Combinatorial-Entropy-Driven Aggregation in DNA-Grafted Nanoparticles
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99 GENERAL AND MISCELLANEOUS↗
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How Snow Aggregate Ellipsoid Shape and Orientation Variability Affects Fall Speed and Self-Aggregation Rates
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54 ENVIRONMENTAL SCIENCES↗
The Ice Particle and Aggregate Simulator (IPAS). Part II: Analysis of a Database of Theoretical Aggregates for Microphysical Parameterization
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54 ENVIRONMENTAL SCIENCES↗
Exciton Delocalization in Indolenine Squaraine Aggregates Templated by DNA Holliday Junction Scaffolds
Exciton delocalization plays a prominent role in the photophysics of molecular aggregates, ultimately governing their particular function or application. DNA is a compelling scaffold in which to template molecular aggregates and promote exciton delocalization. As individual dye molecules are the basis of exciton delocalization in molecular aggregates, their judicious selection is important. Motivated by their excellent photostability and spectral properties, here we examine the ability of squaraine dyes to undergo exciton delocalization when aggregated via a DNA Holliday junction (HJ) template. A commercially available indolenine squaraine dye was chosen for the study given its strong structural resemblance to Cy5, a commercially available cyanine dye previously shown to undergo exciton delocalization in DNA HJs. Three types of DNA-dye aggregate configurations—transverse dimer, adjacent dimer, and tetramer—were investigated. Signatures of exciton delocalization were observed in all squaraine-DNA aggregates. Specifically, strong blue shift and Davydov splitting were observed in steady-state absorption spectroscopy and exciton-induced features were evident in circular dichroism spectroscopy. Strongly suppressed fluorescence emission provided additional, indirect evidence for exciton delocalization in the DNA-templated squaraine dye aggregates. To quantitatively evaluate and directly compare the excitonic Coulombic coupling responsible for exciton delocalization, the strength of excitonic hopping interactions between the dyes were obtained by simultaneous fitting the experimental steady-state absorption and CD spectra via a Holstein-like Hamiltonian in which, following the theoretical approach of Kühn, Renger, and May, the dominant vibrational mode is explicitly considered. The excitonic hopping strength within indolenine squaraines was found to be comparable to that of the analogous Cy5 DNA-templated aggregate. The squaraine aggregates adopted primarily an H-type (dyes oriented parallel to each other) spatial arrangement. Extracted geometric details of dye mutual orientation in the aggregates enabled close comparison of aggregate configurations and the elucidation of the influence of dye angular relationship on excitonic hopping interactions in squaraine aggregates. Furthermore, these results encourage the application of squaraine-based aggregates in next generation systems driven by molecular excitons.
36 MATERIALS SCIENCE↗
Spatial and Temporal Uncertainty of Crop Yield Aggregations
The aggregation of simulated gridded crop yields to national or regional scale requires information on temporal and spatial patterns of crop-specific harvested areas. This analysis estimates the uncertainty of simulated gridded yield time series related to the aggregation with four different harvested area data sets. We compare aggregated yield time series from the Global Gridded Crop Model Inter-comparison project for four crop types from 14 models at global, national, and regional scale to determine aggregation-driven differences in mean yields and temporal patterns as measures of uncertainty. The quantity and spatial patterns of harvested areas differ for individual crops among the four datasets applied for the aggregation. Also simulated spatial yield patterns differ among the 14 models. These differences in harvested areas and simulated yield patterns lead to differences in aggregated productivity estimates, both in mean yield and in the temporal dynamics. Among the four investigated crops, wheat yield (17% relative difference) is most affected by the uncertainty introduced by the aggregation at the global scale. The correlation of temporal patterns of global aggregated yield time series can be as low as for soybean (r = 0.28).For the majority of countries, mean relative differences of nationally aggregated yields account for10% or less. The spatial and temporal difference can be substantial higher for individual countries. Of the top-10 crop producers, aggregated national multi-annual mean relative difference of yields can be up to 67% (maize, South Africa), 43% (wheat, Pakistan), 51% (rice, Japan), and 427% (soybean, Bolivia).Correlations of differently aggregated yield time series can be as low as r = 0.56 (maize, India), r = 0.05∗Corresponding (wheat, Russia), r = 0.13 (rice, Vietnam), and r = −0.01 (soybean, Uruguay). The aggregation to sub-national scale in comparison to country scale shows that spatial uncertainties can cancel out in countries with large harvested areas per crop type. We conclude that the aggregation uncertainty can be substantial for crop productivity and production estimations in the context of food security, impact assessment, and model evaluation exercises.
