Predicting Nanoparticle Arrangement in Membranes Formed by Nonsolvent-Induced Phase Separation Using the Combined SCFT/DFT Approach

Blending hydrophilic nanoparticles (NPs) with polymer dope solutions is an efficient method to obtain membranes with improved water treatment performance through the nonsolvent-induced phase separation (NIPS) process. However, it is challenging to control the spatial location and arrangement of NPs for maximum interfacial segregation while minimizing leaching. Herein, we demonstrate that a combined self-consistent field theory and density functional theory (SCFT/DFT) approach can be applied to precisely tune the arrangement of spherical NPs in membranes prepared by the NIPS process. Due to nonperiodic boundary conditions imposed by nonsolvent bath (top surface) and glass slide (bottom surface), the modified diffusion equation of the SCFT/DFT model is solved by collocation with a Chebyshev polynomial basis. Based on the Chebyshev-based SCFT/DFT approach, the effects of relative size of the NP to the polymer chain, surface chemistry, and volume fraction of the NP on the entropic/enthalpic contributions and NP preferential localization in the polymer-rich and polymer-poor phases and at the interface of the phases of the membranes are elucidated. The loss in conformational entropy arisen by the large NPs and the enthalpic attraction between NPs and the nonsolvent push the NPs toward the interface, while the enthalpic interaction between small NPs and the polymer chains retains the NPs in the polymer-rich phase. Theoretical calculations on the NP leaching during the NIPS process and the top surface coverage of NPs quantitatively reproduce the corresponding experimental results from the literature. The applied SCFT/DFT framework will pave the way for designing targeted NPs to prepare nanocomposite membranes with tailored NP localization and surface properties.