Advancing the thermodynamic modeling of fluid Sorption in glassy polymers via equations of state and machine learning

Abstract

The solubility of fluids in polymers is a vital property for the design and optimization of efficient separation processes. Although the underlying thermodynamics is well understood and supported by a diverse array of physical models, the component- and mixture-specific adjustable parameters in these theories must be fitted to experimental data to enable the practical determination of the solubility, thereby limiting their predictive capabilities. Moreover, the full potential of well-established models has not been fully leveraged to describe many systems of relevance to membrane science. This thesis has two primary objectives: (1) to modify and evaluate state-of-the-art equation of state (EoS) approaches for predicting the sorption of various molecular classes in glassy polymers, and (2) to develop hybrid machine learning (ML) and EoS models for polymer parameter predictions.

In the first part of this work, we investigate the dry glass reference perturbation theory (DGRPT) for modeling the sorption of pure and mixed fluids in polymeric materials.

The DGRPT offers a framework for extending EoS models to glassy systems, whereby the polymer swelling is treated as a perturbative expansion of the chemical potential.

We propose a second-order form of the DGRPT to improve the model’s accuracy, particularly for systems exhibiting dual-mode type sorption isotherms. Additionally, using the perturbed-chain statistical associating fluid theory (PC-SAFT) as the EoS, we systematically examine different association parameterization schemes for alcohol and water sorption. Furthermore, the hetero-segmental (copolymer) PC-SAFT model was used to predict the influence of monomer composition on solubility.

The second part of the thesis focuses on ML–EoS hybrid models for predicting the pure polymer parameters. Our initial implementation combines group contribution methods as a molecular feature representation with machine learning to estimate the parameters of the Sanchez and Lacombe Lattice Fluid (LF) model. Given the limited dataset, we employed simple algorithms such as ridge regression and support vector machines (SVM), which yielded satisfactory agreement with experimental liquid-state volumetric data. In our second implementation, we achieved significant improvements in predictive accuracy by applying transfer learning (TL) and physics-informed techniques to estimate the parameters of the PC-SAFT EoS. This approach involves training the model directly on the volumetric properties, allowing it to learn the EoS parameters in an end-to-end manner.