Aggregation uncertainty↗
Subtle Molecular Changes Largely Modulate Chiral Helical Assemblies of Achiral Conjugated Polymers by Tuning Solution-State Aggregation
Understanding the solution-state aggregate structure and the consequent hierarchical assembly of conjugated polymers is crucial for controlling multiscale morphologies during solid thin-film deposition and the resultant electronic properties. However, it remains challenging to comprehend detailed solution aggregate structures of conjugated polymers, let alone their chiral assembly due to the complex aggregation behavior. Herein, we present solution-state aggregate structures and their impact on hierarchical chiral helical assembly using an achiral diketopyrrolopyrrole-quaterthiophene (DPP-T4) copolymer and its two close structural analogues wherein the bithiophene is functionalized with methyl groups (DPP-T2M2) or fluorine atoms (DPP-T2F2). Combining in-depth small-angle X-ray scattering analysis with various microscopic solution imaging techniques, we find distinct aggregate in each DPP solution: (i) semicrystalline 1D fiber aggregates of DPP-T2F2 with a strongly bound internal structure, (ii) semicrystalline 1D fiber aggregates of DPP-T2M2 with a weakly bound internal structure, and (iii) highly crystalline 2D sheet aggregates of DPP-T4. These nanoscopic aggregates develop into lyotropic chiral helical liquid crystal (LC) mesophases at high solution concentrations. Intriguingly, the dimensionality of solution aggregates largely modulates hierarchical chiral helical pitches across nanoscopic to micrometer scales, with the more rigid 2D sheet aggregate of DPP-T4 creating much larger pitch length than the more flexible 1D fiber aggregates. Combining relatively small helical pitch with long-range order, the striped twist-bent mesophase of DPP-T2F2 composed of highly ordered, more rigid 1D fiber aggregate exhibits an anisotropic dissymmetry factor (g-factor) as high as 0.09. This study can be a prominent addition to our knowledge on a solution-state hierarchical assembly of conjugated polymers and, in particular, chiral helical assembly of achiral organic semiconductors that can catalyze an emerging field of chiral (opto)electronics.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Molecular Mechanisms of Sorbed Ion Effects during Boehmite Particle Aggregation
Classical theories of particle aggregation, such as Derjaguin–Landau–Verwey–Overbeek (DLVO), do not explain recent observations of ion-specific effects or the complex concentration dependence for aggregation. Thus, here, we probe the molecular mechanisms by which selected alkali nitrate ions (Na + , K + , and NO 3 –) influence aggregation of the mineral boehmite (γ-AlOOH) nanoparticles. Nanoparticle aggregation was analyzed using classical molecular dynamics (CMD) simulations coupled with the metadynamics rare event approach for stoichiometric surface terminations of two boehmite crystal faces. Calculated free energy landscapes reveal how electrolyte ions alter aggregation on different crystal faces relative to pure water. Consistent with experimental observations, we find that adding an electrolyte significantly reduces the energy barrier for particle aggregation (~3–4×). However, in this work, we show this is due to the ions disrupting interstitial water networks, and that aggregation between stoichiometric (010) basal–basal surfaces is more favorable than between (001) edge–edge surfaces (~5–6×) due to the higher interfacial water densities on edge surfaces. The interfacial distances in the interlayer between aggregated particles with electrolytes (~5–10 Å) are larger than those in pure water (a few Ångströms). Together, aggregation/disaggregation in salt solutions is predicted to be more reversible due to these lower energy barriers, but there is uncertainty on the magnitudes of the energies that lead to aggregation at the molecular scale. By analyzing the peak water densities of the first monolayer of interstitial water as a proxy for solvent ordering, we find that the extent of solvent ordering likely determines the structures of aggregated states as well as the energy barriers to move between them. Further, the results suggest a path for developing a molecular-level basis to predict the synergies between ions and crystal faces that facilitate aggregation under given solution conditions. Such fundamental understanding could be applied extensively to the aggregation and precipitation utilization in the biological, pharmaceutical, materials design, environmental remediation, and geological regimes.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Simulation of radioactive plume transport in the atmosphere including dynamics of particle aggregation and breakup
