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.

Accounting for Cooperativity in the Thermotropic Volume Phase Transition of Smart Microgels

A full quantitative description of the swelling of smart microgels is still problematic in many cases. The original approach of Flory and Huggins for the monomer–solvent interaction parameter χ cannot be applied to some microgels. The reason for this obviously is that the cross-linking enhances the cooperativity of the volume phase transitions, since all meshes of the network are mechanically coupled. This was ignored in previous approaches, arguing with distinct transition temperatures for different meshes to describe the continuous character of the transition of microgels. Here, we adjust the swelling curves of a series of smart microgels using the Flory–Rehner description, where the polymer–solvent interaction parameter χ is modeled by a Hill-like equation for a cooperative thermotropic transition. This leads to a very good description of all measured microgel swelling curves and yields the physically meaningful Hill parameter ν. A linear decrease of ν is found with increasing concentration of the cross-linker N,N′-methylenebisacrylamide in the microgel particles p(NIPAM), p(NNPAM), and p(NIPMAM). The linearity suggests that the Hill parameter ν corresponds to the number of water molecules per network chain that cooperatively leave the chain at the volume phase transition. Driven by entropy, ν water molecules of the solvate become cooperatively “free” and leave the polymer network.

Revealing compatibility mechanism of nanosilica in asphalt through molecular dynamics simulation

The compatibility between asphalt and nanosilica (nano-SiO₂) is critical to determine the performance of nano-SiO₂-modified asphalt. However, a comprehensive understanding of the compatibility behavior and mechanism of asphalt components and nano-SiO₂ in the modified asphalt is still limited. In this study, the compatibility was revealed through molecular dynamics (MD) simulation. Virgin asphalt, nano-SiO₂-modified asphalt, and oxidation aged asphalt models produced with the COMPASS force field; meanwhile, the proposed models were validated by comparisons with reference data. The compatibility of asphalt and nano-SiO₂ was analyzed by solubility and the Flory-Huggins parameters and interaction energy. Results show that the solubility parameters decreased with the increase of system temperature while increased with the asphalt's oxidation level increase. Meanwhile, the compatibility of the asphaltene, resin, and aromatic components in asphalt is better than the compatibility with saturates, which may be due to saturates being volatile; however, the compatibility of the nano-SiO₂ and saturates is much better than those with asphaltene, resin, and aromatic components. The incorporation of nano-SiO₂ alleviates the volatilization of saturates. The present results provide insights into the understanding of the compatibility behavior and mechanism of nano-SiO₂ and asphalt components.