Revisiting Experimental Techniques and Theoretical Models for Estimating the Solubility Parameter of Rubbery and Glassy Polymer Membranes

The Hildebrand solubility parameter, δ, is used to predict and correlate miscibility among substances, including low molecular weight compounds and polymers, which affects practical applications such as coatings, drug delivery, material formulation, and membrane separations. Estimation and correlation of the Hildebrand solubility parameter (δ) of polymers and small molecules is a common practice in membrane material science and 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, which may be problematic when working with non-commercial, expensive polymers.

Dynamic light scattering 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 a microporous polymers, PIM-1, and a high fractional free volume (FFV) polymer, poly(1-trimethylsilyl-1-propyne) (PTMSP), are among the samples included in this study with great relevance to membrane science. Secondly, 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. (J. Membr. Sci. 636 (2021) 119525). 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 discussed.