Accelerated Sequence Design of Star Block Copolymers: An Unbiased Exploration Strategy via Fusion of Molecular Dynamics Simulations and Machine Learning.

Star block copolymers (s-BCPs) have potential applications as novel surfactants or amphiphiles for emulsification, compatibilization, chemical transformations, and separations. s-BCPs have chain architectures where three or more linear diblock copolymer arms comprised of two chemically distinct linear polymers, e.g., solvophobic and solvophilic chains, are covalently joined at one point. The chemical composition of each of the subunit polymer chains comprising the arms, their molecular weights, and the number of arms can be varied to tailor the surface and interfacial activity of these architecturally unique molecules. This makes identification of the optimal s-BCP design nontrivial as the total number of plausible s-BCP architectures is experimentally or computationally intractable. In this work, we use molecular dynamics (MD) simulations coupled with a reinforcement learning-based Monte Carlo tree search (MCTS) to identify s-BCP designs that minimize the interfacial tension between polar and nonpolar solvents. We first validate the MCTS approach for the design of small- and medium-sized s-BCPs and then use it to efficiently identify sequences of copolymer blocks for large-sized s-BCPs. The structural origins of interfacial tension in these systems are also identified by using the configurations obtained from MD simulations. Chemical insights into the arrangement of copolymer blocks that promote lower interfacial tension were mined using machine learning (ML) techniques. Overall, this work provides an efficient approach to solve design problems via fusion of simulations and ML and provides important groundwork for future experimental investigation of s-BCPs for various applications.

Predicting the pair correlation functions of silicate and borosilicate glasses using machine learning.

Glasses offer a broad range of tunable thermophysical properties that are linked to their compositions. However, it is challenging to establish a universal composition-property relationship of glasses due to their enormous compositions and chemical space. Here, we address this problem and develop a metamodel of the composition-atomistic structure relationship of a class of glassy materials via a machine learning (ML) approach. Within this ML framework, an unsupervised deep learning technique, viz., a convolutional neural network (CNN) autoencoder, and a regression algorithm, viz. random forest (RF), are integrated into a fully automated pipeline to predict the spatial distribution of atoms in a glass. The RF regression model predicts the pair correlation function of a glass in a latent space. Subsequently, the decoder of the CNN converts the latent space representation to the actual pair correlation function of the given glass. The atomistic structures of silicate (SiO2) and sodium borosilicate (NBS) based glasses with varying compositions and dopants are collected from molecular dynamics (MD) simulations to establish and validate this ML pipeline. The model is found to predict the atom pair correlation functions for many unknown glasses very accurately. This method is very generic and can accelerate the design, discovery, and fundamental understanding of the composition-atomistic structure relationship of glasses and other materials.

Developing efficient deep learning model for predicting copolymer properties.

Deep learning models are gaining popularity and potency in predicting polymer properties. These models can be built using pre-existing data and are useful for the rapid prediction of polymer properties. However, the performance of a deep learning model is intricately connected to its topology and the volume of training data. There is no facile protocol available to select a deep learning architecture, and there is a lack of a large volume of homogeneous sequence-property data of polymers. These two factors are the primary bottleneck for the efficient development of deep learning models for polymers. Here we assess the severity of these factors and propose strategies to address them. We show that a linear layer-by-layer expansion of a neural network can help in identifying the best neural network topology for a given problem. Moreover, we map the discrete sequence space of a polymer to a continuous one-dimensional latent space using a feature extraction technique to identify minimal data points for training a deep learning model. We implement these approaches for two representative cases of building sequence-property surrogate models, viz., the single-molecule radius of gyration of a copolymer and copolymer compatibilizer. This work demonstrates efficient methods for building deep learning models with minimal data and hyperparameters for predicting sequence-defined properties of polymers.

Correction: Accelerating copolymer inverse design using monte carlo tree search.

Correction for 'Accelerating copolymer inverse design using monte carlo tree search' by Tarak K. Patra et al., Nanoscale, 2020, 12, 23653-23662, https://doi.org/10.1039/D0NR06091G.

nanoNET: machine learning platform for predicting nanoparticles distribution in a polymer matrix.

