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At least 91 records · Page 5

Prospects of federated machine learning in fluid dynamics

Physics-based models have been mainstream in fluid dynamics for developing predictive models. In recent years, machine learning has offered a renaissance to the fluid community due to the rapid developments in data science, processing units, neural network based technologies, and sensor adaptations. So far in many applications in fluid dynamics, machine learning approaches have been mostly focused on a standard process that requires centralizing the training data on a designated machine or in a data center. In this article, we present a federated machine learning approach that enables localized clients to collaboratively learn an aggregated and shared predictive model while keeping all the training data on each edge device. We demonstrate the feasibility and prospects of such a decentralized learning approach with an effort to forge a deep learning surrogate model for reconstructing spatiotemporal fields. Our results indicate that federated machine learning might be a viable tool for designing highly accurate predictive decentralized digital twins relevant to fluid dynamics.

36 MATERIALS SCIENCE↗

Satellite Embedding-Based Population Imputation for Areas with Missing Building Footprint Data: A Computer Vision-Based Approach

High-resolution population modeling is important for supporting effective decision-making across diverse sectors. LandScan Mosaic generates population estimates at the level of individual buildings and aggregates them to 3 arc-second grids, and this approach performs well in regions where building footprint data are comprehensive and reliable. However, large portions of the globe still suffer from incomplete, sparse, or entirely missing building stock datasets, creating a structural limitation for strictly building-based population models. To address this research gap, this study proposes a computer vision-based framework that employs Google Earth Engine satellite embeddings and UNet, which allows us to directly impute grid-level population estimates in building-data-deficient areas. Applied to Taiwan as a case study, the framework achieved strong predictive performance with R$^{2}$ of 0.89, RMSE of 18.70, and MAE of 8.41, outperforming traditional machine learning approaches. Notably, the proposed framework effectively addressed building false-positive errors inherent in Global Human Settlement Layer (GHSL) data, correctly identifying uninhabited areas that were erroneously classified as populated. The framework also offers significant advantages for global population mapping, particularly in terms of scalability and temporal consistency, thereby extending the coverage and accuracy of high-resolution population products in data-scarce regions worldwide. Urban planners, decision makers, and related stakeholders can obtain granular population distributions to support more accurate and targeted infrastructure investment, service delivery, resource allocation, and risk assessment decisions.

97 MATHEMATICS AND COMPUTING↗

Enabling DER Participation in Frequency Regulation Markets

Distributed energy resources (DERs) are playing an increasing role in ancillary services for the bulk grid, particularly in frequency regulation. In this article, we propose a framework for collections of DERs, combined to form microgrids and controlled by aggregators, to participate in frequency regulation markets. Our approach covers both the identification of bids for the market clearing stage and the mechanisms for the real-time allocation of the regulation signal. The proposed framework is hierarchical, consisting of a top layer and a bottom layer. The top layer consists of the aggregators communicating in a distributed fashion to optimally disaggregate the regulation signal requested by the system operator. The bottom layer consists of the DERs inside each microgrid whose power levels are adjusted so that the tie line power matches the output of the corresponding aggregator in the top layer. The coordination at the top layer requires the knowledge of cost functions, ramp rates, and capacity bounds of the aggregators. We develop meaningful abstractions for these quantities respecting the power flow constraints and taking into account the load uncertainties and propose a provably correct distributed algorithm for optimal disaggregation of regulation signals among the microgrids.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Coherency-Constrained Spectral Clustering for Power Network Reduction

This paper presents a methodology for reducing the complexity of large-scale power network models using spectral clustering, aggregation of electrical components, and cost function approximation. Two approaches are explored using unconstrained and constrained spectral clustering to determine areas for effective system reduction. Once the system areas are determined, both loads and generators by type are aggregated, and their new cost function is approximated through polynomial curve-fitting or statistical methods. The performance of reduced networks is evaluated in terms of their ability to follow the true daily cost of the original system over a 24-hour period considering a set of several days. Two test systems are taken as test beds. Application of the methodology to a modified version of the IEEE 39-bus system reduces it from 17 generators to a 4-bus system and 9 generators with about 93% of accuracy. Similarly, the IEEE 118-bus system is reduced from 19 generators to a 3-bus system with three aggregated units achieving over 99% of accuracy. These findings address scalability challenges and enhance accuracy for high and mid-loading level conditions, and by aggregating thermal units with similar cost functions.

