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At least 145 records · Page 8

Spin-piston problem for a ferromagnetic thin film: Shock waves and solitons

In this report the unsteady, nonlinear magnetization dynamics induced by spin injection in an easy-plane ferromagnetic channel subject to an external magnetic field are studied analytically. Leveraging a dispersive hydrodynamic description, the Landau-Lifshitz equation is recast in terms of hydrodynamic-like variables for the magnetization's perpendicular component (spin density) and azimuthal phase gradient (fluid velocity). Spin injection acts as a moving piston that generates nonlinear, dynamical spin textures in the ferromagnetic channel with downstream quiescent spin density set by the external field. In contrast to the classical problem of a piston accelerating a compressible gas, here, variable spin injection and field lead to a rich variety of nonlinear wave phenomena from oscillatory spin shocks to solitons and rarefaction (expansion) waves. A full classification of solutions is provided using nonlinear wave modulation theory by identifying two key aspects of the fluid-like dynamics: subsonic/supersonic conditions and convex/nonconvex hydrodynamic flux. Familiar waveforms from the classical piston problem such as rarefaction waves and shocks manifest in their spin-based counterparts as smooth and highly oscillatory transitions, respectively, between two distinct magnetic states. The spin shock is an example of a dispersive shock wave, which arises in many physical systems. New features without a gas dynamics counterpart include composite wave complexes with “contact” spin shocks and rarefactions. Magnetic supersonic conditions lead to two pronounced piston edge behaviors including a stationary soliton and an oscillatory wave train. These coherent wave structures have physical implications for the generation of high frequency spin waves from pulsed injection and persistent, stable stationary and/or propagating solitons in the presence of magnetic damping. The analytical results are favorably compared with numerical simulations.

36 MATERIALS SCIENCE↗

Safeguards Material Control And Accountancy Considerations For Molten Salt Reactors

Molten salt reactors are a class of nuclear reactor designs with features and operational characteristics that vary significantly. Variations in design features include the physical, chemical, and isotopic composition of fresh and irradiated fuel, neutron energy spectrums, breeding ratios, and the design’s plans for chemical processing. Specific designs within these variations affect the material control and accountancy approaches implemented by both domestic and international nuclear safeguards. This paper identifies safeguards-relevant design features for molten salt reactors and describes how each feature might influence both domestic and international nuclear safeguards implementation. Additionally, this paper describes two potential general categories of material control and accountancy approaches that may be appropriate for molten salt reactors: a black box material-balance approach with measurements on the feed and waste streams combined with robust containment and surveillance on the nuclear material within the reactor or an approach that aims to quantify the nuclear material throughout the reactor (i.e., a process monitoring approach). This paper describes the benefits and challenges of these approaches to meet technical safeguards objectives and identifies gaps in current technologies.

Hogue, Karen↗

Scalable simulation of coupled adsorption and transport of methane in confined complex porous media with density preconditioning

The growing significance of shales and tight formations in the transition to less carbon-intensive and clean energy drives the research endeavor to understand the physics of gas flow within these systems. However, shales are composed of massively heterogeneous physical and chemical features. Most nano-sized pores connect to millimeter-scale fractures, leading to multiscale transport. These nano-scale pore throats demonstrate non-classical flow behavior, such as non-negligible slip velocities and adsorbed gas layers at the boundary. As a result, classical computational fluid dynamics models do not capture the physics. In this work, we develop a coupling scheme for the multiple-relaxation-time (MRT) lattice Boltzmann (LB) method that integrates the Peng-Robinson equation of state into a pseudo-potential interaction model to capture the physics of methane flow in irregular networks of channels that represent nano-scale porous media. We use atomistic simulations to calibrate and validate our model in slit nano-channels. We propose a preconditioning scheme to initialize the coupled transport and adsorption simulation of methane in complex porous media. The results of this implementation of LB agree with Direct Simulation Monte Carlo (DSMC) and Molecular Dynamics (MD) simulations. We then scale up the LB implementation through vectorization and indirect addressing. We parallelize it using Message Passing Interface (MPI) and OpenMP frameworks to simulate transport and adsorption in complex media with a million lattices. Additionally, we analyze the differences between coupled and transport-only simulations in two case studies and show that considering phase behavior, i.e., adsorption, can significantly change the flow behavior. This work constitutes an important step towards bridging the gap between molecular flow and system-scale behavior of complex disordered porous media.