Accurate prediction of the atmospheric transport of debris particles relies heavily on our knowledge of the size distribution of the particles within a debris cloud. Assuming a fixed particle size during simulations is not always viable since the size distribution of the debris can change during transport. Various microphysical processes, such as aggregation and breakup, influence debris particles and dictate any changes to the size distribution. To track those changes that can occur, a population balance model can be adopted and instituted within a model framework. Nonetheless, many of the models that simulate the transport of radioactive debris following a device-driven fission incident have historically neglected to consider these processes. As such, this work describes our effort to develop a modeling framework capable of simulating the transport and deposition of a radioactive plume generated from a fission incident with a dynamic population balance including particle aggregation and breakup. Herein the impact of aggregation and breakup, individually and collectively, on the particle size distribution is explored using the developed framework. When simulating aggregation, for example, six mechanisms, including Brownian coagulation, the convective enhancement to Brownian coagulation, van der Waals-viscous force correction for Brownian coagulation, gravitational collection, turbulent inertial motion, and turbulent shear, are considered. Brownian coagulation and its corrections have, as one would expect, a large impact on relatively small aggregates. Aggregates with a diameter that is less than or equal to 1.0 μm, for instance, comprise 50.6 vol % of all aggregates in the absence of aggregation and 31.2 vol % when Brownian coagulation and its corrections are considered. Gravitational collection and, to a much lesser extent, turbulent shear and turbulent inertial motion are, conversely, of great importance to relatively large aggregates (i.e., diameter greater than 3.0 μm). Additionally, the individual effects of atmospheric and particle parameters, such as wind speed and particle density, are examined. Of the parameters examined, turbulent energy dissipation and aggregate fractal dimension (i.e., aggregate shape with lower values representing more irregular particles) were of substantial importance since both terms directly impact aggregate stability and, by extension, the breakup rate. Large-scale transport and deposition simulations in a dry atmosphere are also presented and discussed as a proof of concept.
98 NUCLEAR DISARMAMENT, SAFEGUARDS, AND PHYSICAL P↗
A model for the kinetics of homotypic cellular aggregation under static conditions
We present the formulation and testing of a mathematical model for the kinetics of homotypic cellular aggregation. The model considers cellular aggregation under no-flow conditions as a two-step process. Individual cells and cell aggregates 1) move on the tissue culture surface and 2) collide with other cells (or aggregates). These collisions lead to the formation of intercellular bonds. The aggregation kinetics are described by a system of coupled, nonlinear ordinary differential equations, and the collision frequency kernel is derived by extending Smoluchowski's colloidal flocculation theory to cell migration and aggregation on a two-dimensional surface. Our results indicate that aggregation rates strongly depend upon the motility of cells and cell aggregates, the frequency of cell-cell collisions, and the strength of intercellular bonds. Model predictions agree well with data from homotypic lymphocyte aggregation experiments using Jurkat cells activated by 33B6, an antibody to the beta 1 integrin. Since cell migration speeds and all the other model parameters can be independently measured, the aggregation model provides a quantitative methodology by which we can accurately evaluate the adhesivity and aggregation behavior of cells.