42 ENGINEERING↗

RuralAI in Tomato Farming: Integrated Sensor System, Distributed Computing, and Hierarchical Federated Learning for Crop Health Monitoring

Precision horticulture is evolving due to scalable sensor deployment and machine learning (ML) integration. These advancements boost the operational efficiency of individual farms, balancing the benefits of analytics with autonomy requirements. However, given concerns that affect wide geographic regions (e.g., climate change), there is a need to apply models that span farms. Federated learning (FL) has emerged as a potential solution. FL enables decentralized ML across different farms without sharing private data. Traditional FL assumes simple two-tier network topologies and, thus, falls short of operating on more complex networks found in real-world agricultural scenarios. Networks vary across crops and farms and encompass various sensor data modes, extending across jurisdictions. New hierarchical FL (HFL) approaches are needed for more efficient and context-sensitive model sharing, accommodating regulations across multiple jurisdictions. Here, we present the RuralAI architecture deployment for tomato crop monitoring, featuring sensor field units for soil, crop, and weather data collection. HFL with personalization is used to offer localized and adaptive insights. Model management, aggregation, and transfers are facilitated via a flexible approach, enabling seamless communication between local devices, edge nodes, and the cloud.

60 APPLIED LIFE SCIENCES↗

Tri-Level Scheduling Model Considering Residential Demand Flexibility of Aggregated HVACs and EVs Under Distribution LMP

Residential loads, especially heating, ventilation and air conditioners (HVACs) and electric vehicles (EVs), have great potentials to provide demand flexibility which is an attribute of grid-interactive efficient buildings (GEB). Under this new paradigm, first, EV and HVAC aggregator models are developed in this paper to represent the fleet of GEBs, in which the aggregated parameters are obtained based on a new approach of data generation and least squares parameter estimation (DG-LSPE), which can deal with heterogeneous HVACs. Then, a tri-level bidding and dispatching framework is established based on competitive distribution operation with distribution locational marginal price (DLMP). Furthermore, the first two levels form a bilevel model to optimize the aggregators’ payment and to represent the interdependency between load aggregators and the distribution system operator (DSO) using DLMP, and the third level is to dispatch the optimal load aggregation to all residents by the proposed priority list-based demand dispatching algorithm. Finally, case studies on a modified IEEE 33-Bus system illustrate three main technical reasons of payment reduction due to demand flexibility: load shift, DLMP step changes, and power losses. They can be used as general guidelines for better decision-making for future planning and operation of demand response programs.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Robust Adaptive Control for Large-scale Inverter-based Resources with Partial and Complete Loss of Inverters

This article proposes an approach to address the current and the aggregated active power control challenge for large-scale inverter-based resources subjected to partially or completely loss of inverters and grid voltage variations. To address this problem, a distributed active power mechanism is proposed which generates desired inverters current. Then an adaptive mechanism distributes the voltage control input automatically between inverters in response to the partial or complete loss of inverters. An L2-gain-based controller is designed for each inverter to track the desired current and rejects the grid voltage disturbance. Here, simulation results show a significant robust tracking for collective active power and current.

24 POWER TRANSMISSION AND DISTRIBUTION↗

A proximity‐based image‐processing algorithm for colloid assignment in segmented multiphase flow datasets

Summary Colloidal transport and deposition are of both environmental and engineering importance. Easier access to x‐ray microtomography (XMT) coupled with improved imaging resolution has made XMT a unique and viable tool for visualizing and quantifying these processes. Currently, there is scant information in the literature addressing colloid segmentation and analysis in saturated and unsaturated porous media, in particular related to spatial partitioning of colloids. To support this need, an approach to assign segmented colloidal particles and aggregates to different partitioning classes based on their proximity to different phases is presented here. The method uses different markers for each attachment site (e.g. wetting‐nonwetting phase interfaces). An example XMT dataset from a drainage experiment is used to demonstrate the efficacy of the image processing algorithms. Flow conditions, and fluid and colloid properties, can thus be compared to the behaviour of colloids within the porous medium. This algorithm can help elucidate colloidal deposition mechanisms and the importance of different attachment sites, explore the importance of fluid properties, as well as the arrangement and shape of the colloids.

