What are HSP?
Hansen Solubility (Cohesion) Parameters (HSP)
The cohesion energy parameters most widely used for characterizations are those developed by Hansen.1-6 These are now called Hansen solubility (cohesion) parameters. They are based on an extension of the Hildebrand solubility parameter.7,8 The HSP assigned to many liquids and polymers many years ago have recently been confirmed with amazing agreement using a statistical thermodynamics treatment by Panayiotou.9 See Table 1.
The total cohesion energy of a liquid, E, can be divided into at least 3 separate parts by experiment or calculation.1, 4-6, 9 In the Hansen approach these parts quantitatively describe the nonpolar, atomic (dispersion) interactions, ED, permanent dipole-permanent dipole molecular interactions, EP, and the hydrogen bonding (electron interchange) molecular interactions, EH.
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E can be experimentally measured by determining the energy required to evaporate the liquid, thus breaking all of its cohesion bonds in the process.
where 
HV is the measured (or predicted) latent heat of vaporization, R is the universal gas constant, and T is the absolute temperature.
Dividing Equation 1 by the molar volume, V, gives the respective Hansen cohesion energy (solubility) parameters according to Eq. 4.
The total cohesion energy divided by the molar volume is the total cohesion energy density. The square root of this is the Hildebrand total solubility parameter, 
.7,8 The SI units for all of these are MPa½. These units are 2.0455 times larger than the units (cal/cc)½.
HSP characterizations can be conveniently visualized using a spherical representation. The HSP are at the center of the sphere, and the radius of the sphere, Ro, indicates the maximum difference in affinity tolerable for a “good” interaction to take place. Good solvents are within the sphere, and bad ones are outside. A simple composite affinity parameter, RED, standing for Relative Energy Difference, has been defined as the distance according to Equation 5, Ra, divided Ro.
The subscripts are for the sample, 1, and test chemical, 2, respectively. Good solvents will have RED less than 1.0. Progressively poorer solvents will have increasingly higher RED.
The "4" in Equation 5 has been found correct experimentally for all practical purposes in over 1000 correlations using HSP, and agrees with predictions of the Prigogine theory as discussed in references (5) and (6). It differentiates atomic from molecular interactions.
Table 1.
| |
HANSEN |
PANAYIOTOU |
| Toluene |
2.00 |
2.00
|
| Tetralin |
2.90 |
2.90 |
| Acetone |
6.95 |
7.00 |
| Methyl Methacrylate |
5.40 |
5.40 |
| Ethanol |
19.43 |
19.98 |
| 1-Butanol |
15.80 |
15.80 |
| Dimethyl sulfoxide |
10.20 |
10.28 |
| Water |
42.32 |
42.17 |
Table 1. Comparision of the hydrogen bonding parameter (H) in MPa½ between Hansen5,6 and Panayiotou10
How Does Charles M. Hansen Calculate the HSP for Liquids?
In the usual case the latent heat of evaporation can not be found nor calculated with sufficient reliability. If it can then Equation 1 must be maintained.
The dispersion component is best found by the charts given in references (5) or (6). These have been extrapolated linearly to higher values. The critical temperature should be found or estimated by the Lydersen method, also reported in the handbook(s). One can then find the required ED from these figures and then the dispersion Hansen solubility parameter. The group contribution method is not recommended using the tables given in the handbooks. This often ends too low, but these have been included for completeness. Comparison with similar compounds is recommended when there is no other way. There are values now for some 1200 compounds in (6).
The polar component was earlier found using the dipole moment, dielectric constant, refractive index, and molar volume as described in (6). These data are not generally available, for which reason Beerbower’s equation is used wherever possible. This is also described in (6). When a dipole moment is not available, one must resort to group contributions, as given in Chapter 1 in (5) or (6). Comparison with similar compounds is also a possibility.
The hydrogen bonding component has been evaluated using Equation 1 where data are sufficiently accurate to find the other components with accuracy. Experimental confirmation has been possible with many compounds, but this has been a major problem until Prof. Panayiotou confirmed earlier placements (See above) with a statistical thermodynamics procedure.9 Those not able to use this procedure are advised to use the group contributions provided in the handbooks or experimental work to confirm assigned values. Many of the original assignments were confirmed by mixtures of non-solvents that could dissolve polymers where the individual solvents could not do so. This confirmed their assignments as being above and below the HSP of the solute in some respect.
It might be said in conclusion that absolute accuracy is not always required to get good results in practice, although this varies from case to case. In many of the calculation procedures discussed above, the taking of square roots aids immensely in arriving at useful HSP.
Hansen Solubility Parameters for Solids and Surfaces
The Hansen solubility parameters for some solids have been estimated by the techniques described above, more or less ignoring the fact that one is indeed dealing with a low molecular weight solid that has a melting point above room temperature. Other solids are evaluated by solubility, swelling, permeation, or other effect based on solubility. Solid surfaces can be characterized by sedimentation studies for pigments, fillers, and fibers. Plane solid surfaces can be characterized by whether or not a droplet spontaneously spreads, and by whether or not an applied liquid remains as a film. These tests are all described in more detail in references (5) and (6).
Prediction of Affinities
The closer the HSP of two materials, the more likely it is that they have higher affinity than had their HSP been farther apart.
REFERENCES
- Hansen, C. M., The Three Dimensional Solubility Parameter - Key to Paint Component Affinities I. - Solvents, Plasticizers, Polymers, and Resins, J. Paint Techn., 39, No. 505, 104-117 (1967).
- Hansen, C. M., The Three Dimensional Solubility Parameter - Key to Paint Component Affinities II. - Dyes, Emulsifiers, Mutual Solubility and Compatibility, and Pigments, J. Paint Techn. 39, No 511, 505-510 (1967).
- Hansen, C. M., and Skaarup, K., The Three Dimensional Solubility Parameter - Key to Paint Component Affinities III. - Independent Calculation of the Parameter Components, J. Paint Techn. 39, No. 511, 511-514 (1967).
- Hansen, C. M., Doctoral Dissertation, The Three Dimensional Solubility Parameter and Solvent Diffusion Coefficient, Their Importance in Surface Coating Formulation, Danish Technical Press, Copenhagen, 1967.
- Hansen, C. M., Hansen Solubility Parameters: A User’s Handbook, CRC Press, Boca Raton, FL, 1999.
- Hansen, C. M., Hansen Solubility Parameters: A User’s Handbook, Second Ed., CRC Press, Boca Raton, FL, 2007.
- Hildebrand, J. and Scott, R. L., The Solubility of Nonelectrolytes, 3rd Ed., Reinhold, New York, 1950.
- Hildebrand, J. and Scott, R. L., Regular Solutions, Prentice-Hall Inc., Englewood Cliffs, NJ, 1962.
- Panayiotou, C., Statistical Thermodynamics Calculations of the Hydrogen Bonding, Dipolar, and Dispersion Solubility Parameters, Chapter 3 in reference 6.
Charles M. Hansen
May 29, 2007