Polymer nanocomposites (PNCs) offer a broad range of thermophysical properties that are linked to their compositions. However, it is challenging to establish a universal composition-property relationship in PNCs due to their wide-ranging composition and chemical space. Here, we address this problem and develop a new method to model the composition-microstructure relation of a PNC through an intelligent machine-learning pipeline named nanoNET. The nanoNET is a nanoparticles (NPs) distribution predictor, built upon computer vision and image recognition concepts. It integrates unsupervised deep learning and regression in a fully automated pipeline. We conduct coarse-grained molecular dynamics simulations of PNCs and utilize the data to establish and validate the nanoNET. Within this framework, a random forest regression model predicts the distribution of NPs in a PNC in a latent space. Subsequently, a convolutional neural network-based decoder converts the latent space representation to the actual radial distribution function (RDF) of NPs in the given PNC. The nanoNET predicts NPs distribution in many unknown PNCs very accurately. This method is very generic and can accelerate the design, discovery, and fundamental understanding of composition-microstructure relationships in PNCs and other molecular systems.

Dynamic crosslinking compatibilizes immiscible mixed plastics.

The global plastics problem is a trifecta, greatly affecting environment, energy and climate1-4. Many innovative closed/open-loop plastics recycling or upcycling strategies have been proposed or developed5-16, addressing various aspects of the issues underpinning the achievement of a circular economy17-19. In this context, reusing mixed-plastics waste presents a particular challenge with no current effective closed-loop solution20. This is because such mixed plastics, especially polar/apolar polymer mixtures, are typically incompatible and phase separate, leading to materials with substantially inferior properties. To address this key barrier, here we introduce a new compatibilization strategy that installs dynamic crosslinkers into several classes of binary, ternary and postconsumer immiscible polymer mixtures in situ. Our combined experimental and modelling studies show that specifically designed classes of dynamic crosslinker can reactivate mixed-plastics chains, represented here by apolar polyolefins and polar polyesters, by compatibilizing them via dynamic formation of graft multiblock copolymers. The resulting in-situ-generated dynamic thermosets exhibit intrinsic reprocessability and enhanced tensile strength and creep resistance relative to virgin plastics. This approach avoids the need for de/reconstruction and thus potentially provides an alternative, facile route towards the recovery of the endowed energy and materials value of individual plastics.

Polymer sequence design via molecular simulation-based active learning.

Molecular-scale interactions and chemical structures offer an enormous opportunity to tune material properties. However, designing materials from their molecular scale is a grand challenge owing to the practical limitations in exploring astronomically large design spaces using traditional experimental or computational methods. Advancements in data science and machine learning have produced a host of tools and techniques that can address this problem and facilitate the efficient exploration of large search spaces. In this work, a blended approach integrating physics-based methods, machine learning techniques and uncertainty quantification is implemented to effectively screen a macromolecular sequence space and design target structures. Here, we survey and assess the efficacy of data-driven methods within the framework of active learning for a challenging design problem, viz., sequence optimization of a copolymer. We report the impact of surrogate models, kernels, and initial conditions on the convergence of the active learning method for the sequence design problem. This work establishes optimal strategies and hyperparameters for efficient inverse design of polymer sequences via active learning.

Deep learning potential of mean force between polymer grafted nanoparticles.

