Olga Wodo

Computationally efficient solution to the Cahn-Hilliard equation: Adaptive implicit time schemes, mesh sensitivity analysis and the 3D isoperimetric problem

We present an efficient numerical framework for analyzing spinodal decomposition described by the Cahn-Hilliard equation. We focus on the analysis of various implicit time schemes for two and three dimensional problems. We demonstrate that significant computational gains can be obtained by applying embedded, higher order Runge-Kutta methods in a time adaptive setting. This allows accessing time-scales that vary by five orders of magnitude. In addition, we also formulate a set of test problems that isolate each of the sub-processes involved in spinodal decomposition: interface creation and bulky phase coarsening. We analyze the error fluctuations using these test problems on the split form of the Cahn-Hilliard equation solved using the finite element method with basis functions of different orders. Any scheme that ensures at least four elements per interface satisfactorily captures both sub-processes. Our findings show that linear basis functions have superior error-to-cost properties. This strategy - coupled with a domain decomposition based parallel implementation - let us notably augment the efficiency of a numerical Cahn-Hillard solver, and open new venues for its practical applications, especially when three dimensional problems are considered. We use this framework to address the isoperimetric problem of identifying local solutions in the periodic cube in three dimensions. The framework is able to generate all five hypothesized candidates for the local solution of periodic isoperimetric problem in 3D - sphere, cylinder, lamella, doubly periodic surface with genus two (Lawson surface) and triply periodic minimal surface (P Schwarz surface).

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.

Electrode Materials, Thermal Annealing Sequences, and Lateral/Vertical Phase Separation of Polymer Solar Cells from Multiscale Molecular Simulations

The nanomorphologies of the bulk heterojunction (BHJ) layer of polymer solar cells are extremely sensitive to the electrode materials and thermal annealing conditions. In this work, the correlations of electrode materials, thermal annealing sequences, and resultant BHJ nanomorphological details of P3HT:PCBM BHJ polymer solar cell are studied by a series of large-scale, coarse-grained (CG) molecular simulations of system comprised of PEDOT:PSS/P3HT:PCBM/Al layers. Simulations are performed for various configurations of electrode materials as well as processing temperature. The complex CG molecular data are characterized using a novel extension of our graph-based framework to quantify morphology and establish a link between morphology and processing conditions. Our analysis indicates that vertical phase segregation of P3HT:PCBM blend strongly depends on the electrode material and thermal annealing schedule. A thin P3HT-rich film is formed on the top, regardless of bottom electrode material, when the BHJ layer is exposed to the free surface during thermal annealing. In addition, preferential segregation of P3HT chains and PCBM molecules toward PEDOT:PSS and Al electrodes, respectively, is observed. Detailed morphology analysis indicated that, surprisingly, vertical phase segregation does not affect the connectivity of donor/acceptor domains with respective electrodes. However, the formation of P3HT/PCBM depletion zones next to the P3HT/PCBM-rich zones can be a potential bottleneck for electron/hole transport due to increase in transport pathway length. Analysis in terms of fraction of intra- and interchain charge transports revealed that processing schedule affects the average vertical orientation of polymer chains, which may be crucial for enhanced charge transport, nongeminate recombination, and charge collection. The present study establishes a more detailed link between processing and morphology by combining multiscale molecular simulation framework with an extensive morphology feature analysis, providing a quantitative means for process optimization.

Computational characterization of bulk heterojunction nanomorphology

The bulk heterojunction (BHJ) nanomorphology in organic solar cells strongly affects the final efficiency of the device. Progress in experimental techniques now allows visualization of the complex 3D BHJ morphology. It is, therefore, important to characterize the topological properties of the morphology in order to quantify the link between morphology features and performance. Here, we introduce a suite of morphology descriptors which encode the complex nature of the multi-stage photovoltaic process in the BHJ. These morphology descriptors are easily determined using an approach based on converting the morphology into an equivalent weighted, labeled, undirected graph. We show how these descriptors can be used to interrogate BHJ morphologies, allow identification of bottlenecks in the photovoltaic process, and conduct quantitative comparison between morphologies with respect to each sub-process in the photovoltaic phenomena. This framework provides a simple and easy-to-use characterization tool that can be...

A novel framework for visual detection and exploration of performance bottlenecks in organic photovoltaic solar cell materials

Current characterization methods of the so‐called Bulk Heterojunction (BHJ), which is the main material of Organic Photovoltaic (OPV) solar cells, are limited to the analysis of global fabrication parameters. This reduces the efficiency of the BHJ design process, since it misses critical information about the local performance bottlenecks in the morphology of the material. In this paper, we propose a novel framework that fills this gap through visual characterization and exploration of local structure‐performance correlations. We also propose a formula that correlates the structural features with the performance bottlenecks. Since research into BHJ materials is highly multidisciplinary, our framework enables a visual feedback strategy that allows scientists to build intuition about the best choices of fabrication parameters. We evaluate the usefulness of our proposed system by obtaining new BHJ characterizations. Furthermore, we show that our approach could substantially reduce the turnaround time.