Non-NASA Center↗
Aggregation bias and its drivers in large‐scale flood loss estimation: A Massachusetts case study
Abstract Large‐scale estimations of flood losses are often based on spatially aggregated inputs. This makes risk assessments vulnerable to aggregation bias, a well‐studied, sometimes substantial outcome in analyses that model fine‐grained spatial phenomena at coarse spatial units. To evaluate this potential in the context of large‐scale flood risk assessments, we use data from a high‐resolution flood hazard model and structure inventory for over 1.3 million properties in Massachusetts and examine how prominent data aggregation approaches affect the magnitude and spatial distribution of flood loss estimates. All considered aggregation approaches rely on aggregate structure inventories but differ in whether flood hazard is also aggregated. We find that aggregating only structure inventories slightly underestimates overall losses (−10% bias), and when flood hazard data is spatially aggregated to even relatively small spatial units (census block), statewide aggregation bias can reach +366%. All aggregation‐based procedures fail to capture the spatial covariation of inputs distributions in the upper tails that disproportionately generate total expected losses. Our findings are robust to several key assumptions, add important context to published risk assessments and highlight opportunities to improve flood loss estimation uncertainty quantification.
54 ENVIRONMENTAL SCIENCES↗
Third-Party Aggregation Rulemaking in MISO and SPP Footprints
The report highlights key considerations for retail regulators in the footprints of the Southwest Power Pool (SPP) or Midcontinent Independent System Operator (MISO) in states that previously opted out of allowing third-party aggregation participation under FERC Order 719 and that may want to explore reversing the decision due to a changing policy environment under new FERC orders (i.e., 2222) and/or tightening resource adequacy constraints. Through a document review and a series of 27 interviews with regulators, aggregators, and other industry professionals, this document provides a high-level policy overview of the retail regulator’s role in a selection of processes, rules, and regulations to better understand how states have treated and/or integrated aggregators into wholesale markets. The report summarizes findings in two sections: General Findings and Specific Policy Findings. The General Findings offer high level takeaways such as the fact that 17 of the 20 states in MISO and SPP footprints opted out of third party aggregations following Order 719. Additionally, there is only one state that is fully restructured in the MISO and SPP footprints whereas the rest are vertically integrated, and the majority of third-party aggregations in the U.S. take place in restructured states outside of these footprints. Even so, third-party aggregations do take place in MISO and SPP albeit in small numbers and in an ad hoc regulatory environment. The specific policy findings delve deeper into specific examples of state actions on the topics of jurisdiction, registration and licensing, data governance, dual participation, and dispute resolution. Tables in each category organize state actions into Tiers I-III, which roughly correspond to the possible level of involvement or possible change necessary by state regulators and/or legislators to implement these actions. The tier level does not indicate any value judgement, as each state has respective regulatory limitations and each decision comes with various tradeoffs. One main tradeoff is between simplicity and quick implementation versus comprehensive and prolonged implementation. In many cases, actions in Tier I could be implemented without significant changes by relying on the use of existing processes for an aggregator context. On the other hand, many actions in Tier III are more narrowly designed to address aggregators specifically, but often require more significant changes including the involvement of additional parties through stakeholder engagement or legislative action. In some cases, these tiers are discrete. However, state regulators may also choose to progress through these various tiers sequentially as they phase in aggregators while learning from their experience. With the ability to stack bulk system level services, distributed energy resource aggregations in MISO and SPP could provide various private benefits (e.g., increased value streams to the owner) as well as societally beneficial grid services (e.g., peaking capacity, ancillary services, and other services that increase the grid’s overall operational efficiency). In deciding how to best to enable these benefits, states and retail regulators must weigh various tradeoffs if considering reversing a previous opt out.
29 ENERGY PLANNING, POLICY, AND ECONOMY↗
Physical and hydraulic properties of baked ceramic aggregates used for plant growth medium
Baked ceramic aggregates (fritted clay, arcillite) have been used for plant research both on the ground and in microgravity. Optimal control of water and air within the root zone in any gravity environment depends on physical and hydraulic properties of the aggregate, which were evaluated for 0.25-1-mm and 1-2-mm particle size distributions. The maximum bulk densities obtained by any packing technique were 0.68 and 0.64 g cm-3 for 0.25-1-mm and 1-2-mm particles, respectively. Wettable porosity obtained by infiltration with water was approximately 65%, substantially lower than total porosity of approximately 74%. Aggregate of both particle sizes exhibited a bimodal pore size distribution consisting of inter-aggregate macropores and intra-aggregate micropores, with the transition from macro- to microporosity beginning at volumetric water content of approximately 36% to 39%. For inter-aggregate water contents that support optimal plant growth there is 45% change in water content that occurs over a relatively small matric suction range of 0-20 cm H2O for 0.25-1-mm and 0 to -10 cm H2O for 1-2-mm aggregate. Hysteresis is substantial between draining and wetting aggregate, which results in as much as a approximately 10% to 20% difference in volumetric water content for a given matric potential. Hydraulic conductivity was approximately an order of magnitude higher for 1-2-mm than for 0.25-1-mm aggregate until significant drainage of the inter-aggregate pore space occurred. The large change in water content for a relatively small change in matric potential suggests that significant differences in water retention may be observed in microgravity as compared to earth.