42 ENGINEERING↗

Shallow Cumulus Properties as Captured by Adiabatic Fraction in High-Resolution LES Simulations

Abstract Shallow convective clouds are important players in Earth’s energy budget and hydrological cycle, and are abundant in the tropical and subtropical belts. They greatly contribute to the uncertainty in climate predictions due to their unresolved, complex processes that include coupling between the dynamics and microphysics. Analysis of cloud structure can be simplified by considering cloud motions as a combination of moist adiabatic motions like adiabatic updrafts and turbulent motions leading to deviation from adiabaticity. In this work, we study the sizes and occurrence of adiabatic regions in shallow cumulus clouds during their growth and mature stages, and use the adiabatic fraction (AF) as a continuous metric to describe cloud processes and properties from the core to the edge. To do so, we simulate isolated trade wind cumulus clouds of different sizes using the System of Atmospheric Modeling (SAM) model in high resolution (10 m) with the Hebrew University spectral bin microphysics (SBM). The fine features in the clouds’ dynamics and microphysics, including small near-adiabatic volumes and a thin transition zone at the edge of the cloud (∼20–40 m in width), are captured. The AF is shown to be an efficient measure for analyzing cloud properties and key processes determining the droplet-size distribution formation and shape during the cloud evolution. Physical processes governing the properties of droplet size distributions at different cloud regions (e.g., core, edge) are analyzed in relation to AF. Significance Statement 1) This study investigates the evolution of cumulus clouds (Cu) using a 10-m-resolution LES model with spectral bin microphysics. 2) The study improves the understanding of the mutual effects of adiabatic updrafts and lateral entrainment and mixing. 3) The study demonstrates the existence of an adiabatic core in nonprecipitating Cu. 4) Shapes of the droplet size distributions are closely related to the adiabatic fraction values. 5) Utilization of high resolution reveals the existence of physically significant small features in the cloud structure, such as a narrow cloud interface zone and small adiabatic volumes.

54 ENVIRONMENTAL SCIENCES↗

High-resolution multicontrast tomography with an X-ray microarray anode–structured target source

Multicontrast X-ray imaging with high resolution and sensitivity using Talbot–Lau interferometry (TLI) offers unique imaging capabilities that are important to a wide range of applications, including the study of morphological features with different physical properties in biological specimens. The conventional X-ray TLI approach relies on an absorption grating to create an array of micrometer-sized X-ray sources, posing numerous limitations, including technical challenges associated with grating fabrication for high-energy operations. We overcome these limitations by developing a TLI system with a microarray anode–structured target (MAAST) source. The MAAST features an array of precisely controlled microstructured metal inserts embedded in a diamond substrate. Using this TLI system, tomography of a Drum fish tooth with high resolution and tri-contrast (absorption, phase, and scattering) reveals useful complementary structural information that is inaccessible otherwise. The results highlight the exceptional capability of high-resolution multicontrast X-ray tomography empowered by the MAAST-based TLI method in biomedical applications.

47 OTHER INSTRUMENTATION↗

Anisotropic moiré optical transitions in twisted monolayer/bilayer phosphorene heterostructures

Moiré superlattices of van der Waals heterostructures provide a powerful way to engineer electronic structures of two-dimensional materials. Many novel quantum phenomena have emerged in graphene and transition metal dichalcogenide moiré systems. Twisted phosphorene offers another attractive system to explore moiré physics because phosphorene features an anisotropic rectangular lattice, different from isotropic hexagonal lattices previously reported. Here we report emerging anisotropic moiré optical transitions in twisted monolayer/bilayer phosphorenes. The optical resonances in phosphorene moiré superlattice depend sensitively on twist angle and are completely different from those in the constitute monolayer and bilayer phosphorene even for a twist angle as large as 19°. Our calculations reveal that the Γ-point direct bandgap and the rectangular lattice of phosphorene give rise to the remarkably strong moiré physics in large-twist-angle phosphorene heterostructures. This work highlights fresh opportunities to explore moiré physics in phosphorene and other van der Waals heterostructures with different lattice configurations.

