HSP Examples: Nanoparticles
It's often said that nanoparticles must have dispersants around them so they don't clump. The HSP view is that it makes sense to say that nanoparticles can be soluble, so dispersants are not necessary if there is a good HSP match between particle and solvent.
A nice example where dispersants are not necessary, and where HSPiP itself was used to measure the HSP and to create new solvent blends via Solvent Optimizer is the paper from the Ulbricht group in U. Essen, Jan U. Wieneke et al, Systematic Investigation of Dispersions of Unmodified Inorganic Nanoparticles in Organic Solvents with Focus on the Hansen Solubility Parameters, Ind. Eng. Chem. Res. 2012, 51, 327–334. Here they measure the HSP of TiO2 and hydroxyapatite (HA) using the classic Sphere test of whether the particles are "happy" or "unhappy" in a solvent - defining happy as remaining well-dispersed after many days.
HSP theory says that you can make new solvents out of mixtures of old ones. The paper confirms that this technique works for these "soluble" nanoparticles. Not all the predictions are perfect, but they can open up new formulation possibilities that might otherwise never be explored. For example, acetonitrile is hopeless for solubilising HA, yet when Solvent Optimizer predictions of an excellent blend with acetone (also a poor solvent) and benzyl alcohol (not tested on its own in the paper but almost certainly a bad solvent) were tested, the blend gave excellent results.
The measured values are: TiO2 = [17.5, 12.7, 8.9] with a relatively small radius of 4 for the Sphere. HA = [17.6, 14, 9.4] with a radius of 3.
The TiO2 HSP are different from the one discussed by Dr Yamamoto on his Pirika TiO2 page which are [15, 15, 5]. In the Hansen Handbook Pigment 1 in Table 7.28 is TiO2 with values (converted to modern units) [23.6, 14.6 19]. There is no surprise at the differences between different grades. Every method of making TiO2 will create a unique surface. What this means is that just as it's illogical to say that "carbon black is readily dispersed in X" without specifiying the carbon black, it is equally wrong to say that "TiO2 is readily dispersed in Y" without doing the measurements. And in terms of quality control of batches of TiO2 it would seem to be a very good idea to have a standard set of solvents that will show whether this batch shows the same solubility profile as the standard. Although it seems odd to be characterising nanoparticles with trivial experiments in a few test tubes, experience shows that you can learn a great deal from these simple tests that is hidden from more sophisticated tests.
The HSP of fully-coated nanoparticles
We have often said that the HSP of a nanoparticle covered with a dispersing agent will be some unknown mix of the HSP of the two components. But what if you could fully cover the nanoparticles? You would then expect to get a single, clean HSP independent of the particle itself
This effect has now been proved by the Mathioudaki team1 at U Namur in Belgium (the team includes Simon Detriche who provided the data for the CNT example). They took three very different nanoparticles with different HSP values and plasma coated them using cyclopropylamine to give a few nm of a complex polymer containing plenty of amine, imine and other nitrogen functionalities which, of course, will be very useful for integration into other systems. The uncoated (u) and coated (c) comparison of the HSP shows the desired effect:
Are "dispersed" particles really soluble?
A standard argument against dispersions being soluble is that over time they settle. This is only partly true - below a certain size (see Steven's Stokes Sedimentation Calculator for details), nanoparticles receive sufficient thermal energy (Brownian motion) to avoid settling. And even if it is true, take something that is seen as soluble such as a protein or some DNA. With a centrifuge it is easy to get the protein to come to the bottom. So now we define "soluble" as something that doesn't settle under 1g but does under, say, 100g. This is not a logical distinction! It turns out that there are good thermodynamic arguments (based on Gibbs Phase Rule) to show that particles are just as much solutions as conventional solutions (see the free eBook from Steven: Solubility Science: Principles and Practice for more details).
Once it becomes more acceptable to think of particles having solubility then the use of HSP makes more sense. Of course their solubility is generally low, if for no other than entropic reasons. But they are still soluble!
1Stella Mathioudaki, Bastien Barthélémy, Simon Detriche, Cédric Vandenabeele, Joseph Delhalle, Zineb Mekhalif and Stéphane Lucas, Development of Core-shell Structures for a Better and Similar Dispersibility, ACS Appl. Nano Mater., 2018, 1 (7), pp 3464–3473