Revisiting experimental techniques and theoretical models for estimating the solubility parameter of rubbery and glassy polymer membranes

Estimation and correlation of the Hildebrand solubility parameter ($\delta$) of polymers and small molecules is a common practice in membrane material science and is accomplished by experimental and numerical routes. In this paper, we revisit, update, and compare both routes to enhance the accuracy in the determination of $\delta$. Best practices for the experimental determination of polymer solubility parameters are provided, and the viability of Dynamic Light Scattering (DLS) was demonstrated as an alternative to conventional time- and material-consuming techniques, such as Ubbelohde viscometry and swelling measurements. Glassy and rubbery polymers, including high fractional free volume (FFV) microporous polymers such as PIM-1 and poly(1-trimethylsilyl-1-propyne) (PTMSP), are among the samples included in this study with great relevance to membrane science. In an attempt to enhance the accuracy of numerical estimate of polymer solubility parameters via the group contribution method, we provide updated group contribution parameters, along with their uncertainty, according to the technique recently reported by Smith et al. These updated group contribution parameters result in a mean absolute relative error of 9.0% in predicting the solubility parameter 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 does not improve its accuracy. Results of the updated group contribution technique and dynamic light scattering measurements were compared to experimental viscometry on four test polymers, and the difference between the three techniques is compared.