Swarm Intelligence Platform for Multiblock Polymer Inverse Formulation Design

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.

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.

Deep learning enabled inverse design of nanocrystal-based optical diffusers for efficient white LED lighting

Angular color uniformity and luminous flux are the most important figures of merit for a white-light-emitting diode (WLED), and simultaneous improvement of both figures of merit is desired. The cellulose-nanocrystal (CNC)-based optical diffuser has been applied on the WLED module to enhance angular color uniformity, but it inevitably causes the reduction of luminous flux. Here we demonstrate a deep-learning-based inverse design approach to design CNC-coated WLED modules. The developed forward neural network successfully predicts two figures of merit with high accuracy, and the inverse predicting model can rapidly design the structural parameters of CNC film. Further explorations taking advantage of both forward and inverse neutral networks can effectively construct the coating layer for WLED modules to reach the best performance.

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.

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.

Self-Directed Self-Assembly of 3D Tailored Block Copolymer Nanostructures

Directed self-assembly (DSA) of block copolymers (BCPs) provides a powerful tool to fabricate various 2D nanostructures. However, it still remains a challenge to extend DSA to make uniform and complex 3D nanostructures through BCP self-assembly. In this paper, we introduce a method to fabricate various nanostructures in 3D and test it using simulations. In particular, we employ dissipative particle dynamics (DPD) simulation to demonstrate that uniform multilayer nanostructures can be achieved by alternating the stacking of two "orthogonal" BCPs films, AB copolymer film and AC copolymer film, without the need to cross-link or etch any of the components. The assembly of a new layer occurs on top of the previous bottom layer, and thus the structural information from the substrate is propagated upward in the film, a process we refer to as self-directed self-assembly (SDSA). If this process is repeated many times, one can have tailored multilayer nanostructures. Furthermore, the natural (bulk) phases of the block copolymers in each layer do not need to be the same, so one can achieve complex 3D assemblies that are not possible with a single-phase 3D system. This method in conjunction with grapho (or chemo) epitaxy is able to evolve a surface pattern into a 3D nanostructure. Here we show several examples of nanostructures fabricated by this process, which include aligned cylinders, spheres on top of cylinders, and orthogonal nanomeshes. Our work should be useful for creating complex 3D nanostructures using self-assembly.

Kinetic Pathways of Block Copolymer Directed Self-Assembly: Insights from Efficient Continuum Modeling

We introduce a computationally efficient continuum technique to simulate the complex kinetic pathways of block copolymer self-assembly. Subdiffusive chain dynamics is taken into account via nonlocal Onsager coefficients. An application to directed self-assembly of thin films of diblock copolymers on patterned substrates reveals the conditions under which experimentally observed metastable structures intervene in the desired thin-film morphology. The approach generalizes easily to multiblock copolymers and more complex guiding patterns on the substrate, and its efficiency allows for the systematic optimization of guiding patterns and process conditions.

Effect of Poly(vinyl butyral) Comonomer Sequence on Adhesion to Amorphous Silica: A Coarse-Grained Molecular Dynamics Study

Modulating a comonomer sequence, in addition to the overall chemical composition, is the key to unlocking the true potential of many existing commercial copolymers. We employ coarse-grained molecular dynamics (MD) simulations to study the behavior of random-blocky poly(vinyl butyral-co-vinyl alcohol) (PVB) melts in contact with an amorphous silica surface, representing the interface found in laminated safety glass. Our two-pronged coarse-graining approach utilizes both macroscopic thermophysical data and all-atom MD simulation data. Polymer-polymer nonbonded interactions are described by the fused-sphere SAFT-γ Mie equation of state, while bonded interactions are derived using Boltzmann inversion to match the bond and angle distributions from all-atom PVB chains. Spatially dependent polymer-surface interactions are mapped from a hydroxylated all-atom amorphous silica slab model and all-atom monomers to an external potential acting on the coarse-grained sites. We discovered an unexpected complex relationship between the blockiness parameter and the adhesion energy. The adhesion strength between PVB copolymers with intermediate VA content and silica was found to be maximal for random-blocky copolymers with a moderately high degree of blockiness rather than for diblock copolymers. We attribute this to two main factors: (1) changes in morphology, which dramatically alter the number of VA beads interacting with the surface and (2) a non-negligible contribution of vinyl butyral (VB) monomers to adhesion energy because of their preference to adsorb to zones with low hydroxyl density on the silica surface.

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.

Customizing topographical templates for aperiodic nanostructures of block copolymers via inverse design

The limited complexity of self-assembled nanostructures of block copolymers seriously impedes their potential utility in the semiconductor industry. Therefore, the customizability of complex nanostructures has been a long-standing goal for the utilization of directed self-assembly in nanolithography. Herein, we integrated an advanced inverse design algorithm with a well-developed theoretical model to deduce inverse solutions of topographical templates to direct the self-assembly of block copolymers into reproducible target structures. The deduced templates were optimized by finely tuning the input parameters of the inverse design algorithm and through symmetric operation as well as nanopost elimination. More importantly, our developed algorithm has the capability to search inverse solutions of topographical templates for aperiodic nanostructures over exceptionally large areas. These results reveal design rules for guiding templates for the device-oriented nanostructures of block copolymers with prospective applications in nanolithography.

Enhanced Particle Swarm Optimization Algorithm: Efficient Training of ReaxFF Reactive Force Fields

Particle swarm optimization (PSO) is a powerful metaheuristic population-based global optimization algorithm. However, when it is applied to nonseparable objective functions, its performance on multimodal landscapes is significantly degraded. Here we show that a significant improvement in the search quality and efficiency on multimodal functions can be achieved by enhancing the basic rotation-invariant PSO algorithm with isotropic Gaussian mutation operators. The new algorithm demonstrates superior performance across several nonlinear, multimodal benchmark functions compared with the rotation-invariant PSO algorithm and the well-established simulated annealing and sequential one-parameter parabolic interpolation methods. A search for the optimal set of parameters for the dispersion interaction model in the ReaxFF- lg reactive force field was carried out with respect to accurate DFT-TS calculations. The resulting optimized force field accurately describes the equations of state of several high-energy molecular crystals where such interactions are of crucial importance. The improved algorithm also presents better performance compared to a genetic algorithm optimization method in the optimization of the parameters of a ReaxFF- lg correction model. The computational framework is implemented in a stand-alone C++ code that allows the straightforward development of ReaxFF reactive force fields.

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.