Part-2: Determining Solvent Evaporation Rates Faster with Science-based Tool

In Part 1, we looked at how the formulator might go about choosing the right balance of solvent evaporation properties using basic parameters such as:

These properties have to be balanced against other factors such as toxicity, green credentials, odor and the all-important solubility behavior encoded in Hansen Solubility Parameters, HSP.

Here we look at ways in which things become complicated – and what we can do about it. Surprisingly, HSP turn out to be a helpful pragmatic tool for dealing with the complications.

It’s not ideal

A good way to create a real-world solvent for a specific application is to create a blend of two solvents that can deliver properties neither can deliver on their own. For example, HSP shows that you can take two rather poor solvents for a given solute and create a good solvent via a smart blend. This is because the HSP of the mix is the weighted average of the individual components.

This means that a solvent with parameters that are too large can be offset with another solvent with parameters that are too small. In the extreme, two bad solvents can create a good one, as indicated in the diagram where each solvent is far from the center that defines the HSP of the solute, but a 50:50 blend would be perfectly in the middle.



Via the simple evaporation theory discussed in Part 1 we can readily estimate how the blend will evaporate. The one with the higher RER will evaporate faster, meaning that the HSP of the blend will change with time. An app shows this well:



We start with a 50:50 blend of heptane:cyclohexanone. The red line shows the overall % solvent over time. The heptane evaporates faster than the cyclohexanone and from the yellow and blue lines, you can see how the original 50:50 blend quickly becomes 100% cyclohexanone.

The Ra value, in green, describes how far the solvent blend is in HSP terms from the polymer. The original distance is 5.7, not very good but adequate. Because cyclohexanone is closer in HSP space as the heptane disappears, the Ra decreases to ~3, i.e. solubility increases.

There’s a problem with this simulation. Heptane and cyclohexanone are rather dissimilar, so their mix is non-ideal. This means that when heptane is in a minority in the solution it is uncomfortable being near cyclohexanone, so its vapor pressure will be higher than expected. This non-ideal behavior is expressed as an activity coefficient.

Another app (based on UNIFAC theory, not shown) tells us that heptane’s activity coefficient is in the 1.2-1.3 range when at a lower concentration in cyclohexanone, so the evaporation will be 20-30% faster than expected from the simple evaporation app.

We can also get non-ideal behavior with respect to the solute, so the activity coefficient might be somewhat larger again. And in some cases, the solvent interactions are sufficient to create an azeotrope where the evaporation is at constant composition.


 » Continue reading to learn how to deal with the non-ideality of solvent evaporation and modeling diffusion-limited rate!