Genetic Algorithm for Discovery of Globally Stable Phases in Block Copolymers

Automated Search Strategy for Novel Ordered Structures of Block Copolymers

Block copolymers with different architectures can possibly generate innumerable stable or metastable structures and thus provide an irreplaceable platform for theoretically exploring novel structures. Self-consistent field theory (SCFT) is a powerful tool to predict the ordered structures of block copolymers; however, it is sensitively dependent on its initial condition. Here we propose to use multiple symmetry-adapted basis functions to generate the initial conditions of SCFT and then apply Bayesian optimization to search for ordered structures by navigating the coefficient space of these basis functions. Without any prior knowledge, our scheme can automatically recover hundreds of ordered structures for two simple block copolymers, including most of the common structures and complex Frank-Kasper structures, together with many novel structures. By applying the automated scheme to various block copolymers, a huge number of novel structures can be obtained to expand the structural library, which may create new opportunities for the scientific community.

Screening potential dye sensitizers for water splitting photocatalysts using a genetic algorithm

Addressing the global fossil energy crisis necessitates the efficient utilization of sustainable energy sources. Hydrogen, a green fuel, can be generated using sunlight, water, and a photocatalyst. Employing sensitizers holds promise for enhancing photocatalyst performance, enabling high rates of hydrogen evolution through increased visible light absorption. However, sifting through millions of diverse molecules to identify suitable dyes for specific photocatalysts poses a significant challenge. In this study, we integrate genetic algorithm and geometry-frequency-noncovalent extended tight binding methods to efficiently screen 2.6 million potential sensitizers with a D-π-A-π-AA structure within a short timeframe. Subsequently, these optimized sensitizers are rigorously reassessed by using DFT/TDDFT methods, elucidating why they may serve as superior dyes compared to the reference dye WS5F, particularly in terms of light absorption, driving force, binding energy, etc. Additionally, our methodology uncovers molecular motifs of particular interest, including the furan π-bridge and the double cyano anchoring acceptor, which are prevalent in the most promising set of molecules. The developed genetic algorithm workflow and dye design principles can be extended to various compelling projects, such as dye-sensitized solar cells, organic photovoltaics, photo-induced redox reactions, pharmaceuticals, and beyond.

Gaming self-consistent field theory: Generative block polymer phase discovery

Block polymers are an attractive platform for uncovering the factors that give rise to self-assembly in soft matter owing to their relatively simple thermodynamic description, as captured in self-consistent field theory (SCFT). SCFT historically has found great success explaining experimental data, allowing one to construct phase diagrams from a set of candidate phases, and there is now strong interest in deploying SCFT as a screening tool to guide experimental design. However, using SCFT for phase discovery leads to a conundrum: How does one discover a new morphology if the set of candidate phases needs to be specified in advance? This long-standing challenge was surmounted by training a deep convolutional generative adversarial network (GAN) with trajectories from converged SCFT solutions, and then deploying the GAN to generate input fields for subsequent SCFT calculations. The power of this approach is demonstrated for network phase formation in neat diblock copolymer melts via SCFT. A training set of only five networks produced 349 candidate phases spanning known and previously unexplored morphologies, including a chiral network. This computational pipeline, constructed here entirely from open-source codes, should find widespread application in block polymer phase discovery and other forms of soft matter.

Template Design for Complex Block Copolymer Patterns Using a Machine Learning Method

This study represents the first attempt to address the inverse design problem of the guiding template for directed self-assembly (DSA) patterns using solely machine learning methods. By formulating the problem as a multi-label classification task, the study shows that it is possible to predict templates without requiring any forward simulations. A series of neural network (NN) models, ranging from the basic two-layer convolutional neural network (CNN) to the large NN models (32-layer CNN with 8 residual blocks), have been trained using simulated pattern samples generated by thousands of self-consistent field theory (SCFT) calculations; a number of augmentation techniques, especially suitable for predicting morphologies, have been also proposed to enhance the performance of the NN model. The exact match accuracy of the model in predicting the template of simulated patterns was significantly improved from 59.8% for the baseline model to 97.1% for the best model of this study. The best model also demonstrates an excellent generalization ability in predicting the template for human-designed DSA patterns, while the simplest baseline model is ineffective in this task.

