molecular weight. This dependance on surface area explains why conversions between Kauri-Butanol numbers and Hildebrand values for paraffins must include calculations for molecular size. The intermolecular forces between paraffin molecules are entirely due to dispersion forces, and are therefore size dependant.


Dispersion forces are present to some degree in all molecules, but in polar molecules there are also stronger forces at work. Some atomic elements attract electrons more vigorously than others, and permanent dipoles are created when electrons are unequally shared between the individual atoms in a molecule. If the molecule is symmetrical, these dipoles may cancel out. If, on the other hand, the electron density is permanently imbalanced, with some atoms in the molecule harboring a greater share of the negative charge distribution, the molecule itself will be polar. The polarity of a molecule is related to its atomic composition, its geometry, and its size. Water and alcohol are strongly polar molecules, toluene is only slightly polar, and the paraffin hydrocarbons such as hexane and stoddard solvent are considered to be nonpolar (again, the attractions between nonpolar molecules are due entirely to dispersion forces).

Polar molecules tend to arrange themselves head to tail, positive to negative, and these orientations lead to further increases in intermolecular attraction. These dipole-dipole forces, called Keesom interactions, are symmetrical attractions that depend on the same properties in each molecule. Because Keesom interactions are related to molecular arrangements, they are temperature dependant. Higher temperatures cause increased molecular motion and thus a decrease in Keesom interactions.

On the other hand, any molecule, even if nonpolar, will be temporarily polarized in the vicinity of a polar molecule, and the induced and permanent dipoles will be mutually attracted. These dipole-induced dipole forces, called Debye interactions, are not as temperature dependant as Keesom interactions because the induced dipole is free to shift and rotate around the nonpolar molecule as the molecules move. Both Debye induction effects and Keesom orientation effects are considered similar in terms of solubility behavior and are collectively referred to as polar interactions or simply polarities.


A particularly strong type of polar interaction occurs in molecules where a hydrogen atom is attached to an extremely electron-hungry atom such as oxygen, nitrogen, or fluorine. In such cases, the hydrogen's sole electron is drawn toward the electronegative atom, leaving the strongly charged hydrogen nucleus exposed. In this state the exposed positive nucleus can exert a considerable attraction on electrons in other molecules, forming a protonic bridge that is substantially stronger than most other types of dipole interactions. This type of polarity is so strong compared to other van der Waals interactions, that it is given its own name: hydrogen bonding. Understandably, hydrogen bonding plays a significant role in solubility behavior.

The inconsistencies in Fig. 1 stem from a difference in hydrogen bonding between the chlorinated solvents and the ketones. The intermolecular forces in linseed oil are primarily due to dispersion forces, with practically no hydrogen bonding involved. These polar configurations are perfectly matched by the intermolecular forces between chloroform molecules, thus encouraging interpenetration and swelling of the linseed oil polymer. Acetone and methyl ethyl ketone, however, are more polar molecules, with moderate hydrogen bonding capabilities. Even though the total cohesive energy density is similar in all four solvents, the differences in component forces, primarily hydrogen bonding, lead to the observed differences. Acetone and MEK would much rather be attracted to each other than to linseed oil.

Next: Part 5 - Two component parameters

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