36 MATERIALS SCIENCE↗

Recent Advances in Radiation-Induced Actinide Redox Chemistry

The actinide series boasts many unique physical and chemical features worthy of both fundamental and applied study. However, the chemical influence of their inherent radiation field is often overlooked, especially as we begin to explore the late actinides in more detail than ever possible before. From the perspective of used nuclear fuel reprocessing, the absorption of ionizing radiation induces the formation of a variety of transient and steady-state excited states, radicals, ions, and molecular degradation products, many of which are highly redox active and can lead to significant changes in a reprocessing solvent system’s physical and chemical properties. For example, radiolysis of the actinides can drive steady-state redox distributions and the formation of non-traditional oxidation states which can complicate their separation and recovery from fission products. This scenario is further exacerbated when complexation is taken into account. Consequently, a molecular-level understanding of radiation effects on the actinides over multiple time, distance, and material domains is essential for supporting innovation in used nuclear fuel reprocessing technologies. Attaining this knowledge necessitates a firm grasp of actinide radiation chemistry to develop predictive, mechanistic, multiscale models to support engineering efforts. Presented here are several recent studies that highlight recent advances in actinide radiation chemistry, in particular, the effect of actinide complexation on ligand reactivity towards radiation-induced transients.

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗

Building confidence in models for complex barrier systems for radionuclides

The modeling and simulation of the Cement-clay Interaction-Diffusion field (CI-D) experiment at the Mont Terri site in Switzerland presented here demonstrates that it is possible to capture the multiscale physical and chemical features of natural and engineered barrier systems for radionuclides. The simulations are successfully carried out with the newly developed CrunchODiTi high-performance computing software that accounts for multiple continua, including a continuum representing the electrical double layer (EDL) developed along negatively charged clay particles in clay rock. The simulation also accounts for both the complex three-dimensional (3D) geometry, expected as the norm in a geological waste repository, and the anisotropy of the geological formation. In addition, the high resolution of the model makes it possible to include "skin effects" developed at the interface between highly reactive materials, in this case between the high pH cement and the circumneutral but electrostatic Opalinus Clay. The successful history matching with the field experiment demonstrates that the distinct geochemical and physical properties of the cement and the Opalinus Clay in the CI-D experiment can be accounted for. Such analyses are essential for developing a defensible safety case for the underground storage of radioactive waste.

Sarsenbayev, Dauren↗

Physiochemical Machine Learning Models Predict Operational Lifetimes of CH3NH3PbI3 Perovskite Solar Cells

Halide perovskites are promising photovoltaic (PV) materials with the potential to lower the cost of electricity and greatly expand the penetration of PV if they can demonstrate long-term stability under illumination in the presence of moisture and oxygen. The solar cell service lifetime as quantified by the T80 (the time required for the power conversion efficiency to drop to 80% of its starting value) is a useful metric to assess stability. The T80 for utility, commercial, or residential PV systems needs to be several decades in order to yield low-cost electricity, and thus it is not practical to directly measure the T80. It would be useful if T80 could be predicted from the initial dynamics of a solar cell’s performance, but until now no models have been developed to forecast T80. In this work, we report the development of machine learning models to predict T80 of ITO/NiOx/CH3NH3PbI3/C60/BCP/Ag solar cells operating at maximum power point under 1-sun equivalent photon flux in air at varying temperatures and relative humidities. Efficiency losses are driven by short-circuit current and fill factor, indicating that chemical decomposition of the perovskite is a major contributor to degradation. Spatial patterns evident from in situ dark field optical microscopy suggest that the electric field gradient at device edges plays a significant role in perovskite decomposition, along with photochemical reactions with O2 and H2O. Models are trained using a menu of features from three distinct categories: (i) features based on measurements of the initial rates of change of device parameters, (ii) features based on the ambient conditions during operation (temperature, & partial pressure of H2O), and (iii) features based on underlying physics and chemistry. We show that a theory-based physiochemical feature derived from a model of the chemical reaction kinetics of the rate of degradation of the CH3NH3PbI3 is particularly valuable for prediction. This physiochemical feature was selected as the first or second most dominant feature in the best performing models. With a dataset consisting of 45 accelerated degradation experiments with T80 that range over a factor of 30, the model predicts T80 with an accuracy of about 40% (|predicted T80 - observed T80| / observed T80) on samples not used in training. This hybrid ML approach should be effective when applied to other compositions, device architectures, and advanced packaging schemes.

