Never use Hildebrand Solubility Parameters

We have the highest respect for Professor Hildebrand’s pioneering work on solubility parameters. Without Hildebrand’s work, HSP would not exist.

But the blunt truth is that if you are using Hildebrand parameters you are making a major mistake. The chances are very high that they will lead you astray or miss the target significantly.

Why is this? Because Hildebrand (and Scott, and Scatchard) dealt with a theory where the assumptions were not directly applicable to the real world. Hydrogen bonding and polar solvents were not included since the theory was based on the behaviour of hydrocarbon solvents.

As such Hildebrand was dealing with abstract entities rather than real-world solvents. The assumptions behind the theory are therefore very restrictive. This is not a criticism of his work – it was necessary to make such abstract arguments in order to reach the fundamental insights of Solubility Parameters.

Almost as soon as his work came out, it was taken up by the paints and lacquers industry and it immediately became obvious to the users and to Hildebrand himself that the single parameter was not powerful enough. Many different schemes started to emerge which added terms on to the single Hildebrand parameter, but these didn’t do a great job. Soon Hildebrand’s parameter was split into Dispersion and Polar terms. Even this split became untenable because the effects of alcohols just didn’t fit into such a scheme. That’s when Hansen added the final split with the Hydrogen Bonding term and powerful predictivity emerged once the first self-consistent set of HSP was published.

Let’s give a simple example of a Hildebrand failure. The Hildebrand parameters for n-Butanol and Nitroethane are identical (23). But neither solvent dissolves a typical Epoxy. Yet a 50:50 mixture of the two solvents is a good solvent for the Epoxy. Not only does the Hildebrand parameter fail spectacularly, but there isn’t even a coherent theory of how to deal with solvent blends. Yet we all know that solvent blends are crucial for real-world work.

In HSP terms there is no mystery. A typical Epoxy has HSP of [17, 8, 8]. Butanol is [16, 5.7, 15.8] and an HSP distance (Ra) of 8.4. Nitroethane is [16.0, 15.5, 4.5] with an Ra of 8.5. The 50:50 mix is [16, 10.5, 10.3] with an Ra of 3.9. Although the dividing line between “solvent” and “non-solvent” for a polymer can vary, an Ra of 8 is typically a good estimate. Both Nitroethane and n-Butanol are beyond that Ra but their mixture is well inside.

And these are real, lab-based experimental data. You really cannot dissolve Epikote 1001 in n-Butanol or Nitroethane, but you really can dissolve it in the 50:50 mixture. And this isn’t a one-off result. Hansen personally found in his lab more than 60 pairs of non-solvents which, in the right proportions, were able to dissolve 22 different polymers. Here are some more examples:

• Urea is insoluble in ethanol or butyrolactone but readily soluble in a 2:1 mixture.
• Cholesterol is insoluble in hexane and ethanol, but is readily soluble in hexane with 10% ethanol. This may, incidentally, be one reason why alcohol helps reduce heart disease – it may help the cholesterol to dissolve away from blood vessels and into cells via their lipid (“hexane-like” membranes).
• A PMMA [17.7, 9.1, 7.1] is insoluble in butanol [16.0, 5.7, 15.8] (Ra=9.9) and insoluble in diethyl sulfide [16.8, 3.1, 2.0] (Ra=8.1) but soluble in a 50:50 mix [16.4, 4.4, 8.8] (Ra=5.6). Similarly PMMA is insoluble in benzene [18.4, 0.0, 2.0] (Ra=10.5) and insoluble in nitromethane [15.8, 18.8, 6.1] (Ra=10.5) but soluble in a 50:50 mix [16.1, 11.6, 7.5] (Ra=4).
• Another example is that a polystyrene [18.6, 6, 4.5] is insoluble in diethyl ether [14.5, 2.9, 4.6] (Ra=8.8) and insoluble in propylene carbonate [20.0, 18.0,4.1] (Ra=12.4) but is soluble in a 50:50 mixture [17.3, 10.5, 4.3] (Ra=5.3).

We’re not suggesting that you would want to dissolve PMMA in benzene/nitromethane, we’re simply showing that the power of HSP means that you can come up with interesting alternatives to solvents, by including non-solvents that most people would never think of using. These examples, none of which can be explained using the Hildebrand approach, show that at a fundamental level, the Hildebrand solubility parameter cannot and does not work.

We don’t claim that Hansen Solubility Parameters are perfect. But if you hear someone say “Solubility Parameters don’t work”, just check if they are referring to work using Hildebrand parameters, in which case they are probably right!

From negative to positive

Suppose that you or a colleague have done all the hard work to gain some insights from Hildebrand parameters and have been disappointed in the outcome. Typically they will have used some hydrocarbons and some alcohols to give a bit of hydrogen bonding. The good news is that all those experimental data are still valid. You don’t have to re-do the work. You simply need to re-evaluate the results using Hansen parameters. Software such as HSPiP makes this very easy to do (we’ve often done it ourselves when reviewing literature data based on Hildebrand parameters), but a simple spreadsheet and a list of Hansen parameters is all you need for basic analyses.

It is possible that the Hildebrand experiment might, in Hansen terms, be incomplete. The experiments may have explored a range of Hildebrand parameters without exploring enough of the polar and/or hydrogen-bonding space. Again, this isn’t a big problem. The data points gathered for the Hildebrand work are still valid. You simply need to do a few tests with some solvents chosen to ensure that a wider range of Hansen space is investigated. Although solvents such as DMSO, DMF, NMP and propylene carbonate are unlikely to be used in final formulation, they make excellent test solvents because they are in "interesting" parts of HSP space.