Modeling morphology evolution during solvent-based fabrication of organic solar cells

Solvent-based techniques usually involve preparing dilute blends of electron-donor and electron-acceptor materials dissolved in a volatile solvent. After some form of coating onto a substrate, the solvent evaporates. An initially homogeneous mixture separates into electron-acceptor rich and electron-donor rich regions as the solvent evaporates. Depending on the specifics of the blend and processing conditions different morphologies are typically formed. Experimental evidence consistently confirms that the morphology critically affects device performance. A computational framework that can predict morphology evolution can significantly augment experimental analysis. Such a framework will also allow high throughput analysis of the large phase space of processing parameters, thus yielding insight into the process-structure-property relationships. In this paper, we formulate a computational framework to predict evolution of morphology during solvent-based fabrication of organic thin films. This is accomplished by developing a phase field-based model of evaporation-induced and substrate-induced phase-separation in ternary systems. This formulation allows all the important physical phenomena affecting morphology evolution during fabrication to be naturally incorporated. We discuss the various numerical and computational challenges associated with a three dimensional, finite-element based, massively parallel implementation of this framework. This formulation allows, for the first time, to model 3D morphology evolution over large time spans on device scale domains. We illustrate this framework by investigating and quantifying the effect of various process and system variables on morphology evolution. We explore ways to control the morphology evolution by investigating different evaporation rates, blend ratios and interaction parameters between components

How do evaporating thin films evolve? Unravelling phase-separation mechanisms during solvent-based fabrication of polymer blends

Solvent-based fabrication is a flexible and affordable approach to manufacture polymer thin films. The properties of products made from such films can be tailored by the internal organization (morphology) of the films. However, a precise knowledge of morphology evolution leading to the final film structure remains elusive, thus limiting morphology control to a trial and error approach. In particular, understanding when and where phases are formed, and how they evolve would provide rational guidelines for more rigorous control. Here, we identify four modes of phase formation and subsequent propagation within the thinning film during solvent-based fabrication. We unravel the origin and propagation characteristics of each of these modes. Finally, we construct a mode diagram that maps processing conditions with individual modes. The idea introduced here enables choosing processing conditions to tailor film morphology characteristics and paves the ground for a deeper understanding of morphology control with the ultimate goal of precise, yet affordable, morphology manipulation for a large spectrum of applications

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)

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

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

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

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 used to unravel the impact of morphology on complex transport phenomena