14 SOLAR ENERGY↗

Physiochemical Machine Learning Models Predict Operational Lifetimes of CH3NH3PbI3 Perovskite Solar Cells

Halide perovskites are promising photovoltaic (PV) materials with the potential to lower the cost of electricity and greatly expand the penetration of PV if they can demonstrate long-term stability under illumination in the presence of moisture and oxygen. The solar cell service lifetime as quantified by the T80 (the time required for the power conversion efficiency to drop to 80% of its starting value) is a useful metric to assess stability. The T80 for utility, commercial, or residential PV systems needs to be several decades in order to yield low-cost electricity, and thus it is not practical to directly measure the T80. It would be useful if T80 could be predicted from the initial dynamics of a solar cell’s performance, but until now no models have been developed to forecast T80. In this work, we report the development of machine learning models to predict T80 of ITO/NiOx/CH3NH3PbI3/C60/BCP/Ag solar cells operating at maximum power point under 1-sun equivalent photon flux in air at varying temperatures and relative humidities. Efficiency losses are driven by short-circuit current and fill factor, indicating that chemical decomposition of the perovskite is a major contributor to degradation. Spatial patterns evident from in situ dark field optical microscopy suggest that the electric field gradient at device edges plays a significant role in perovskite decomposition, along with photochemical reactions with O2 and H2O. Models are trained using a menu of features from three distinct categories: (i) features based on measurements of the initial rates of change of device parameters, (ii) features based on the ambient conditions during operation (temperature, & partial pressure of H2O), and (iii) features based on underlying physics and chemistry. We show that a theory-based physiochemical feature derived from a model of the chemical reaction kinetics of the rate of degradation of the CH3NH3PbI3 is particularly valuable for prediction. This physiochemical feature was selected as the first or second most dominant feature in the best performing models. With a dataset consisting of 45 accelerated degradation experiments with T80 that range over a factor of 30, the model predicts T80 with an accuracy of about 40% (|predicted T80 - observed T80| / observed T80) on samples not used in training. This hybrid ML approach should be effective when applied to other compositions, device architectures, and advanced packaging schemes.

14 SOLAR ENERGY↗

Domestic Safeguards Material Control and Accountancy Considerations for Molten Salt Reactors

Molten salt reactors (MSRs) are a class of nuclear reactor designs with features and operational characteristics that vary significantly more than the class of light water reactors (LWRs). MSR design concepts can be broadly categorized as solid-fueled reactors with molten salt as the coolant, liquid-fueled reactors with fuel dissolved in molten salt coolant and liquid-fueled reactors with fuel dissolved in molten salt that is contained in distinct fuel tubes with a nonfissile coolant. Proposed MSR concepts include features that are specific to each design. MSR concepts vary widely across these design features, including the physical, chemical, and isotopic composition of fresh and irradiated fuel. Operational neutron energy spectrums and breeding ratios also vary significantly across design concepts. Some concepts are burner reactors designed to transmute the spent nuclear fuel from LWRs or pressurized heavy water reactors (PHWRs), while others are breeder reactors designed to breed fissile 233 U from naturally occurring fertile 232 Th. Some MSR concepts are designed to be a part of a once-through fuel cycle, while others involve chemical separation. Those that include plans to recycle the fuel differ by whether the chemical processing would be done onsite, as a process connected to the fuel salt itself, or offsite at a reprocessing facility similar to how LWR or PHWR spent fuel is reprocessed in some countries. Each overall design concept contains various aspects of each of these features to produce a unique facility

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Advances for QCD and the standard model: color-confining light-front holography and the principle of maximum conformality

Here, I review how the application of superconformal quantum mechanics and light-front holography leads to new insights into the physics of color confinement, the spectroscopy and dynamics of hadrons, as well as surprising supersymmetric relations between the masses of mesons, baryons, and tetraquarks. Spontaneous chiral symmetry breaking is automatically fulfilled by supersymmetric Light-Front QCD. The light-front holographic approach (HLFQCD) also predicts the behavior of the QCD running coupling and other observables from the nonperturbative color-confining domain to the perturbative domain. One can determine the QCD running coupling to high precision from the data of just a single experiment over the entire perturbative regime by using the Principle of Maximum Conformality (PMC). The PMC, which generalizes the conventional Gell-Mann-Low method for scale-setting in perturbative QED to non-Abelian QCD, provides a rigorous method for achieving unambiguous scheme-independent, fixed-order Standard Model predictions, consistent with the principles of the renormalization group. I also briefly review a novel feature of hadronic physics predicted by QCD: intrinsic heavy quarks.

