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

Shape-design for stabilizing micro-particles in inertial microfluidic flows

Design of microparticles which stabilize at the centerline of a channel flow when part of a dilute suspension is examined numerically for moderate Reynolds numbers ($10 \le Re \le 80$). Stability metrics for particles with arbitrary shapes are formulated based on linear-stability theory. Particle shape is parametrized by a compact, Non-Uniform Rational B-Spline (NURBS)-based representation. Shape-design is posed as an optimization problem and solved using adaptive Bayesian optimization. We focus on designing particles for maximal stability at the channel-centerline robust to perturbations. Our results indicate that centerline-focusing particles are families of characteristic "fish"/"bottle"/"dumbbell"-like shapes, exhibiting fore-aft asymmetry. A parametric exploration is then performed to identify stable particle-designs at different k's (particle chord-to-channel width ratio) and Re's ($0.1 \le k \le 0.4, 10 \le Re \le 80$). Particles at high-k's and Re's are highly stabilized when compared to those at low-k's and Re's. A comparison of the modified dumbbell designs from the current framework also shows better performance to perturbations in Fluid-Structure Interaction (FSI) when compared to the rod-disk model reported previously (Uspal & Doyle 2014) for low-Re Hele-Shaw flow. We identify basins of attraction around the centerline, which span larger release-angle-ranges and lateral locations (tending to the channel width) for narrower channels, which effectively standardizes the notion of global focusing in such configurations using the current stability-paradigm. The present framework is illustrated for 2D cases and is potentially generalizable to stability in 3D flow-fields. The current formulation is also agnostic to Re and particle/channel geometry which indicates substantial potential for integration with imaging flow-cytometry tools and microfluidic biosensing-assays.Comment: 27 pages, 18 figures, modified the LaTeX document template, corrected typo