BRUECK, C. L.↗

Transfer Factors for the FRMAC Assessment Manual and Turbo FRMAC to Improve Radiological Dose Assessment

The Turbo FRMAC analysis tool is used to perform complex calculations to quickly evaluate radiological consequences and aid in decision making during an emergency response by assessing impacts to the public, workers, and the food supply. Turbo FRMAC calculations are based on methods established by the Federal Radiological Monitoring and Assessment Center (FRMAC). To be able to assess impacts, input data called transfer factors that describe radionuclide uptake by local plants and animals are required. During the code application exercises in late 2016, identifying, finding, and validating nonstandard transfer factors proved to be time consuming and diverted the teams’ activity away from other critical tasks. As a result, a task was undertaken to dramatically expand the list of available transfer factors (food and non-food) and incorporate these factors into Turbo FRMAC. This will ultimately result in improved efficiency of the assessment team to perform calculations during times when the FRMAC is activated and provide more defensible, vetted data from which to calculate results. As a result of these and subsequent exercises, transfer factors were needed for the following items: bell peppers, Christmas tree, deer, flowers, fresh cucumbers, tomatoes, grapefruit, lichens, mushrooms, oranges, snap beans, squash, strawberries, sugarcane for sugar and seed, sweet corn, tea, tobacco, tree bark, and watermelon. To expand the applicability of the information tables, generic transfer data were also provided for common categories and recommendations were made for expanding the list of chemicals based on chemical similarity. The data presented in this report were compiled from recent literature with most of the data encompassing the period from 2000 to 2018. The following radionuclides were targeted during the literature search: elements associated with reactor accidents or nuclear detonations (Sr 89/90, Cs 134/137, Ce 141/144, Ru 103/106, I 129/131/133, Pu 238/239, Am 241, Zr 95, and Nb 95) and elements associated with industrial accidents or dirty bombs (Ir 192 and Co 60). Data from other elements were evaluated if they were identified during the literature search. In addition, reports were evaluated that were recommended by the research consultants. For each plant or animal transfer factor, the goal was to determine the geometric mean, the geometric standard deviation, the minimum, the maximum, and the number of measurements used. If only one measurement was available that was presented as the mean. Concentration ratios with large geometric standard deviations (GSDs) were generally the result of a paucity of measurements or a few disparate measurements. Measurement disparity was observed for data from different soil types. The geometric mean (GM) is a good reference value for planning and responses purposes, but the location-specific concentrations are unlikely to be similar to the model results. Recommendations for further work include: segregating the data to reflect the influence of soil type, developing approaches to incorporate animal data based on aggregated transfer measurements, and including data for foliar deposition on plants.

61 RADIATION PROTECTION AND DOSIMETRY↗

Privacy-Preserving Control of Partitioned Energy Resources

Distributed energy resources are an increasingly important part of the electric grid. We examine the problem of partitioning a distributed energy resource among many users while providing privacy to them. In this model, clients can send requests to a server, the server can verify that the requests are valid and aggregate them, but it cannot see the actual values in the requests. Without privacy, each user is forced to reveal their daily schedule or energy use. Energy resources add a novel challenge that prior systems do not address: they require verifying limits on private power (a rate over time) and energy (a sum) values. Furthermore, the cryptographic mechanisms must run on embedded energy control systems. We describe Weft, a novel cryptographic system that verifies both power (rate) and energy (integral) constraints on private client values and aggregates them. The key insight behind the approach is to rely on additively homomorphic secret shares, which allows servers to compute sums from rates. We present 3 cryptographic proof systems with different system trade-off for embedded systems: bit-splitting proofs minimize memory use, sorting proofs minimize computation, and commitment proofs minimize network communication. Using bit-splitting proofs, it takes an IoT client using a CortexM microcontroller 4 minutes of compute time to privately control its share of an energy resource for a day at 20s granularity.

