Critical Assessment of the Hildebrand and Hansen Solubility Parameters for Polymers

Solubility parameter models are widely
used to select suitable
solvents/nonsolvents for polymers in a variety of processing and engineering
applications. In this study, we focus on two well-established models,
namely, the Hildebrand and Hansen solubility parameter models. Both
models are built on the basis of the notion of “like dissolves
like” and identify a liquid as a good solvent for a polymer
if the solubility parameters of the liquid and the polymer are close
to each other. Here we make a critical and quantitative assessment
of the accuracy/utility of these two models by comparing their predictions
against actual experimental data. Using a data set of 75 polymers,
we find that the Hildebrand model displays a predictive accuracy of
60% for solvents and 76% for nonsolvents. The Hansen model leads to
a similar performance; on the basis of a data set of 25 polymers for
which Hansen parameters are available, we find that it has an accuracy
of 67% for solvents and 76% for nonsolvents. The availability of the
Hildebrand parameters for a large polymer data set makes it a widely
applicable capability, as the Hildebrand parameter for a new polymer
may be determined using this data set and machine learning methods
as we have done before; the predicted Hildebrand parameter for a new
polymer may then be used to determine suitable solvents and nonsolvents.
Such predictions are difficult to make with the Hansen model, as the
data set of Hansen parameters for polymers is rather small. Nevertheless,
the Hildebrand approach must be used with caution. Our analysis shows
that while the Hildebrand model has a predictive accuracy of 70–75%
for nonpolar polymers, it performs rather poorly for polar polymers
(with an accuracy of 57%). Going forward, determination of solvents
and nonsolvents for polymers may benefit by developing classification
models built directly on the basis of available experimental data
sets rather than utilizing the solubility parameter approach, which
is limited in versatility and accuracy.