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.