Laufer, Evan↗

Large-scale scenarios of electric vehicle charging with a data-driven model of control

Transportation electrification is forecast to bring millions of new electric vehicles to roads worldwide this decade. Planning to support those vehicles depends on detailed scenarios of their electricity demand in both uncontrolled and controlled or smart charging scenarios. In this work, we present a novel modeling approach to enable rapid generation of demand estimates that represent the impact of controlled charging for large-scale scenarios with millions of individual drivers. To model the effect of load modulation control on aggregate charging profiles, we propose a novel machine learning approach that replaces traditional optimization approaches. We demonstrate its performance modeling workplace charging control under a range of electricity rate schedules, achieving small errors (2.5%–4.5%) while accelerating computations by more than 4000 times. To generate the uncontrolled charging demand for scenarios with residential, workplace, and public charging we use statistical representations of a large data set of real charging sessions. We demonstrate the methodology by generating diverse sets of scenarios for California's charging demand in 2030 which consider multiple charging segments and controls, each run locally in under 50 s. We further demonstrate support for rate design by modeling the large-scale impact of a new, custom rate schedule for workplace charging.

33 ADVANCED PROPULSION SYSTEMS↗

A hierarchical framework for aggregating grid-interactive buildings with thermal and battery energy storage

The behind-the-meter (BTM) thermal and battery energy storage can help improve energy efficiency, reduce energy costs, and enhance energy resilience, particularly in rural areas and for disadvantaged communities. Aggregating numerous BTM energy storage systems can act as a price influencer with a significant source of load shifting and peak demand reduction. An integrated and scalable control mechanism is required to effectively utilize energy storage systems and flexible building loads to maximize the economic benefits, considering various distribution system constraints. Here, this paper presents an innovative hierarchical coordination framework for energy storage and flexible load in buildings, considering various factors such as electricity prices, thermal comfort, and distribution system modeling and constraints. At the upper level, a distribution system operator optimizes the power flow to minimize its power procurement costs from the electricity wholesale market, while at the lower level, aggregators determine the optimal dispatch of battery and thermal energy storage systems in multiple buildings on behalf of end-users to minimize operating costs according to the power prices. These problems are solved using a game-theoretic approach through negotiations between the distribution system operator and aggregators as a bi-level decision model. Simulation case studies have been performed for a test distribution network with a number of building end-users using energy storage systems to quantify the performance of aggregators. The results demonstrate that the proposed strategy can reduce peak load for a reliable electricity distribution network while saving electricity bills for customers.

25 ENERGY STORAGE↗

An Integrated Framework for Memory-Centric Analysis: From Trace Collection to Co-Design

The memory wall phenomenon—where advances in processor performance significantly outpace those in memory subsystems—poses a fundamental challenge for contemporary computing systems. In memory-bound applications, memory subsystem behavior dominates performance, yet existing analysis approaches present significant limitations: detailed microarchitectural simulators require days to weeks to simulate modest workloads; hardware performance counters provide only aggregate statistics that obscure temporal and spatial access patterns; and scaled simulation approaches face challenges in capturing certain behaviors that emerge at larger scales. These limitations reflect a processor-centric design philosophy increasingly misaligned with memory-bound workloads where detailed understanding of memory access patterns, cache hierarchy interactions, and contention is critical for effective optimization. This paper presents an integrated framework for memory-centric analysis that enables effective hardware-software co-design. We describe practical trace collection techniques, including hardware-assisted processor tracing with minimal overhead and portable software-based instrumentation with statistical sampling. We present multi-perspective analysis methods that examine memory behavior from temporal, sequential, spatial, and relational viewpoints, revealing distinct optimization opportunities invisible in aggregate metrics. We detail an architectural modeling framework that uses sampled traces with temporal interpolation and confidence-based filtering to evaluate cache and memory configurations. Evaluation on representative benchmarks demonstrates that this framework achieves practical accuracy (L2 cache errors of 2.64\%, confidence-filtered L3 errors of 9.92\%, bandwidth errors of 7.33\%) while providing substantial speedup (26.8×) over cycle-accurate simulation, enabling rapid design space exploration. We demonstrate how this integrated framework enables systematic identification of both hardware optimizations (memory controller tuning, bank partitioning, NUMA configuration) and software optimizations (data layout restructuring, prefetching strategies, memory-aware scheduling). Through this comprehensive treatment of the memory-centric analysis pipeline—from trace collection through architectural modeling to co-design application—we provide researchers and practitioners with practical techniques for addressing memory bottlenecks in contemporary computing systems.