NASA Center JSC↗
Light scattering study of highly absorptive, non-fractal, hematite aggregates
In this paper, we present measurements of the scattered light intensity by aerosolized hematite aggregate particles. The measurements were made at a wavelength of 532 nm in the scattering angle range from 0.32° to 157°. Hematite has high values of the real and imaginary parts of the refractive index m = n + iκ = 3 + i0.5 at the studied wavelength. Scanning electron micrographs (SEM) indicated that the particles were aggregates whereas the optical microscope pictures showed that the aerosol had a bimodal distribution with effective mean diameters of roughly 1 and 10 µm. This is consistent with the light scattering results which displayed two Guinier regimes. The aggregates were composed of smaller grains with an approximate size of 200 nm. Ultra Small-Angle X-ray Scattering (USAXS) indicate that the aggregates were uniform and non-fractal. Mie calculations for a sphere equivalent to the aggregate size were compared to the experimentally observed results. The observed results showed an enhanced backscattering, whereas the Mie calculations did not due to the large imaginary part of the refractive index. Hematite aggregates were simulated by assuming they were composed of spherical monomers inside a spherical volume. Then the light scattering was calculated using the T-matrix method for these simulated aggregates. The calculated results show an enhanced backscattering. We present a dimensional analysis to estimate the extent of multiple scattering within the aggregate and find a correlation between the average number of scattering events within the aggregate and the enhancement in the backscattering.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
ATCUN-like Copper Site in βB2-Crystallin Plays a Protective Role in Cataract-Associated Aggregation
Cataract is the leading cause of blindness worldwide, and it is caused by crystallin damage and aggregation. Senile cataractous lenses have relatively high levels of metals, while some metal ions can directly induce the aggregation of human γ-crystallins. Here, for this work, we evaluated the impact of divalent metal ions in the aggregation of human βB2-crystallin, one of the most abundant crystallins in the lens. Turbidity assays showed that Pb 2+ , Hg 2+ , Cu 2+ , and Zn 2+ ions induce the aggregation of βB2-crystallin. Metal-induced aggregation is partially reverted by a chelating agent, indicating the formation of metal-bridged species. Our study focused on the mechanism of copper-induced aggregation of βB2-crystallin, finding that it involves metal-bridging, disulfide-bridging, and loss of protein stability. Circular dichroism and electron paramagnetic resonance (EPR) revealed the presence of at least three Cu 2+ binding sites in βB2-crystallin, one of them with spectroscopic features typical for Cu 2+ bound to an amino-terminal copper and nickel (ATCUN) binding motif, which is found in Cu transport proteins. The ATCUN-like Cu binding site is located at the unstructured N-terminus of βB2-crystallin, and it could be modeled by a peptide with the first six residues in the protein sequence (NH 2 -ASDHQF-). Isothermal titration calorimetry indicates a nanomolar Cu 2+ binding affinity for the ATCUN-like site. An N-truncated form of βB2-crystallin is more susceptible to Cu-induced aggregation and is less thermally stable, indicating a protective role for the ATCUN-like site. EPR and X-ray absorption spectroscopy studies reveal the presence of a copper redox active site in βB2-crystallin that is associated with metal-induced aggregation and formation of disulfide-bridged oligomers. Our study demonstrates metal-induced aggregation of βB2-crystallin and the presence of putative copper binding sites in the protein. Whether the copper-transport ATCUN-like site in βB2-crystallin plays a functional/protective role or constitutes a vestige from its evolution as a lens structural protein remains to be elucidated.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Anomalous Anisotropic Nanoparticle Aggregation in Cu 2 (OH) 3 Br Gels
