Modeling Microstructure Formation in Block Copolymer Membranes Using Dynamical Self-Consistent Field Theory

Efficient dynamical field-theoretic simulations for multi-component systems

Understanding the phase behavior and dynamics of multi-component polymeric systems is essential for designing materials used in applications ranging from biopharmaceuticals to consumer products. While computational tools for understanding the equilibrium properties of such systems are relatively mature, simulation platforms for investigating non-equilibrium behavior are comparatively less developed. Dynamic self-consistent field theory (DSCFT) is a method that retains essential microscopic thermodynamics while enabling a continuum-level understanding of multi-component, multi-phase diffusive transport. A challenge with DSCFT is its high computational complexity and cost, along with the difficulty of incorporating thermal fluctuations. External potential dynamics (EPD) offers a more efficient approach to studying inhomogeneous polymers out of equilibrium, providing similar accuracy to DSCFT but with significantly lower computational cost. In this work, we introduce an extension of EPD to enable efficient and stable simulations of multi-species, multi-component polymer systems while embedding thermodynamically consistent noise. We validate this framework through simulations of a triblock copolymer melt and spinodally decomposing binary and ternary polymer blends, demonstrating its capability to capture key features of phase separation and domain growth. Furthermore, we highlight the role of thermal fluctuations in early stage coarsening. This study provides new insights into the interplay between stochastic and deterministic effects in the dynamic evolution of polymeric fluids, with the EPD framework offering a robust and scalable approach for investigating the complex dynamics of multi-component polymeric materials.

Toward Predicting the Formation of Integral-Asymmetric, Isoporous Diblock Copolymer Membranes

The self-assembly and nonsolvent-induced phase separation (SNIPS) process of block copolymers and solvents enables the fabrication of integral-asymmetric, isoporous membranes. An isoporous top layer is formed by evaporation-induced self-assembly (EISA) and imparts selectivity for ultrafiltration of functional macromolecules or water purification. This selective layer is supported by a macroporous bottom structure that is formed by nonsolvent-induced phase separation (NIPS) providing mechanical stability. Thereby the permeability/selectivity tradeoff is optimized. The SNIPS fabrication involves various physical phenomena-e.g., evaporation, self-assembly, macrophase separation, vitrification - and multiple structural, thermodynamic, kinetic, and process parameters. Optimizing membrane properties and rationally designing fabrication processes is a challenge which particle simulation can significantly contribute to. Using large-scale particle simulations, it is observed that 1) a small incompatibility between matrix-forming block of the copolymer and nonsolvent, 2) a glassy arrest that occurs at a smaller polymer concentration, or 3) a higher dynamical contrast between polymer and solvent results in a finer, spongy substructure, whereas the opposite parameter choice gives rise to larger macropores with an elongated shape. These observations are confirmed by comparison to experiments on polystyrene (PS)-block-poly(4-vinylpyridine) (P4VP) diblock copolymer membranes, varying the chemical nature of the coagulant or the temperature of coagulation bath.

Investigating microstructure evolution in block copolymer membranes

Block copolymer self-assembly in conjunction with nonsolvent-induced phase separation (SNIPS) has been increasingly leveraged to fabricate integral-asymmetric membranes. The large number of formulation and processing parameters associated with SNIPS, however, has prevented the reliable construction of high performance membranes. In this study, we apply dynamical self-consistent field theory to model the SNIPS process and investigate the effect of various parameters on the membrane morphology: solvent selectivity, nonsolvent selectivity, initial film composition, and glass transition composition. We examine how solvent selectivity and concentration of polymers in the film impact the structure of micelles that connect to form the membrane matrix. In particular, we find that preserving the order in the surface layer and forming a connection between the supporting and surface layer are nontrivial and sensitive to each parameter studied. The effect of each parameter is discussed, and suggestions are made for successfully fabricating viable block copolymer membranes.

Simulation of Membrane Fabrication via Solvent Evaporation and Nonsolvent-Induced Phase Separation

Block copolymer membranes offer a bottom-up approach to form isoporous membranes that are useful for ultrafiltration of functional macromolecules, colloids, and water purification. The fabrication of isoporous block copolymer membranes from a mixed film of an asymmetric block copolymer and two solvents involves two stages: First, the volatile solvent evaporates, creating a polymer skin, in which the block copolymer self-assembles into a top layer, comprised of perpendicularly oriented cylinders, via evaporation-induced self-assembly (EISA). This top layer imparts selectivity onto the membrane. Subsequently, the film is brought into contact with a nonsolvent, and the exchange between the remaining nonvolatile solvent and nonsolvent through the self-assembled top layer results in nonsolvent-induced phase separation (NIPS). Thereby, a macroporous support for the functional top layer that imparts mechanical stability onto the system without significantly affecting permeability is fabricated. We use a single, particle-based simulation technique to investigate the sequence of both processes, EISA and NIPS. The simulations identify a process window, which allows for the successful in silico fabrication of integral-asymmetric, isoporous diblock copolymer membranes, and provide direct insights into the spatiotemporal structure formation and arrest. The role of the different thermodynamic (e.g., solvent selectivity for the block copolymer components) and kinetic (e.g., plasticizing effect of the solvent) characteristics is discussed.

Coarsening dynamics of ternary polymer solutions with mobility and viscosity contrasts

Using phase-field simulations, we investigate the bulk coarsening dynamics of ternary polymer solutions undergoing a glass transition for two models of phase separation: diffusion only and with hydrodynamics. The glass transition is incorporated in both models by imposing mobility and viscosity contrasts between the polymer-rich and polymer-poor phases of the evolving microstructure. For microstructures composed of polymer-poor clusters in a polymer-rich matrix, the mobility and viscosity contrasts significantly hinder coarsening, effectively leading to structural arrest. For microstructures composed of polymer-rich clusters in a polymer-poor matrix, the mobility and viscosity contrasts do not impede domain growth; rather, they change the transient concentration of the polymer-rich phase, altering the shape of the discrete domains. This effect introduces several complexities to the coarsening process, including percolation inversion of the polymer-rich and polymer-poor phases-a phenomenon normally attributed to viscoelastic phase separation.

Non-Equilibrium Block Copolymer Self-Assembly Based Porous Membrane Formation Processes Employing Multicomponent Systems

Porous polymer-derived membranes are useful for applications ranging from filtration and separation technologies to energy storage and conversion. Combining block copolymer (BCP) self-assembly with the industrially scalable, non-equilibrium phase inversion technique (SNIPS) yields membranes comprising periodically ordered top surface structures supported by asymmetric, hierarchical substructures that together overcome performance tradeoffs typically faced by materials derived from equilibrium approaches. This review first reports on recent advances in understanding the top surface structural evolution of a model SNIPS-derived system during standard membrane formation. Subsequently, the application of SNIPS to multicomponent systems is described, enabling pore size modulation, chemical modification, and transformation to non-polymeric materials classes without compromising the structural features that define SNIPS membranes. Perspectives on future directions of both single-component and multicomponent membrane materials are provided. This points to a rich and fertile ground for the study of fundamental as well as applied problems using non-equilibrium-derived asymmetric porous materials with tunable chemistry, composition, and structure.