Gajaria, Dhruv Mayur↗

Hierarchical Model-Free Transactive Control of Building Loads to Support Grid Services

Residential buildings consume 4.4 quads of electricity annually, approximately 37% of the total electricity consumption in the United States. This represents a vast resource that can be used for demand management and other ancillary services. This project aims to develop a robust, scalable hierarchical transactional control mechanism incorporating elements of model-free control (MFC) and game theory to harness buildings to provide ancillary services to the grid. This approach is being taken to address the challenges of incorporating traditional transactional control schemes into existing buildings. The challenges include small individual building sizes requiring aggregation of many buildings, unpredictable energy usage that makes model identification difficult, and satisfying the sensitive occupant comfort constraints. In the proposed approach, by separating the control mechanism into two layers above and below the load aggregator, MFC can be used below the aggregator to modulate flexible building loads in response to pricing signals with guaranteed performance. This allows the burden of identifying an accurate model of the system to be shifted to the above-aggregator layer, where fluctuations in individual building usage have less impact on predicted building system behavior. Game theory concepts can then be used to determine pricing curves and control signals among regional aggregators. Managing this control in a game-theoretic approach will allow us to build in financial incentives that increase customer engagement. Additionally, the usage of MFC necessitates less burdensome computational and communication requirements, thus, it is easily deployable on small, embedded devices. In a broader sense, developing a strategy capable of effectively incorporating residential and small commercial buildings will allow greater throughput of existing and emerging grid services in addition to future transactive energy grid management methods. Using MFC within a hierarchical control architecture will allow the shifting of existing forecasting challenges to an aggregate level, where dynamics are slower and more predictable. This will enable a smooth interface between the grid services requests of utilities and the reliable control required by participating buildings. MFC, which supports distributed control architecture, permits a scalable solution that can be deployed to neighborhood-size systems as well as individual buildings. This project focuses on three objectives: (1) developing the mathematical framework, algorithm toolkit, and software toolset of the two-layer transactive control testbed; (2) developing a scalable solution for application over many residential and small-size commercial buildings with sparse distributed communication; and (3) field testing and implementation on hardware of the control strategies developed in the previous two objectives. The research and development activities are focused and designed to be impactful within the relevant 2025 targets timeframe. An open-source control framework for exploiting variability and dispatchability of building loads will be delivered as the outcome of the project. This capability enables greater participation of loads in electricity markets and ancillary services that are both useful for the utility and financially beneficial for building owners.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

