A finite element approach to self-consistent field theory calculations of multiblock polymers

Self-consistent field theory (SCFT) has proven to be a powerful tool for modeling equilibrium microstructures of soft materials, particularly for multiblock polymers. A very successful approach to numerically solving the SCFT set of equations is based on using a spectral approach. While widely successful, this approach has limitations especially in the context of current technologically relevant applications. These limitations include non-trivial approaches for modeling complex geometries, difficulties in extending to non-periodic domains, as well as non-trivial extensions for spatial adaptivity. As a viable alternative to spectral schemes, we develop a finite element formulation of the SCFT paradigm for calculating equilibrium polymer morphologies. We discuss the formulation and address implementation challenges that ensure accuracy and efficiency. We explore higher order chain contour steppers that are efficiently implemented with Richardson Extrapolation. This approach is highly scalable and suitable for systems with arbitrary shapes. We show spatial and temporal convergence and illustrate scaling on up to 2048 cores. Finally, we illustrate confinement effects for selected complex geometries. This has implications for materials design for nanoscale applications where dimensions are such that equilibrium morphologies dramatically differ from the bulk phases

Optimization of micropillar sequences for fluid flow sculpting

Inertial fluid flow deformation around pillars in a microchannel is a new method for controlling fluid flow. Sequences of pillars have been shown to produce a rich phase space with a wide variety of flow transformations. Previous work has successfully demonstrated manual design of pillar sequences to achieve desired transformations of the flow cross-section, with experimental validation. However, such a method is not ideal for seeking out complex sculpted shapes as the search space quickly becomes too large for efficient manual discovery. We explore fast, automated optimization methods to solve this problem. We formulate the inertial flow physics in microchannels with different micropillar configurations as a set of state transition matrix operations. These state transition matrices are constructed from experimentally validated streamtraces. This facilitates modeling the effect of a sequence of micropillars as nested matrix-matrix products, which have very efficient numerical implementations. With this new forward model, arbitrary micropillar sequences can be rapidly simulated with various inlet configurations, allowing optimization routines quick access to a large search space. We integrate this framework with the genetic algorithm and showcase its applicability by designing micropillar sequences for various useful transformations. We computationally discover micropillar sequences for complex transformations that are substantially shorter than manually designed sequences. We also determine sequences for novel transformations that were difficult to manually design. Finally, we experimentally validate these computational designs by fabricating devices and comparing predictions with the results from confocal microscopy

Parallel Framework for Dimensionality Reduction of Large-Scale Datasets

Dimensionality reduction refers to a set of mathematical techniques used to reduce complexity of the original high-dimensional data, while preserving its selected properties. Improvements in simulation strategies and experimental data collection methods are resulting in a deluge of heterogeneous and high-dimensional data, which often makes dimensionality reduction the only viable way to gain qualitative and quantitative understanding of the data. However, existing dimensionality reduction software often does not scale to datasets arising in real-life applications, which may consist of thousands of points with millions of dimensions. In this paper, we propose a parallel framework for dimensionality reduction of large-scale data. We identify key components underlying the spectral dimensionality reduction techniques, and propose their efficient parallel implementation. We show that the resulting framework can be used to process datasets consisting of millions of points when executed on a 16,000-core cluster, which is beyond the reach of currently available methods. To further demonstrate applicability of our framework we perform dimensionality reduction of 75,000 images representing morphology evolution during manufacturing of organic solar cells in order to identify how processing parameters affect morphology evolution

Achieving Bicontinuous Microemulsion Like Morphologies in Organic Photovoltaics

It is believed that the optimal morphology of an organic solar cell may be characterized by cocontinuous, interpenetrating donor and acceptor domains with nanoscale dimensions and high interfacial areas. One well-known equilibrium morphology that fits these characteristics is the bicontinuous microemulsion achieved by the addition of block copolymer compatibilizers to flexible polymer–polymer blends. However, there does not exist design rules for using block copolymer compatibilizers to produce bicontinuous microemulsion morphologies from the conjugated polymer/fullerene mixtures typically used to form the active layer of organic solar cells. Motivated by these considerations, we use single chain in mean field simulations to study the equilibrium phase behavior of semiflexible polymer + flexible–semiflexible block copolymer + solvent mixtures. Based on our results, we identify design rules for producing large channels of morphologies with characteristics like that of the bicontinuous microemulsion

Quantifying organic solar cell morphology: a computational study of three-dimensional maps

Establishing how fabrication conditions quantitatively affect the morphology of organic blends opens the possibility of rationally designing higher efficiency materials; yet such a relationship remains elusive. One of the major challenges stems from incomplete three-dimensional representations of morphology, which is due to the difficulties of performing accurate morphological measurements. Recently, three-dimensional measurements of mixed organic layers using electron tomography with high-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM) provided maps of morphology with high resolution and detail. Using a simple, yet powerful, computational tool kit, these complex 3D datasets are converted into a set of physically meaningful morphology descriptors. These descriptors provide means for converting these large, complicated datasets (∼5 × 107 voxels) into simple, descriptive parameters, enabling a quantitative comparison among morphologies fabricated under different conditions. A set of P3HT:endohedral fullerene bulk-heterojunctions, fabricated under conditions specifically chosen to yield a wide range of morphologies, are examined. The effects of processing conditions and electrode presence on interfacial area, domain size distribution, connectivity, and tortuosity of charge transport paths are herein determined directly from real-space data for the first time. Through this characterization, quantitative insights into the role of processing in morphology are provided, as well as a more complete picture of the consequences of a three-phase morphology. The analysis demonstrates a methodology which can enable a deeper understanding into morphology control

Hierarchical Feature Extraction for Efficient Design of Microfluidic Flow Patterns

Deep neural networks are being widely used for feature representation learning in diverse problem areas ranging from object recognition and speech recognition to robotic perception and human disease prediction. We demonstrate a novel, perhaps the first application of deep learning in mechanical design, specifically to learn complex microfluidic flow patterns in order to solve inverse problems in fluid mechanics. A recent discovery showed the ability to control the fluid deformations in a microfluidic channel by placing a sequence of pillars. This provides a fundamental tool for numerous material science, manufacturing and biological applications. However, designing pillar sequences for user-defined deformations is practically infeasible as the current process requires laborious and time-consuming design iterations in a very large, highly nonlinear design space that can have as large as 1015 possibilities. We demonstrate that hierarchical feature extraction can potentially lead to a scalable design tool via learning semantic representations from a relatively small number of flow pattern examples. The paper compares the performances of pre-trained deep neural networks and deep convolutional neural networks as well as their learnt features. We show that a balanced training data generation process with respect to a metric on the output space improves the feature extraction performance. Overall, the deep learning based design process is shown to expedite the current state-of-the-art design approaches by more than 600 times