Brodsky, Stanley J. [SLAC National Accelerator Lab↗

Dynamical Anyon Generation in Kitaev Honeycomb Non-Abelian Spin Liquids

Relativistic Mott insulators known as “Kitaev materials” potentially realize spin liquids hosting non-Abelian anyons. Motivated by fault-tolerant quantum-computing applications in this setting, we introduce a dynamical anyon-generation protocol that exploits universal edge physics. The setup features holes in the spin liquid, which define energetically cheap locations for non-Abelian anyons, connected by a narrow bridge that can be tuned between spin liquid and topologically trivial phases. We show that modulating the bridge from trivial to spin liquid over intermediate time scales—quantified by analytics and extensive simulations—deposits non-Abelian anyons into the holes with O(1) probability. The required bridge manipulations can be implemented by integrating the Kitaev material into magnetic tunnel junction arrays that engender locally tunable exchange fields. Combined with existing readout strategies, our protocol reveals a path to topological qubit experiments in Kitaev materials at zero applied magnetic field.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Search for new physics in the final state with a single photon and large missing transverse momentum in proton-proton collisions at √𝑠 =13 TeV

A search for new physics in events featuring a single photon and missing transverse momentum is presented, using proton-proton √𝑠 =13 TeV collision data corresponding to an integrated luminosity of 101 fb −1 collected by the CMS experiment at the CERN LHC between 2017 and 2018. This analysis, combined with a previous study of 36 fb −1 of 2016 data (totaling 137 fb −1 ), reveals no significant deviations from standard model expectations. The results are then used to establish 95% confidence level limits on parameters in theoretical models involving dark matter and large extra dimensions. Compared to the 2016-only analysis, this search achieves up to a 14% improvement in exclusion reach for mediator masses in simplified dark matter models, along with 11% and 10% enhancements in the limits on the effective field theory suppression scale and the fundamental Planck scale, respectively. These results are the most stringent constraints on these parameters to date.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

One-Pot Synthesis of Melamine Formaldehyde Resin-Derived N-Doped Porous Carbon for CO 2 Capture Application

The design and synthesis of porous carbons for CO 2 adsorption have attracted tremendous interest owing to the ever-soaring concerns regarding climate change and global warming. Herein, for the first time, nitrogen-rich porous carbon was prepared with chemical activation (KOH) of commercial melamine formaldehyde resin (MF) in a single step. It has been shown that the porosity parameters of the as-prepared carbons were successfully tuned by controlling the activating temperature and adjusting the amount of KOH. Thus, as-prepared N-rich porous carbon shows a large surface area of 1658 m 2 /g and a high N content of 16.07 wt%. Benefiting from the unique physical and textural features, the optimal sample depicted a CO 2 uptake of up to 4.95 and 3.30 mmol/g at 0 and 25 °C under 1 bar of pressure. More importantly, as-prepared adsorbents show great CO 2 selectivity over N 2 and outstanding recyclability, which was prominently important for CO 2 capture from the flue gases in practical application. An in-depth analysis illustrated that the synergetic effect of textural properties and surface nitrogen decoration mainly determined the CO 2 capture performance. However, the textural properties of carbons play a more important role than surface functionalities in deciding CO 2 uptake. In view of cost-effective synthesis, outstanding textural activity, and the high adsorption capacity together with good selectivity, this advanced approach becomes valid and convenient in fabricating a unique highly efficient N-rich carbon adsorbent for CO 2 uptake and separation from flue gases.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Valence Effects of Fe Impurity for Recovered LiNi 0.6 Co 0.2 Mn 0.2 O 2 Cathode Materials