Grafting polymer chains on the surfaces of nanoparticles is a well-known route to control their self-assembly and distribution in a polymer matrix. A wide variety of self-assembled structures are achieved by changing the grafting patterns on the surface of an individual nanoparticle. However, an accurate estimation of the effective potential of mean force between a pair of grafted nanoparticles that determines their assembly and distribution in a polymer matrix is an outstanding challenge in nanoscience. We address this problem via deep learning. As a proof of concept, here we report a deep learning framework that learns the interaction between a pair of single-chain grafted spherical nanoparticles from their molecular dynamics trajectory. Subsequently, we carry out the deep learning potential of mean force-based molecular simulation that predicts the self-assembly of a large number of single-chain grafted nanoparticles into various anisotropic superstructures, including percolating networks and bilayers depending on the nanoparticle concentration in three-dimensions. The deep learning potential of mean force-predicted self-assembled superstructures are consistent with the actual superstructures of single-chain polymer grafted spherical nanoparticles. This deep learning framework is very generic and extensible to more complex systems including multiple-chain grafted nanoparticles. We expect that this deep learning approach will accelerate the characterization and prediction of the self-assembly and phase behaviour of polymer-grafted and unfunctionalized nanoparticles in free space or a polymer matrix.

Data-Driven Methods for Accelerating Polymer Design.

Optimal design of polymers is a challenging task due to their enormous chemical and configurational space. Recent advances in computations, machine learning, and increasing trends in data and software availability can potentially address this problem and accelerate the molecular-scale design of polymers. Here, the central problem of polymer design is reviewed, and the general ideas of data-driven methods and their working principles in the context of polymer design are discussed. This Review provides a historical perspective and a summary of current trends and outlines future scopes of data-driven methods for polymer research. A few representative case studies on the use of such data-driven methods for discovering new polymers with exceptional properties are presented. Moreover, attempts are made to highlight how data-driven strategies aid in establishing new correlations and advancing the fundamental understanding of polymers. This Review posits that the combination of machine learning, rapid computational characterization of polymers, and availability of large open-sourced homogeneous data will transform polymer research and development over the coming decades. It is hoped that this Review will serve as a useful reference to researchers who wish to develop and deploy data-driven methods for polymer research and education.

Angstrom-Scale Transparent Overcoats: Interfacial Nitrogen-Driven Atomic Intermingling Promotes Lubricity and Surface Protection of Ultrathin Carbon.

Lubricity, a phenomenon which enables the ease of motion of objects, and wear resistance, which minimizes material damage or degradation, are important fundamental characteristics for sustainable technology developments. Ultrathin coatings that promote lubricity and wear resistance are of huge importance for a number of applications, including magnetic storage and micro-/nanoelectromechanical systems. Conventional ultrathin coatings have, however, reached their limit. Graphene-based materials that have shown promise to reduce friction and wear have many intrinsic limitations such as high temperature and substrate-specific growth. To address these concerns, a great deal of research is currently ongoing to optimize graphene-based materials. Here we discover that angstrom-thick carbon (8 Å) significantly reduces interfacial friction and wear. This lubricant shows ultrahigh optical transparency and can be directly deposited on a wide range of surfaces at room temperature. Experiments combined with molecular dynamics simulations reveal that the lubricating efficacy of 8 Å carbon is further improved via interfacial nitrogen.

Accelerating copolymer inverse design using monte carlo tree search.

There exists a broad class of sequencing problems in soft materials such as proteins and polymers that can be formulated as a heuristic search that involves decision making akin to a computer game. AI gaming algorithms such as Monte Carlo tree search (MCTS) gained prominence after their exemplary performance in the computer Go game and are decision trees aimed at identifying the path (moves) that should be taken by the policy to reach the final winning or optimal solution. Major challenges in inverse sequencing problems are that the materials search space is extremely vast and property evaluation for each sequence is computationally demanding. Reaching an optimal solution by minimizing the total number of evaluations in a given design cycle is therefore highly desirable. We demonstrate that one can adopt this approach for solving the sequencing problem by developing and growing a decision tree, where each node in the tree is a candidate sequence whose fitness is directly evaluated by molecular simulations. We interface MCTS with MD simulations and use a representative example of designing a copolymer compatibilizer, where the goal is to identify sequence specific copolymers that lead to zero interfacial energy between two immiscible homopolymers. We apply the MCTS algorithm to polymer chain lengths varying from 10-mer to 30-mer, wherein the overall search space varies from 210 (1024) to 230 (∼1 billion). In each case, we identify a target sequence that leads to zero interfacial energy within a few hundred evaluations demonstrating the scalability and efficiency of MCTS in exploring practical materials design problems with exceedingly vast chemical/material search space. Our MCTS-MD framework can be easily extended to several other polymer and protein inverse design problems, in particular, for cases where sequence-property data is either unavailable and/or is resource intensive.

