Temperature and initial composition dependence of pattern formation and dynamic behavior in phase separation under deep-quenched conditions

Pattern dynamics of density and velocity fields in segregation of fluid mixtures

We present comprehensive numerical results from a study of model H, which describes phase separation kinetics in binary fluid mixtures. We study the pattern dynamics of both density and velocity fields in d = 2, 3. The density length scales show three distinct regimes, in accordance with analytical arguments. The velocity length scale shows a diffusive behavior. We also study the scaling behavior of the morphologies for density and velocity fields and observe dynamical scaling in the relevant correlation functions and structure factors. Finally, we study the effect of quenched random field disorder on spinodal decomposition in model H.

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.

Phase-field simulation for the formation of porous microstructures due to phase separation in polymer solutions on substrates with different wettabilities

The porous microstructure has been widely observed in a variety of polymer solutions that have been broadly applied in many industry fields. Phase separation is one of the common mechanisms for the formation of the porous microstructure in binary polymeric mixtures. Previous studies for the formation of porous microstructures mostly focus on the separation of the bulk phase. However, there is a paucity of investigation for the phase separation of polymer mixtures contacting the solid substrate. When the polymeric liquid mixtures interact with the solid substrate, the wetting boundary condition has to be taken into account. In this work, we present a phase-field model which is coupled with the wetting boundary condition to study the phase separation in binary polymer solutions. Our consideration is based on the polymerization-induced phase separation, and thermally induced phase separation by using the Flory-Huggins model. By taking the wetting effect into account, we find that polymer droplets spontaneously occur in the microstructure, even though the bulk composition is outside the spinodal region. This phenomenon is caused by the surface composition resulting from the wetting effect that was often overlooked in literature. For the phase separation in the binary polymer mixture, we also study the impact of the temperature gradient on the microstructural evolution. The porosity, the number of droplets, and the mean radius of the droplets are rationalized with the temperature gradient.

Phase separation of mixtures after a second quench: composition heterogeneities

We investigate binary mixtures undergoing phase separation after a second (deeper) temperature quench into two- and three-phase coexistence regions. The analysis is based on a lattice theory previously developed for gas-liquid separation in generic mixtures. Our previous results, which considered an arbitrary number of species and a single quench, showed that, due to slow changes in composition, dense colloidal mixtures can phase-separate in two stages. Moreover, the denser phase contains long-lived composition heterogeneities that originate as the interfaces of shrunk domains. Here we predict several new effects that arise after a second quench, mostly associated with the extent to which crowding can slow down 'fractionation', i.e. equilibration of compositions. They include long-lived regular arrangements of secondary domains; wetting of fractionated interfaces by oppositely fractionated layers; 'surface'-directed spinodal 'waves' propagating from primary interfaces; a 'dead zone' where no phase separation occurs; and, in the case of three-phase coexistence, filamentous morphologies arising out of secondary domains.