Aerogels are of interest for their ability to uniformly incorporate nanoscale features into macroscopic assemblies, which enabled applications that require low density, high surface area, and/or bicontinuous networks. The structure of the nanoporous network is intrinsically linked to the macroscopic properties of aerogels. Hence, control of this structure is of paramount importance. Small-angle X-ray scattering (SAXS) is used here to monitor nanoparticle aggregation in situ in Cu 2 (OH) 3 Br aerogels formed via epoxide-assisted gelation. Anomalous anisotropic aggregation is observed in the absence of templating agents and is attributed to the molecular structure of the inorganic nanoparticles themselves. This is a fundamental departure from the models currently used to describe traditional inorganic sol–gel chemistry where nanoparticles are believed to undergo isotropic diffusion- and/or kinetically limited aggregation. Time-resolved SAXS indicates that Cu 2 (OH) 3 Br nanoparticles nucleate rapidly from solution to form unbranched chain-like aggregates rather than branched mass-fractal aggregates. Sizes of primary particles (~1.5 nm) and the chain-like structure of their aggregates are independent of particle concentration (gel density), while rates of particle aggregation, gelation time, and aggregate size are strongly dependent upon particle concentration, which implies that the chemistry of particle formation and the physics of particle aggregation are independent processes. Because the conditions necessary for creating anisotropic structures are not unique to Cu 2 (OH) 3 Br, these results could provide insight into the structure and gelation mechanisms of other inorganic aerogels.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
What Role Do Aggregators Play in Power System Security and Resilience?
Barriers to the participation of distributed energy resources (DERs) in wholesale electricity markets have limited the use of DERs for power system security and resilience. In September 2020, the Federal Energy Regulatory Commission (FERC) approved an order to reduce these barriers. FERC Order No. 2222 enables the participation of DER aggregators in wholesale electricity markets. DERs include renewable generation and technologies that support the integration of renewable generation by increasing grid flexibility and resilience. Requiring wholesale energy markets to allow DER aggregator participation provides a path for DERs to become competitive in these markets. As the contribution from aggregated DERs continues to increase, the aggregator's role in supporting grid security and resilience will become more critical. This paper reviews work that demonstrates how DER aggregators can provide resilience support through technical capabilities, operational strategies, and secure communication architectures. Socioeconomic influences and impacts of aggregators, including implications for social resilience, are presented. In surveying the current state-of-the-art across different but interconnected topics, we illustrate how aggregators can be power system participants that enhance grid security. There is no one-size-fits-all approach to enhancing resilience in a power grid that includes a growing cohort of DER aggregators, but there are many options for aggregators to contribute to a more resilient and secure power grid.
aggregator↗
Aggregation of Leslie matrix models with application to ten diverse animal species
Some grouping is necessary when constructing a Leslie matrix model because it involves discretizing a continuous process of births and deaths. Here, the level of grouping is determined by the number of age classes and frequency of sampling. It is largely unknown what is lost or gained by using fewer age classes, and I address this question using aggregation theory. I derive an aggregator for a Leslie matrix model using weighted least squares, determine what properties an aggregated matrix inherits from the original matrix, evaluate aggregation error, and measure the influence of aggregation on asymptotic and transient behaviors. To gauge transient dynamics, I employ reactivity of the standardized Leslie matrix. I apply the aggregator to 10 Leslie models developed for animal populations drawn from a diverse set of species. Several properties are inherited by the aggregated matrix: (a) it is a Leslie matrix; (b) it is irreducible whenever the original matrix is irreducible; (c) it is primitive whenever the original matrix is primitive; and (d) its stable population growth rate and stable age distribution are consistent with those of the original matrix if the least squares weights are equal to the original stable age distribution. In the application, depending on the population modeled, when the least squares weights do not follow the stable age distribution, the stable population growth rate of the aggregated matrix may or may not be approximately consistent with that of the original matrix. Transient behavior is lost with high aggregation.
54 ENVIRONMENTAL SCIENCES↗
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↗