Ligand dynamics control structure, elasticity, and high-pressure behavior of nanoparticle superlattices.

Precise engineering of nanoparticle superlattices (NPSLs) for energy applications requires a molecular-level understanding of the physical factors governing their morphology, periodicity, mechanics, and response to external stimuli. Such knowledge, particularly the impact of ligand dynamics on physical behavior of NPSLs, is still in its infancy. Here, we combine coarse-grained molecular dynamics simulations, and small angle X-ray scattering experiments in a diamond anvil cell to demonstrate that coverage density of capping ligands (i.e., number of ligands per unit area of a nanoparticle's surface), strongly influences the structure, elasticity, and high-pressure behavior of NPSLs using face-centered cubic PbS-NPSLs as a representative example. We demonstrate that ligand coverage density dictates (a) the extent of diffusion of ligands over NP surfaces, (b) spatial distribution of the ligands in the interstitial spaces between neighboring NPs, and (c) the fraction of ligands that interdigitate across different nanoparticles. We find that below a critical coverage density (1.8 nm-2 for 7 nm PbS NPs capped with oleic acid), NPSLs collapse to form disordered aggregates via sintering, even under ambient conditions. Above the threshold ligand coverage density, NPSLs surprisingly preserve their crystalline order even under high applied pressures (∼40-55 GPa), and show a completely reversible pressure behavior. This opens the possibility of reversibly manipulating lattice spacing of NPSLs, and in turn, finely tuning their collective electronic, optical, thermo-mechanical, and magnetic properties.

Universal localization transition accompanying glass formation: insights from efficient molecular dynamics simulations of diverse supercooled liquids.

The origin of the precipitous dynamic arrest known as the glass transition is a grand open question of soft condensed matter physics. It has long been suspected that this transition is driven by an onset of particle localization and associated emergence of a glassy modulus. However, progress towards an accepted understanding of glass formation has been impeded by an inability to obtain data sufficient in chemical diversity, relaxation timescales, and spatial and temporal resolution to validate or falsify proposed theories for its physics. Here we first describe a strategy enabling facile high-throughput simulation of glass-forming liquids to nearly unprecedented relaxation times. We then perform simulations of 51 glass-forming liquids, spanning polymers, small organic molecules, inorganics, and metallic glass-formers, with longest relaxation times exceeding one microsecond. Results identify a universal particle-localization transition accompanying glass formation across all classes of glass-forming liquid. The onset temperature of non-Arrhenius dynamics is found to serve as a normalizing condition leading to a master collapse of localization data. This transition exhibits a non-universal relationship with dynamic arrest, suggesting that the nonuniversality of supercooled liquid dynamics enters via the dependence of relaxation times on local cage scale. These results suggest that a universal particle-localization transition may underpin the glass transition, and they emphasize the potential for recent theoretical developments connecting relaxation to localization and emergent elasticity to finally explain the origin of this phenomenon. More broadly, the capacity for high-throughput prediction of glass formation behavior may open the door to computational inverse design of glass-forming materials.

Defect Dynamics in 2-D MoS2 Probed by Using Machine Learning, Atomistic Simulations, and High-Resolution Microscopy.

