Phase-Field Simulation of the Effect of Coagulation Bath Temperature on the Structure and Properties of Polyvinylidene Fluoride Microporous Membranes Prepared by a Nonsolvent-Induced Phase Separation

Ternary Phase-Field Simulation of Poly(vinylidene fluoride) Microporous Membrane Structures Prepared by Nonsolvent-Induced Phase Separation with Different Additives and Solvent Treatments

In this study, an existing ternary membrane system based on nonsolvent-induced phase separation (NIPS) with a phase-field model was optimized. To study and analyze the effects of different additives on the formation of the skin layer and the effects of the three solvents on membrane characterization under the same conditions, two-dimensional simulations of the relevant parameters of a poly(vinylidene fluoride) (PVDF) membrane system were performed. The specific application of quaternary substances in ternary membrane systems was elaborated by determining the cohesive energy density between the additives and solvents, followed by the interaction parameters χ under the joint effect of the two. The results showed that the PVDF microporous membrane formed a dense surface layer at the mass transfer exchange interface, and with an increase in the poly(ethylene glycol) (PEG) concentration, the phase separation of the skin layer was predominantly transformed from liquid-solid partitioning to liquid-liquid partitioning; the number of membrane pores increased with increasing poly(vinylpyrrolidone) (PVP) concentration. The N,N-dimethylacetamide (DMAc) solvent system had the most stable thermodynamic properties; the dimethyl sulfoxide (DMSO) solvent system had mostly large pores running through the membrane and exhibited a porous structure. Related experiments also validated the model. Therefore, this model can be applied to other PVDF ternary membrane systems to better understand the structural development of microporous PVDF membranes under different conditions.

Connecting Structural Characteristics and Material Properties in Phase-Separating Polymer Solutions: Phase-Field Modeling and Physics-Informed Neural Networks

The formed morphology during phase separation is crucial for determining the properties of the resulting product, e.g., a functional membrane. However, an accurate morphology prediction is challenging due to the inherent complexity of molecular interactions. In this study, the phase separation of a two-dimensional model polymer solution is investigated. The spinodal decomposition during the formation of polymer-rich domains is described by the Cahn-Hilliard equation incorporating the Flory-Huggins free energy description between the polymer and solvent. We circumvent the heavy burden of precise morphology prediction through two aspects. First, we systematically analyze the degree of impact of the parameters (initial polymer volume fraction, polymer mobility, degree of polymerization, surface tension parameter, and Flory-Huggins interaction parameter) in a phase-separating system on morphological evolution characterized by geometrical fingerprints to determine the most influential factor. The sensitivity analysis provides an estimate for the error tolerance of each parameter in determining the transition time, the spinodal decomposition length, and the domain growth rate. Secondly, we devise a set of physics-informed neural networks (PINN) comprising two coupled feedforward neural networks to represent the phase-field equations and inversely discover the value of the embedded parameter for a given morphological evolution. Among the five parameters considered, the polymer-solvent affinity is key in determining the phase transition time and the growth law of the polymer-rich domains. We demonstrate that the unknown parameter can be accurately determined by renormalizing the PINN-predicted parameter by the change of characteristic domain size in time. Our results suggest that certain degrees of error are tolerable and do not significantly affect the morphology properties during the domain growth. Moreover, reliable inverse prediction of the unknown parameter can be pursued by merely two separate snapshots during morphological evolution. The latter largely reduces the computational load in the standard data-driven predictive methods, and the approach may prove beneficial to the inverse design for specific needs.