Descriptors derived from atomic structure and quantum chemical calculations for small molecules representing polymer repeat elements were evaluated for machine learning models to predict the Hildebrand solubility parameters of the corresponding polymers. Since reliable cohesive energy density data and solubility parameters for polymers are difficult to obtain, the experimental heat of vaporization ΔHvap of a set of small molecules was used as a proxy property to evaluate the descriptors. Using the atomistic descriptors, the multilinear regression model showed good accuracy in predicting ΔHvap of the small-molecule set, with a mean absolute error of 2.63 kJ/mol for training and 3.61 kJ/mol for cross-validation. Kernel ridge regression showed similar performance for the small-molecule training set but slightly worse accuracy for the prediction of ΔHvap of molecules representing repeating polymer elements. The Hildebrand solubility parameters of the polymers derived from the atomistic descriptors of the repeating polymer elements showed good correlation with values from the CROW polymer database.
Solubility of small molecules in macromolecular compounds is of fundamental importance for a number of applications, including the growing field of nanomedicine. Here, approaches for in silico solubility predictions based on atomistic models are evaluated. A computationally efficient atomistic simulation procedure based on the concept of inherent structures is proposed for statistical sampling of polymer conformations. Comprehensive test simulations of several polymers and common solvents confirm the accuracy of the procedure for calculation of physicochemical properties such as cohesive energy densities, which along with the Hansen solubility parameters and the Flory-Huggins (FH) theory facilitate rapid, qualitative solubility predictions. However, the FH theory fails to model specific interactions such as hydrogen bonding. Therefore, more accurate predictions are obtained employing the perturbed hard sphere chain (PHSC) equation of state (EOS). As test case, aqueous poly(ethylene oxide) (PEO) solutions revealing strong hydrogen bonding are used. The physicochemical properties including the PEO-water phase diagram calculated by the PHSC EOS show good agreement with experimental observations. Consequently, the combination of qualitative predictions using the FH theory for rapid prescreening with computationally more demanding parameterization of the PHSC EOS provides a promising tool for in silico solubility predictions with potential applications in nanomedicine.
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