Structural defects govern various physical, chemical, and optoelectronic properties of two-dimensional transition-metal dichalcogenides (TMDs). A fundamental understanding of the spatial distribution and dynamics of defects in these low-dimensional systems is critical for advances in nanotechnology. However, such understanding has remained elusive primarily due to the inaccessibility of (a) necessary time scales via standard atomistic simulations and (b) required spatiotemporal resolution in experiments. Here, we take advantage of supervised machine learning, in situ high-resolution transmission electron microscopy (HRTEM) and molecular dynamics (MD) simulations to overcome these limitations. We combine genetic algorithms (GA) with MD to investigate the extended structure of point defects, their dynamical evolution, and their role in inducing the phase transition between the semiconducting (2H) and metallic (1T) phase in monolayer MoS2. GA-based structural optimization is used to identify the long-range structure of randomly distributed point defects (sulfur vacancies) for various defect densities. Regardless of the density, we find that organization of sulfur vacancies into extended lines is the most energetically favorable. HRTEM validates these findings and suggests a phase transformation from the 2H-to-1T phase that is localized near these extended defects when exposed to high electron beam doses. MD simulations elucidate the molecular mechanism driving the onset of the 2H to 1T transformation and indicate that finite amounts of 1T phase can be retained by increasing the defect concentration and temperature. This work significantly advances the current understanding of defect structure/evolution and structural transitions in 2D TMDs, which is crucial for designing nanoscale devices with desired functionality.

Neural-Network-Biased Genetic Algorithms for Materials Design: Evolutionary Algorithms That Learn.

Machine learning has the potential to dramatically accelerate high-throughput approaches to materials design, as demonstrated by successes in biomolecular design and hard materials design. However, in the search for new soft materials exhibiting properties and performance beyond those previously achieved, machine learning approaches are frequently limited by two shortcomings. First, because they are intrinsically interpolative, they are better suited to the optimization of properties within the known range of accessible behavior than to the discovery of new materials with extremal behavior. Second, they require large pre-existing data sets, which are frequently unavailable and prohibitively expensive to produce. Here we describe a new strategy, the neural-network-biased genetic algorithm (NBGA), for combining genetic algorithms, machine learning, and high-throughput computation or experiment to discover materials with extremal properties in the absence of pre-existing data. Within this strategy, predictions from a progressively constructed artificial neural network are employed to bias the evolution of a genetic algorithm, with fitness evaluations performed via direct simulation or experiment. In effect, this strategy gives the evolutionary algorithm the ability to "learn" and draw inferences from its experience to accelerate the evolutionary process. We test this algorithm against several standard optimization problems and polymer design problems and demonstrate that it matches and typically exceeds the efficiency and reproducibility of standard approaches including a direct-evaluation genetic algorithm and a neural-network-evaluated genetic algorithm. The success of this algorithm in a range of test problems indicates that the NBGA provides a robust strategy for employing informatics-accelerated high-throughput methods to accelerate materials design in the absence of pre-existing data.

Localization and stretching of polymer chains at the junction of two surfaces.

We present a molecular dynamics study on the stretching of a linear polymer chain that is adsorbed at the junction of two intersecting flat surfaces of varying alignments. We observe a transition from a two-dimensional to one-dimensional (1D) structure of the adsorbed polymer when the alignment, i.e., the angle between the two surfaces that form a groove, θ, is below 135°. We show that the radius of gyration of the polymer chain Rg scales as Rg ∼ N(3/4) with the degree of polymerization N for θ = 180° (planer substrate), and the scaling changes to Rg ∼ N(1.0) for θ < 135° in good solvents. At the crossover point, θ = 135°, the exponent becomes 1.15. The 1D stretching of the polymer chain is found to be 84% of its contour length for θ ⩽ 90°. The center of mass diffusion coefficient D decreases sharply with θ. However, the diffusion coefficient scales with N as D ∼ N(-1), and is independent of θ. The relaxation time τ, for the diffusive motion, scales as τ ∼ N(2.5) for θ = 180° (planar substrate), which changes to τ ∼ N(3.0) for θ ⩽ 90°. At the crossover point, the exponent is 3.4, which is slightly higher than the 1D value of 3.0. Further, a signature of reptation-like dynamics of the polymer chain is observed at the junction for θ ⩽ 90° due to its strong 1D localization and stretching.

Polymer directed aggregation and dispersion of anisotropic nanoparticles.