Inverse Design of Complex Block Copolymers for Exotic Self-Assembled Structures Based on Bayesian Optimization

Variable chain topologies of multiblock copolymers provide great opportunities for the formation of numerous self-assembled nanostructures with promising potential applications. However, the consequent large parameter space poses new challenges for searching the stable parameter region of desired novel structures. In this Letter, by combining Bayesian optimization (BO), fast Fourier transform-assisted 3D convolutional neural network (FFT-3DCNN), and self-consistent field theory (SCFT), we develop a data-driven and fully automated inverse design framework to search for the desired novel structures self-assembled by ABC-type multiblock copolymers. Stable phase regions of three exotic target structures are efficiently identified in high-dimensional parameter space. Our work advances the new research paradigm of inverse design in the field of block copolymers.

Active control of equilibrium, near-equilibrium, and far-from-equilibrium colloidal systems

The development of top-down active control over bottom-up colloidal assembly processes has the potential to produce materials, surfaces, and objects with applications in a wide range of fields spanning from computing to materials science to biomedical engineering. In this review, we summarize recent progress in the field using a taxonomy based on how active control is used to guide assembly. We find there are three distinct scenarios: (1) navigating kinetic pathways to reach a desirable equilibrium state, (2) the creation of a desirable metastable, kinetically trapped, or kinetically arrested state, and (3) the creation of a desirable far-from-equilibrium state through continuous energy input. We review seminal works within this framework, provide a summary of important application areas, and present a brief introduction to the fundamental concepts of control theory that are necessary for the soft materials community to understand this literature. In addition, we outline current and potential future applications of actively-controlled colloidal systems, and we highlight important open questions and future directions.

Bayesian modeling of pattern formation from one snapshot of pattern

Partial differential equations (PDEs) have been widely used to reproduce patterns in nature and to give insight into the mechanism underlying pattern formation. Although many PDE models have been proposed, they rely on the pre-request knowledge of physical laws and symmetries, and developing a model to reproduce a given desired pattern remains difficult. We propose a method, referred to as Bayesian modeling of PDEs (BM-PDEs), to estimate the best dynamical PDE for one snapshot of a objective pattern under the stationary state without ground truth. We apply BM-PDEs to nontrivial patterns, such as quasicrystals (QCs), a double gyroid, and Frank-Kasper structures. We also generate three-dimensional dodecagonal QCs from a PDE model. This is done by using the estimated parameters for the Frank-Kasper A15 structure, which closely approximates the local structures of QCs. Our method works for noisy patterns and the pattern synthesized without the ground-truth parameters, which are required for the application toward experimental data.

Open-source platform for block polymer formulation design using particle swarm optimization

Facile exploration of large design spaces is critical to the development of new functional soft materials, including self-assembling block polymers, and computational inverse design methodologies are a promising route to initialize this task. We present here an open-source software package coupling particle swarm optimization (PSO) with an existing open-source self-consistent field theory (SCFT) software for the inverse design of self-assembling block polymers to target bulk morphologies. To lower the barrier to use of the software and facilitate exploration of novel design spaces, the underlying SCFT calculations are seeded with algorithmically generated initial fields for four typical morphologies: lamellae, network phases, cylindrical phases, and spherical phases. In addition to its utility within PSO, the initial guess tool also finds generic applicability for stand-alone SCFT calculations. The robustness of the software is demonstrated with two searches for classical phases in the conformationally symmetric diblock system, as well as one search for the Frank-Kasper [Formula: see text] phase in conformationally asymmetric diblocks. The source code for both the initial guess generation and the PSO wrapper is publicly available.

Machine Learning Predictions of Block Copolymer Self-Assembly

Directed self-assembly of block copolymers is a key enabler for nanofabrication of devices with sub-10 nm feature sizes, allowing patterning far below the resolution limit of conventional photolithography. Among all the process steps involved in block copolymer self-assembly, solvent annealing plays a dominant role in determining the film morphology and pattern quality, yet the interplay of the multiple parameters during solvent annealing, including the initial thickness, swelling, time, and solvent ratio, makes it difficult to predict and control the resultant self-assembled pattern. Here, machine learning tools are applied to analyze the solvent annealing process and predict the effect of process parameters on morphology and defectivity. Two neural networks are constructed and trained, yielding accurate prediction of the final morphology in agreement with experimental data. A ridge regression model is constructed to identify the critical parameters that determine the quality of line/space patterns. These results illustrate the potential of machine learning to inform nanomanufacturing processes.