Initial Mobility Analysis for ORNL VA-EDH Synthetic Populations

Travel burdens are a major barrier to healthcare access among US Veteran patient populations, particularly those residing in rural areas. Spatial accessibility to points of care for US Veteran populations is commonly assessed in two ways. The first approach uses open data from the US Census to represent collective travel burdens, for example the distance between population-weighted census tract centroids and VHA points of care. The second approach uses restricted-access VHA patient data to measure travel costs (e.g., distance, time) for accessing points of care with respect to geolocated patient addresses and real or approximated transportation networks. While the advantage of the open data approach lies in its reproducibility, it has notable limitations in its tendency to infer individual travel behavior from aggregate population characteristics, a problem known as ecological fallacy. Conversely, while the patient data approach is able to account for individual travel behavior, its ability to account for localized access disparities (e.g., a neighborhood with exceptionally high transportation costs) and patient demographics is limited as protecting individual patient data requires their storage in closed systems with limited capacity for adequately modeling real-world travel patterns or for supplementing patient attributes. Additionally, the patient data approach cannot account for veterans who are not enrolled in the VHA system but who may be eligible for care. These challenges limit the ability to perform “what if” analyses on the effects of place-specific interventions on veteran populations with high access barriers to healthcare. To address these challenges, we explore the application of realistic synthetic populations to examine travel burdens and spatial accessibility issues among veteran patient populations. Synthetic populations provide a virtual, individually-resolved and cross-sectional representation of the veteran patient population that enables investigation of spatial access to points of care in ways in which aggregate data and patient data do not. First, synthetic populations allow one to directly assess how individuals access points of care, from synthesized residential locations to outpatient facilities on real-world transportation networks. Modeling access to points of care at the individual scale addresses the ecological fallacy problem associated with using aggregated census data to represent veteran populations and patterns of movement. Second, synthetic populations provide a means of completely representing an area’s veteran population using only publicly available, anonymized census microdata from the American Community Survey (ACS) to ensure the privacy of real-world individuals. Generating synthetic populations from the ACS also expands descriptive characteristics beyond what patient data typically offers to include socio-demographic, economic, housing, and mobility attributes. More detailed profiles of both VHA patient populations and veterans not enrolled in the VA system will provide a comprehensive picture of groups that may benefit from interventions or outreach. As an initial exercise for using synthetic populations to measure veteran travel burdens to VA care, we apply Oak Ridge National Laboratory’s (ORNL) UrbanPop capability to generate a series of synthetic VHA patient populations for 9 Veterans Integrated Services Networks (VISN) market areas in 9 Census Divisions across the continental United States, which are listed in Table 1. We use UrbanPop to produce synthetic populations for the VISN markets selected for each US Census Division, then assign VA outpatient clinic destinations to synthetic VHA patients based on travel about each VISN market’s road network. To demonstrate using the synthetic populations to evaluate healthcare travel burdens, we compare the time-based impedance between simulated home locations and VA outpatient clinics in each VISN market. We then perform validation exercises on the synthetic populations with respect to neighborhood (block group) demographic composition as well as patient mobility, comparing aggregate origin-destination statistics for the synthetic population to outpatient visits available in restricted patient data from the VA’s Corporate Data Warehouse (CDW) database.

97 MATHEMATICS AND COMPUTING↗

What Role Do Aggregators Play in Power System Security and Resilience? Preprint

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. 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↗

Distribution Feeder-Scale Fast Frequency Response via Optimal Coordination of Net-load Resources Part I: Solution Design

This work is the first of a two-part series that develops and experimentally demonstrates a first-of-its-kind hierarchical control solution for optimally dispatching thousands of deferrable loads and distributed energy resources (DERs) across a distribution feeder to provide fast frequency response (FFR) within 500 ms to the bulk power system. This approach rapidly coordinates resources online after a frequency event occurs, allowing fast-changing, behind-the-meter (BTM) resources to be incorporated and aggregate FFR power set points to be achieved more quickly and accurately than existing approaches. We also present a solution for determining the optimal amount of headroom to operate solar inverters with to minimize opportunity cost while ensuring the FFR response viability of a building with the inverter and deferrable loads. In Part I, we develop practical algorithms for fast, cost-based optimal dispatch at multiple aggregation scales (single building, multiple buildings, and full distribution feeder), establish their optimality, and demonstrate via simulation that they are faster than state-of-the-art, coordinated frequency response approaches. In Part II, the entire platform is implemented and experimentally verified using a unique power hardware-in-the-loop demonstration, including more than 100 powered loads and DERs connected to a real-world distribution network model and over 10,000 net-load resources dispatched.

24 POWER TRANSMISSION AND DISTRIBUTION↗

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↗