Microstructure design using graphs

Thin films with tailored microstructures are an emerging class of materials with applications such as battery electrodes, organic electronics, and biosensors. Such thin film devices typically exhibit a multi-phase microstructure that is confined, and show large anisotropy. Current approaches to microstructure design focus on optimizing bulk properties, by tuning features that are statistically averaged over a representative volume. Here, we report a tool for morphogenesis posed as a graph-based optimization problem that evolves microstructures recognizing confinement and anisotropy constraints. We illustrate the approach by designing optimized morphologies for photovoltaic applications, and evolve an initial morphology into an optimized morphology exhibiting substantially improved short circuit current (68% improvement over a conventional bulk-heterojunction morphology). We show optimized morphologies across a range of thicknesses exhibiting self-similar behavior. Results suggest that thicker films (250 nm) can be used to harvest more incident energy. Our graph based morphogenesis is broadly applicable to microstructure-sensitive design of batteries, biosensors and related applications.MATERIALS DESIGN: The power of graphsRepresenting microstructures with graphs, and mapping their properties mathematically, can help improve material properties. Morphogenesis is the process of optimizing performance in devices; representing the candidate structure with an appropriate mathematical framework in order to probe their properties and then mapping the structure to a property. Current approaches rely on computationally heavy methods for both stages, but now a team from Iowa State University and University at Buffalo simplify the process by representing the structures with labelled, weighted, undirected graphs. On this basis, one can create a “surrogate” model through generic physics graph descriptors (e.g. path lengths, domain sizes) and weighting functions for the particular property of interest. This approach reveals new designs for improved organic solar cells, but could expanded to other devices.

Using graphs to quantify energetic and structural order in semicrystalline oligothiophene thin films

In semicrystalline conjugated polymer thin films, the mobility of charges depends on the arrangement of the individual polymer chains. In particular, the ordering of the polymer backbones affects the charge transport within the film, as electron transfer generally occurs along the backbones with alternating single and double bonds. In this paper, we demonstrate that polymer ordering should be discussed not only in terms of structural but also energetic ordering of polymer chains. We couple data from molecular dynamics simulations and quantum chemical calculations to quantify both structural and energetic ordering of polymer chains. We leverage a graph-based representation of the polymer chains to quantify the transport pathways in a computationally efficient way. Next, we formulate the morphological descriptors that correlate well with hole mobility determined using kinetic Monte Carlo simulations. We show that the shortest and fastest path calculations are predictive of mobility in equilibrated morphologies. In this sense, we leverage graph-based descriptors to provide a basis for the quantitative structure property relationships.

Comparative Visual Analysis of Structure-Performance Relations in Complex Bulk-Heterojunction Morphologies

The structure of Bulk‐Heterojunction (BHJ) materials, the main component of organic photovoltaic solar cells, is very complex, and the relationship between structure and performance is still largely an open question. Overall, there is a wide spectrum of fabrication configurations resulting in different BHJ morphologies and correspondingly different performances. Current state‐of‐the‐art methods for assessing the performance of BHJ morphologies are either based on global quantification of morphological features or simply on visual inspection of the morphology based on experimental imaging. This makes finding optimal BHJ structures very challenging. Moreover, finding the optimal fabrication parameters to get an optimal structure is still an open question. In this paper, we propose a visual analysis framework to help answer these questions through comparative visualization and parameter space exploration for local morphology features. With our approach, we enable scientists to explore multivariate correlations between local features and performance indicators of BHJ morphologies. Our framework is built on shape‐based clustering of local cubical regions of the morphology that we call patches. This enables correlating the features of clusters with intuition‐based performance indicators computed from geometrical and topological features of charge paths.

A Diffuse Interface Model for Incompressible Two-Phase Flow with Large Density Ratios

In this chapter, we explore numerical simulations of incompressible and immiscible two-phase flows. The description of the fluid–fluid interface is introduced via a diffuse interface approach. The two-phase fluid system is represented by a coupled Cahn–Hilliard Navier–Stokes set of equations. We discuss challenges and approaches to solving this coupled set of equations using a stabilized finite element formulation, especially in the case of a large density ratio between the two fluids. Specific features that enabled efficient solution of the equations include: (i) a conservative form of the convective term in the Cahn–Hilliard equation which ensures mass conservation of both fluid components; (ii) a continuous formula to compute the interfacial surface tension which results in lower requirement on the spatial resolution of the interface; and (iii) a four-step fractional scheme to decouple pressure from velocity in the Navier–Stokes equation. These are integrated with standard streamline-upwind Petrov–Galerkin stabilization to avoid spurious oscillations. We perform numerical tests to determine the minimal resolution of spatial discretization. Finally, we illustrate the accuracy of the framework using the analytical results of Prosperetti for a damped oscillating interface between two fluids with a density contrast.