The aggregation and dispersion of two anisotropic nanoparticles (NPs), cubes and tetrahedrons, in a polymer matrix are studied in this work using coarse-grained molecular dynamics simulations. We present the phase diagrams of NP-polymer composites, depicting microscopically phase-separated, dispersed, and bridged cubes and tetrahedrons in a polymer matrix, which depend on the interaction between the NPs and polymer (εnp), along with the NPs' volume fraction (ϕ). The microscopic phase separation occurs at very low εnp, where NPs self-organize into multidimensional structures, depending on ϕ. In particular, for tetrahedrons, a cross-over from an ordered spherical aggregate to a disordered sheet-like aggregate is observed with increasing ϕ. In the case of cubes, a transition from cubic array → square column → square array (sheet) is identified with increasing ϕ. The clusters of NPs are characterized by their asphericity and principal radii of gyration. The free energy profile for a structured assembly is estimated, which clearly shows that the successful assembly of NPs is energetically favorable at a lower temperature. However, there exists an energy barrier for the successful assembly of all the NPs in the system. At intermediate εnp, a transition from a clustered state to a state comprising dispersed cubes and tetrahedrons in a polymer matrix is observed. At higher εnp, a further transition takes place, where gas-like dispersed NPs form a liquid-like aggregate via polymer layers. Therefore, the findings in this work illustrate that the effective interaction between anisotropic NPs in a polymer matrix is very diverse, which can generate multidimensional structured assemblies, with the disordered clustering, dispersion, and bridging-induced aggregation of NPs.

Coarse-grain molecular dynamics simulations of nanoparticle-polymer melt: dispersion vs. agglomeration.

In this work, we study the influence of polymer chain length (m), based on Lennard-Jones potential, and nanoparticle (NP)-polymer interaction strength (ɛnp) on aggregation and dispersion of soft repulsive spherically structured NPs in polymer melt using coarse-grain molecular dynamics simulations. A phase diagram is proposed where transitions between different structures in the NP-polymer system are shown to depend on m and ɛnp. At a very weak interaction strength ɛnp = 0.1, a transition from dispersed state to collapsed state of NPs is found with increasing m, due to the polymer's excluded volume effect. NPs are well dispersed at intermediate interaction strengths (0.5 ⩽ ɛnp ⩽ 2.0), independent of m. A transition from dispersion to agglomeration of NPs, at a moderately high NP-polymer interaction strength ɛnp = 5.0, for m = 1-30, is identified by a significant decrease in the second virial coefficient, excess entropy, and potential energy, and a sharp increase in the Kirkwood-Buff integral. We also find that NPs undergo the following transitions with increasing m at ɛnp ⩾ 5.0: string-like → branch-like → sphere-like → dispersed state.

Vapor-liquid phase coexistence and transport properties of two-dimensional oligomers.

Grand-canonical transition-matrix Monte Carlo and histogram reweighting techniques are used herein to study the vapor-liquid coexistence properties of two-dimensional (2D) flexible oligomers with varying chain lengths (m = 1-8). The phase diagrams of the various 2D oligomers follow the correspondence state (CS) principle, akin to the behavior observed for bulk oligomers. The 2D critical density is not influenced by the oligomer chain length, which contrasts with the observation for the bulk oligomers. Line tension, calculated using Binder's formalism, in the reduced plot is found to be independent of chain length in contrast to the 3D behavior. The dynamical properties of 2D fluids are evaluated using molecular dynamics simulations, and the velocity and pressure autocorrelation functions are investigated using Green-Kubo (GK) relations to yield the diffusion and viscosity. The viscosity determined from 2D non-equilibrium molecular dynamics simulation is compared with the viscosity estimated from the GK relations. The GK relations prove to be reliable and efficient for the calculation of 2D transport properties. Normal diffusive regions are identified in dense oligomeric fluid systems. The influence of molecular size on the diffusivity and viscosity is found to be diminished at specific CS points for the 2D oligomers considered herein. In contrast, the viscosity and diffusion of the 3D bulk fluid, at a reduced temperature and density, are strongly dependent on the molecular size at the same CS points. Furthermore, the viscosity increases and the diffusion decreases multifold in the 2D system relative to those in the 3D system, at the CS points.