Field theoretic approach for block polymer melts: SCFT and FTS

This perspective addresses the development of polymer field theory for predicting the equilibrium phase behavior of block polymer melts. The approach is tailored to the high-molecular-weight limit, where universality reduces all systems to the standard Gaussian chain model, an incompressible melt of elastic threads interacting by contact forces. Using mathematical identities, this particle-based version of the model is converted to an equivalent field-based version that depends on fields rather than particle coordinates. The statistical mechanics of the field-based model is typically solved using the saddle-point approximation of self-consistent field theory (SCFT), which equates to mean field theory, but it can also be evaluated using field theoretic simulations (FTS). While SCFT has matured into one of the most successful theories in soft condensed matter, FTS are still in its infancy. The two main obstacles of FTS are the high computational cost and the occurrence of an ultraviolet divergence, but fortunately there has been recent groundbreaking progress on both fronts. As such, FTS are now well poised to become the method of choice for predicting fluctuation corrections to mean field theory.

Open-source code for self-consistent field theory calculations of block polymer phase behavior on graphics processing units

Self-consistent field theory (SCFT) is a powerful approach for computing the phase behavior of block polymers. We describe a fast version of the open-source Polymer Self-Consistent Field (PSCF) code that takes advantage of the massive parallelization provided by a graphical processing unit (GPU). Benchmarking double-precision calculations indicate up to 30× reduction in time to converge SCFT calculations of various diblock copolymer phases when compared to the Fortran CPU version of PSCF using the same algorithms, with the speed-up increasing with increasing unit cell size for the diblock polymer problems examined here. Where double-precision accuracy is not needed, single-precision calculations can provide speed-up of up to 60× in convergence time. These improvements in speed within an open-source format open up new vistas for SCFT-driven block polymer materials discovery by the community at large.

Optimizing self-consistent field theory block copolymer models with X-ray metrology

A block copolymer self-consistent field theory (SCFT) model is used for direct analysis of experimental X-ray scattering data obtained from thin films of polystyrene-b-poly(methyl methacrylate) (PS-b-PMMA) made from directed self-assembly. In a departure from traditional approaches, which reconstruct the real space structure using simple geometric shapes, we build on recent work that has relied on physics-based models to determine shape profiles and extract thermodynamic processing information from the scattering data. More specifically, an SCFT model, coupled to a covariance matrix adaptation evolutionary strategy (CMAES), is used to find the set of simulation parameters for the model that best reproduces the scattering data. The SCFT model is detailed enough to capture the essential physics of the copolymer self-assembly, but sufficiently simple to rapidly produce structure profiles needed for interpreting the scattering data. The ability of the model to produce a matching scattering profile is assessed, and several improvements are proposed in order to more accurately recreate the experimental observations. The predicted parameters are compared to those extracted from model fits via additional experimental methods and with predicted parameters from direct particle-based simulations of the same model, which incorporate the effects of fluctuations. The Flory-Huggins interaction parameter for PS-b-PMMA is found to be in agreement with reported ranges for this material. These results serve to strengthen the case for relying on physics-based models for direct analysis of scattering and light signal based experiments.

Process-Accessible States of Block Copolymers

Process-directed self-assembly of block copolymers refers to thermodynamic processes that reproducibly direct the kinetics of structure formation from a starting, unstable state into a selected, metastable mesostructure. We investigate the kinetics of self-assembly of linear ACB triblock copolymers after a rapid transformation of the middle C block from B to A. This prototypical process (e.g., photochemical transformation) converts the initial, equilibrium mesophase of the ABB copolymer into a well-defined but unstable, starting state of the AAB copolymer. The spontaneous structure formation that ensues from this unstable state becomes trapped in a metastable mesostructure, and we systematically explore which metastable mesostructures can be fabricated by varying the block copolymer composition of the initial and final states. In addition to the equilibrium mesophases of linear AB diblock copolymers, this diagram of process-accessible states includes 7 metastable periodic mesostructures, inter alia, Schoen's F-RD periodic minimal surface. Generally, we observe that the final, metastable mesostructure of the AAB copolymer possesses the same symmetry as the initial, equilibrium mesophase of the ABB copolymer.