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# Hansen Solubility Parameters

Hansen Solubility Parameters were developed by Charles Hansen as a way of predicting if one material will dissolve in another and form a solution [1]. 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 $\ MPa^{0.5}$:

• $\ \delta_{d}$ The energy from dispersion bonds between molecules
• $\ \delta_{p}$ The energy from polar bonds between molecules
• $\ \delta_{h}$ 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 (R0) is given to the substance being dissolved. This value determines the radius of the sphere in Hansen space and it's center is the three Hansen parameters. To calculate the distance (Ra) between Hansen parameters in Hansen space the following formula is used:

    $\ (Ra)^2=4(\delta_{d2}-\delta_{d1})^2+(\delta_{p2}-\delta_{p1})^2+(\delta_{h2}-\delta_{h1})^2$


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

    $\ RED=Ra/R_{0}$

• RED < 1 the molecules are alike and will dissolve
• RED = 1 the system will partially dissolve
• RED > 1 the system will not dissolve

## Limitations

The following limitations were acknowledged by Charles Hansen:

• The parameters will vary with temperature
• The parameters are an approximation. Bonding between molecules is more subtle than the three parameters suggest. Molecular shape is relevant. As are other types of bonding such as induced dipole, metallic and electrostatic interactions.
• The size of the molecules also plays a significant role in whether two molecules actually dissolve in a given period
• The parameters are hard to measure

## References

1. ^ Hansen, Charles (2000). Hansen Solubility Parameters: A user's handbook. Boca Raton, Fla: CRC Press. ISBN 0-8493-1525-5.