(32i) Revisiting Experimental Techniques and Theoretical Models for Estimating the Solubility Parameter of Rubbery and Glassy Membranes

The Hildebrand solubility parameter, δ, is a well-known thermodynamic quantity used to predict and correlate miscibility among substances, including low molecular weight compounds and polymers, which affects practical applications such as membrane separations, coatings, drug delivery, and new material formulation. As a further example, liquid solvent flux through organic solvent nanofiltration (OSN) and organic solvent reverse osmosis (OSRO) membranes exhibits systematic correlations with the polymer and penetrant solubility parameters. Therefore, knowing δ helps predict solvent permeability in polymer membranes, with minimum experimental efforts. Estimation of δ for polymers and small molecules is accomplished by both experimental and numerical routes. Intrinsic viscosity, as well as swelling measurements, are commonly used to study polymer interactions with solvents and determine polymer δ values. These experimental routes, however, require viscosity data in numerous solvents at various concentrations, and therefore they are time and material consuming.

Dynamic light scattering (DLS) offers a quicker solution while consuming less material, by correlating δ to the hydrodynamic diameter of polymers in various solvents. Rubbery and glassy polymers, including microporous polymers, such as PIM-1, and poly(1-trimethylsilyl-1-propyne) (PTMSP), are among the samples included in this study with great relevance, particularly, to membrane science. To enhance the accuracy of the numerical estimate of polymer δ values via the group contribution method, we provide updated group contribution parameters, along with their uncertainty. These updated parameters result in a mean absolute relative error of 9.0% in predicting δ on a test set of 40 polymers, which is on par with the average 10% error reported previously. We also show, using machine learning techniques, that augmenting the group contribution model with extra parameters or non-linear relationships did not improve its accuracy. Results among techniques were then compared.