Hansen solubility parameter

Hansen solubility parameters were developed by Charles M. Hansen in his Ph. D thesis in 1967 as a way of predicting if one material will dissolve in another and form a solution. They are based on the idea that like dissolves like where one molecule is defined as being 'like' another if it bonds to itself in a similar way. Specifically, each molecule is given three Hansen parameters, each generally measured in MPa0.5:
The energy from dispersion forces between molecules
The energy from dipolar intermolecular forces between molecules
The energy from hydrogen bonds between molecules. These three parameters can be treated as co ordinates for a point in three dimensions also known as the Hansen space. The nearer two molecules are in this three dimensional space, the more likely they are to dissolve into each other. To determine if the parameters of two molecules (usually a solvent and a polymer) are within range, a value called interaction radius is given to the substance being dissolved. This value determines the radius of the sphere in Hansen space and its center is the three Hansen parameters. To calculate the distance between Hansen parameters in Hansen space the following formula is used:

Combining this with the interaction radius gives the relative energy difference (RED) of the system:

If the molecules are alike and will dissolve
If the system will partially dissolve
If the system will not dissolve

HSP have been criticized for lacking the formal theoretical derivation of Hildebrand solubility parameters. All practical correlations of phase equilibrium involve certain assumptions that may or may not apply to a given system. In particular, all solubility parameter based theories have a fundamental limitation that they apply only to associated solutions (i. e., they can only predict positive deviations from Raoult's law): they cannot account for negative deviations from Raoult's law that result from effects such as solvation (often important in water soluble polymers) or the formation of electron donor acceptor complexes. Like any simple predictive theory, HSP are best used for screening with data used to validate the predictions. Hansen parameters have been used to estimate Flory Huggins Chi parameters, often with reasonable accuracy. The factor of 4 in front of the dispersion term in the calculation of Ra has been the subject of debate. There is some theoretical basis for the factor of four (see Ch 2 of Ref 1 and also. However, there are clearly systems (e. g. Bottino et al., "Solubility parameters of poly(vinylidene fluoride)" J. Polym. Sci. Part B: Polymer Physics 26(4), 785 79, 1988) where the regions of solubility are far more eccentric than predicted by the standard Hansen theory. HSP effects can be over ridden by size effects (small molecules such as methanol can give "anomalous results"). It has been shown that it is possible to calculate HSP via molecular dynamics techniques, though currently the polar and hydrogen bonding parameters cannot reliably be partitioned in a manner that is compatible with Hansen's values.