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Phase separation in multicomponent mixtures is of significant interest in both fundamental research and technology. Although the thermodynamic principles governing phase equilibria are straightforward, practical determination of equilibrium phases and constituent compositions for multicomponent systems is often laborious and computationally intensive. Here, we present a machine-learning workflow that simplifies and accelerates phase-coexistence calculations. We specifically analyze capabilities of neural networks to predict the number, composition, and relative abundance of equilibrium phases of systems described by Flory-Huggins theory. We find that incorporating physics-informed material constraints into the neural network architecture enhances the prediction of equilibrium compositions compared to standard neural networks with minor errors along the boundaries of the stable region. However, introducing additional physics-informed losses does not lead to significant further improvement. These errors can be virtually eliminated by using machine-learning predictions as a warm-start for a subsequent optimization routine. This work provides a promising pathway to efficiently characterize multicomponent phase coexistence. 

Abstract 2D hybrid organic–inorganic perovskites are potentially promising materials as passivation layers that can enhance the efficiency and stability of perovskite photovoltaics. The ability to suppress ion transport is proposed as a stabilization mechanism, yet an effective characterization of relevant modes of halide diffusion in 2D perovskites is nascent. In light of this knowledge gap, molecular dynamics simulations with enhanced sampling and experimental validation to systematically characterize how ligand chemistry in seven (R‐NH₃)₂PbI₄systems impacts halide diffusion, particularly in the out‐of‐plane direction is combined. It is found that increasing stiffness and length of ligands generally inhibits ion transport, while increasing ligand polarization generally enhances it. Structural and energetic analyses of the migration pathways provide quantitative explanations for these trends, which reflect aspects of the disorder of the organic layer. Overall, this mechanistic analysis greatly enhances the current understanding of halide migration in 2D hybrid organic–inorganic perovskites and yields insights that can inform the design of future passivation materials. 

We introduce a lattice framework that incorporates elements of Flory–Huggins solution theory and the q-state Potts model to study the phase behavior of polymer solutions and single-chain conformational characteristics. Without empirically introducing temperature-dependent interaction parameters, standard Flory–Huggins theory describes systems that are either homogeneous across temperatures or exhibit upper critical solution temperatures. The proposed Flory–Huggins–Potts framework extends these capabilities by predicting lower critical solution temperatures, miscibility loops, and hourglass-shaped spinodal curves. We particularly show that including orientation-dependent interactions, specifically between monomer segments and solvent particles, is alone sufficient to observe such phase behavior. Signatures of emergent phase behavior are found in single-chain Monte Carlo simulations, which display heating- and cooling-induced coil–globule transitions linked to energy fluctuations. The framework also capably describes a range of experimental systems. Importantly, and by contrast to many prior theoretical approaches, the framework does not employ any temperature- or composition-dependent parameters. This work provides new insights regarding the microscopic physics that underpin complex thermoresponsive behavior in polymers. 

Cannabidiol (CBD) is viewed as a promising therapeutic agent against a variety of health ailments; however, its efficacy is limited by poor aqueous solubility. Amorphous solid dispersions (ASDs) can enhance the solubility of therapeutics by distributing them throughout a polymer matrix. In consideration of ASD formulations with CBD, we investigate the interactions of CBD with various polymers: poly(vinylpyrrolidone) (PVP), poly(vinylpyrrolidone)/vinyl acetate (PVP/VA) copolymer, hydroxypropyl methylcellulose phthalate (HPMCP), hydroxypropyl methylcellulose acetate succinate (HPMCAS), and poly(methyl methacrylate) (PMMA). Both the experiment and molecular dynamics simulation reveal diverse mixing behavior among the set of polymers. Detailed structural and nanoscale interaction analyses suggest that positive deviations from ideal mixing behavior arise from the formation of stable polymer–CBD hydrogen bonds, whereas negative deviations are associated with disruptions to the polymer–polymer hydrogen bond network. Polymer–water interaction analyses indicate the significance of polymer hydrophobicity that can lead to poor dissolution of CBD. These results have implications for drug dissolution rates based on how CBD and water interact with each polymer. Furthermore, these insights may be used to guide ASD formulations for CBD or other small-molecule therapeutic agents. 

This dataset holds 1036 ternary phase diagrams and how points on the diagram phase separate if they do. The data is provided as a serialized object using the `pickle' Python module. The data was compiled using Python version 3.8.  ReferencesThe specific applications and analyses of the data are described in 1.  Dhamankar, S.; Jiang, S.; Webb, M.A. "Accelerating Multicomponent Phase-Coexistence Calculations with Physics-informed Neural Networks" UsageTo access the data in the .pickle file, users can execute the following: # LOAD SIMULATION DATADATA_DIR = "your/custom/dir/" filename = os.path.join(DATA_DIR, f"data_clean.pickle")with open(filename, "rb") as handle:    (x, y_c, y_r, phase_idx, num_phase, max_phase) = pickle.load(handle) x: Input x = (χ_AB, χ_BC, χ_AC, v_A, v_B, v_C, φ_A, φ_B) ∈ ℝ^8. y_c: Output one-hot encoded classification vector y_c ∈ ℝ^3. y_r: Output equilibrium composition and abundance vector y_r = (φ_A^α, φ_B^α, φ_A^β, φ_B^β, φ_A^γ, φ_B^γ, w^α, w^β, w^γ) ∈ ℝ^9. phase_idx: A single integer indicating which unique phase system it belongs to. num_phase: A single integer indicates the number of equilibrium phases the input splits into. max_phase: A single integer indicates the maximum number of equilibrium phases the system splits into. Help, Suggestions, Corrections?If you need help, have suggestions, identify issues, or have corrections, please send your comments to Shengli Jiang at sj0161@princeton.edu GitHubAdditional data and code relevant for this study is additionally accessible at hthttps://github.com/webbtheosim/ml-ternary-phase 

The emergence of data-intensive scientific discovery and machine learning has dramatically changed the way in which scientists and engineers approach materials design. Nevertheless, for designing macromolecules or polymers, one limitation is the lack of appropriate methods or standards for converting systems into chemically informed, machine-readable representations. This featurization process is critical to building predictive models that can guide polymer discovery. Although standard molecular featurization techniques have been deployed on homopolymers, such approaches capture neither the multiscale nature nor topological complexity of copolymers, and they have limited application to systems that cannot be characterized by a single repeat unit. Herein, we present, evaluate, and analyze a series of featurization strategies suitable for copolymer systems. These strategies are systematically examined in diverse prediction tasks sourced from four distinct datasets that enable understanding of how featurization can impact copolymer property prediction. Based on this comparative analysis, we suggest directly encoding polymer size in polymer representations when possible, adopting topological descriptors or convolutional neural networks when the precise polymer sequence is known, and using chemically informed unit representations when developing extrapolative models. These results provide guidance and future directions regarding polymer featurization for copolymer design by machine learning.