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

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

A Transfer Operator Methodology for Optimal Sensor Placement Accounting for Uncertainty

Sensors in buildings are used for a wide variety of applications such as monitoring air quality, contaminants, indoor temperature, and relative humidity. These are used for accessing and ensuring indoor air quality, and also for ensuring safety in the event of chemical and biological attacks. It follows that optimal placement of sensors become important to accurately monitor contaminant levels in the indoor environment. However, contaminant transport inside the indoor environment is governed by the indoor flow conditions which are affected by various uncertainties associated with the building systems including occupancy and boundary fluxes. Therefore, it is important to account for all associated uncertainties while designing the sensor layout. The transfer operator based framework provides an effective way to identify optimal placement of sensors. Previous work has been limited to sensor placements under deterministic scenarios. In this work we extend the transfer operator based approach for optimal sensor placement while accounting for building systems uncertainties. The methodology provides a probabilistic metric to gauge coverage under uncertain conditions. We illustrate the capabilities of the framework with examples exhibiting boundary flux uncertainty

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)

Thermal comparison between ceiling diffusers and fabric ductwork diffusers for green buildings

Continuously increasing energy standards have driven the need for increasing the efficiency of buildings. Most enhancements to building efficiency have been a result of changes to the heating/cooling systems, improvements in construction materials, or building design code improvements. These approaches neglect the way in which air is dispersed into individual rooms or in a building – i.e., the ducting system. This opens up the possibility of significant energy savings by making ductwork systems lighter and better insulating while ensuring cost effectiveness. The current study explores this idea by comparing the performance of conventional ductwork with recent advancements in fabric-based ductwork. We focus on the transient behavior of an on/off control system, as well as the steady state behavior of the two ductwork systems. Transient, fully three dimensional validated computational (CFD) simulations are performed to determine flow patterns and thermal evolution in rooms containing either conventional or fabric ductwork. This analysis is used to construct metrics on efficiency. A number of different flow rates are examined to determine the performance over a range of operating conditions. Transient finite volume simulations consisted of over 13 million degrees of freedom for over 10,000 time steps. The simulations utilized HPC (High Performance Computing) for the large scale analysis. The results conclusively show that fabric ducting systems are superior to the conventional systems in terms of efficiency. Observations from the data show that fabric ducting systems heat the room faster, more uniformly, and more efficiently. The increase in performance demonstrates the potential benefits of moving away from conventional systems to fabric systems for the construction of green buildings: particularly in conjunction with adaptive control systems

Equilibrium microstructures of diblock copolymers under 3D confinement

We investigate equilibrium microstructures exhibited by diblock copolymers in confined 3D geometries. We perform Self-Consistent Field Theory (SCFT) simulations using a finite-element based computational framework (Ackerman et al. 2017), that provides the flexibility to compute equilibrium structures under arbitrary geometries. We consider a sequence of 3D geometries (tetrahedron to sphere) that have the same volume but exhibit varying curvature. This allows us to study the interplay between edge and curvature effects of the 3D geometries on the equilibrium microstructures. We observe that beyond a length scale, the equilibrium structure changes from an interconnected network to a multi-layered concentric shell as the curvature of the 3D geometry is reduced. However, below this length scale the equilibrium structure remains a multi-layered concentric shell independent of curvature. We additionally explore variations in the equilibrium microstructures at a few discrete volume fractions. This study provides insight into possible frustrated phases that can arise in AB diblock systems while varying the shape of confinement geometry

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

Cantilever deflection associated with hybridization of monomolecular DNA film

Recent experiments show that specific binding between a ligand and surface immobilized receptor, such as hybridization of single stranded DNA immobilized on a microcantilever surface, leads to cantilever deflection. The binding-induced deflection may be used as a method for detection of biomolecules, such as pathogens and biohazards. Mechanical deformation induced due to hybridization of surface-immobilized DNA strands is a commonly used system to demonstrate the efficacy of microcantilever sensors. To understand the mechanism underlying the cantilever deflections, a theoretical model that incorporates the influence of ligand/receptor complex surface distribution and empirical interchain potential is developed to predict the binding-induced deflections. The cantilever bending induced due to hybridization of DNA strands is predicted for different receptor immobilization densities, hybridization efficiencies, and spatial arrangements. Predicted deflections are compared with experimental reports to validate the modeling assumptions and identify the influence of various components on mechanical deformation. Comparison of numerical predictions and experimental results suggest that, at high immobilization densities, hybridization-induced mechanical deformation is determined, primarily by immobilization density and hybridization efficiency, whereas, at lower immobilization densities, spatial arrangement of hybridized chains need to be considered in determining the cantilever deflection

Optimizing isotope substitution in graphene for thermal conductivity minimization by genetic algorithm driven molecular simulations

We present results from a computational framework integrating genetic algorithm and molecular dynamics simulations to systematically design isotope engineered graphene structures for reduced thermal conductivity. In addition to the effect of mass disorder, our results reveal the importance of atomic distribution on thermal conductivity for the same isotopic concentration. Distinct groups of isotope-substituted graphene sheets are identified based on the atomic composition and distribution. Our results show that in structures with equiatomic compositions, the enhanced scattering by lattice vibrations results in lower thermal conductivities due to the absence of isotopic clusters