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:
δ d {\displaystyle \ \delta _{\text{d}}} The energy from dispersion forces between molecules
δ p {\displaystyle \ \delta _{\text{p}}} The energy from dipolar intermolecular forces between molecules
δ h {\displaystyle \ \delta _{\text{h}}} 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 ( R 0 {\displaystyle R_{\mathrm {0} }} ) 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 ( R a {\displaystyle \ Ra} ) between Hansen parameters in Hansen space the following formula is used:
( R a ) 2 = 4 ( δ d 2 − δ d 1 ) 2 + ( δ p 2 − δ p 1 ) 2 + ( δ h 2 − δ h 1 ) 2 {\displaystyle \ (Ra)^{2}=4(\delta _{d2}-\delta _{d1})^{2}+(\delta _{p2}-\delta _{p1})^{2}+(\delta _{h2}-\delta _{h1})^{2}}
Combining this with the interaction radius R 0 {\displaystyle R_{\mathrm {0} }} gives the relative energy difference (RED) of the system:
R E D = R a R 0 {\displaystyle \ RED=\textstyle {\frac {Ra}{R_{0}}}}
If R E D < 1 {\displaystyle \ RED<1} the molecules are alike and will dissolve If R E D = 1 {\displaystyle \ RED=1} the system will partially dissolve If R E D > 1 {\displaystyle \ RED>1} the system will not dissolve
Uses Historically Hansen solubility parameters (HSP) have been used in industries such as paints and coatings where understanding and controlling solvent–polymer interactions was vital. Over the years their use has been extended widely to applications such as:
Environmental stress cracking of polymers Controlled dispersion of pigments, such as carbon black Understanding of solubility/dispersion properties of carbon nanotubes, Buckyballs, and quantum dots Adhesion to polymers Permeation of solvents and chemicals through plastics to understand issues such as glove safety, food packaging barrier properties and skin permeation Diffusion of solvents into polymers via understanding of surface concentration based on RED number Cytotoxicity via interaction with DNA Artificial noses (where response depends on polymer solubility of the test odor) Safer, cheaper, and faster solvent blends where an undesirable solvent can be rationally replaced by a mix of more desirable solvents whose combined HSP equals the HSP of the original solvent.
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