Iron impurities are generally included in the obtained leaching liquor solution during the hydrometallurgical recycling method of spent lithium-ion batteries (LIBs) due to the usage of iron in battery casings and machinery parts of recycling equipment, which would definitely affect the physical and electrochemical features of the recovered active materials. In this paper, the effects of iron impurity with different valence states (Fe 2+ and Fe 3+ ) and gradient concentrations (0.2, 1.0, and 5.0 at. %) for the obtained LiNi 0.6 Co 0.2 Mn 0.2 O 2 (NCM622) cathodes are fully studied. It is found that Fe3+ impurity could easily lower the tap density and average size of NCM622 particles and even introduce some impurity phases in the NCM622 structure at high concentration (5.0 at. %), leading to much lower specific capacity, worse rate capability, and cycling performance of the Fe 3+ -based NCM622 cathode. On contrast, with certain concentrations of Fe 2+ impurity (0.2 and 1.0 at. %), the NCM622 cathode material exhibits comparable and much better electrochemical properties compared with the virgin NCM622 materials. Based on these results, the valence of Fe impurity should be considered and controlled as well as its concentration during the recycling process design for spent LIBs.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

A Solenoid With Partial Yoke for the Dune Near Detector

The Deep Underground Neutrino Experiment (DUNE) at Fermilab is one the most challenging next-generation experiments in the field of neutrino physics. It will feature two detectors for a detailed study of neutrino oscillations using an unprecedentedly intense neutrino beam. The two detectors are a Near Detector located on the Fermilab site, 574 m away from the neutrino generation, and a Far Detector in South Dakota, 1300 km away. The Near Detector consists of three subdetectors, based on different technologies in order to achieve the best understanding of the neutrino beam. One key element of the Near Detector is a High Pressure Argon TPC surrounded by a calorimeter. This detector will need a 0.5 Tesla magnetic field transverse to the neutrino beam direction, with a 7 m diameter, 8 m long warm bore. A thin superconducting solenoid with a partial yoke, needed in order to minimise the amount of material along the path particles take crossing the different elements of the Near Detector is proposed. In this paper we present a detailed magnetic analysis and a preliminary study of the cooling, the cable and the mechanics for this magnet.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Understanding Solution State Conformation and Aggregate Structure of Conjugated Polymers via Small Angle X-ray Scattering

Donor-acceptor (D-A) conjugated polymers are high-performance organic electronic materials that exhibit complex aggregation behavior. Understanding the solution state conformation and aggregation of conjugated polymers is crucial for controlling morphology during thin-film deposition and the subsequent electronic performance. However, a precise multiscale structure of solution state aggregates is lacking. Here, we present an in-depth small-angle X-ray scattering (SAXS) analysis of the solution state structure of an isoindigo-bithiophene-based D-A polymer (PII-2T) in chlorobenzene and decane as our primary system. Modeling the system as a combination of hierarchical fibrillar aggregates mixed with dispersed polymers, we extract information about conformation and multiscale aggregation and also clarify the physical origin of features often observed but unaddressed or misinterpreted in small-angle scattering patterns of conjugated polymers. The persistence length of the D-A polymer extracted from SAXS agrees well with a theoretical model based on the dihedral potentials. Additionally, we show that the broad high q structure factor peak seen in scattering profiles can be attributed to lamellar stacking occurring within the fibril aggregates and that the low q aggregate scattering is strongly influenced by the polymer molecular weight. Overall, the SAXS profiles of D-A polymers in general exhibit a sensitive dependence on the co-existence of fibrillar aggregate and dispersed polymer chain populations. We corroborate our findings from SAXS with electron microscopy of freeze-dried samples for direct imaging of fibrillar aggregates. Finally, we demonstrate the generality of our approach by fitting the scattering profiles of a variety of D-A polymers based on thieno-isoindigo (PTII-2T), diketopyrrolopyrrole (DPP2T-TT, DPP-BTZ, PDPP2FT-C- 16 ), naphthalenediimide (P(NDI2OD-T2)), and a conjugated block copolymer P3HT-b-DPPT-T. The results presented here establish a picture of the D-A polymer solution state structure and provide a general method of interpreting and analyzing their scattering profiles.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