For 50 years, HSP have worked very well with polymers, nanoparticles, dispersions etc. but many of us have noticed that with smaller, crystalline solutes fits and predictions can be less good. An Open Access paper, Manuel J. Louwerse, Ana Maldonado, Simon Rousseau, Chloe Moreau-Masselon, Bernard Roux, and Gadi Rothenberg, Revisiting Hansen solubility parameters by including thermodynamics, ChemPhysChem, 18, 2999–3006, 2017, published jointly by the groups of Prof Gadi Rothenberg at the University of Amsterdam, and of Dr. Bernard Roux at the Solvay Lab of the Future in Bordeaux, which combines a deep theoretical analysis with extensive experimental data (used for fitting and prediction testing) from Solvay, may explain what the issues are.
It has always been known (and Hansen knew this right from the start) that the size of the solvent molecule plays a significant part in the thermodynamics of solvation, with smaller solvents being thermodynamically superior. However, attempts by Hansen and others (e.g. within HSPiP) to include size effects within the HSP scheme provided little benefit for more complexity.
The thorough review of the basic thermodynamics in this paper shows that when calculating a Hansen Sphere, there is an effective radius, reff, that depends on the standard radius of the solute, r, and the radius of each individual solvent, rsolv.
1/reff = 1/r + 1/rsolv
The solvent radius can be determined from the MVol. So what about the solute radius? It turns out that for polymers this radius is super-small in terms of the key calculation (there is an internal conversion to a different "standard state"), so the relatively large solvent radius hardly affects the value of reff. Therefore, as has been seen regularly, solvent size effects are rather small and the HSP community has been right to choose the pragmatic simplicity of not over-complicating things.
But for small molecule solutes, the solvent size correction can be significant, and that is what has been missing for those who regularly use HSP with such solutes.
It turns out that properly applying the correction and obtaining a reliable fitting process is far from easy. Happily, the team have provided a Matlab package zip file, nicely documented, that can be downloaded and used by anyone who is keen to get better fits to tricky small solutes.
The paper includes other improvements (e.g. the ability to compare yes/no solubility results at different target concentrations and a correction for the melting point of the given solute) which are not discussed further here but which the reader will enjoy exploring.
We thank Dr Manuel Louwerse for his help in explaining to us many of the subtleties of the new technique and for the permission from himself and the team to allow us to provide the Matlab package to interested readers.