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At least 163 records · Page 9

Gas Stopper Developments for Improved Purity and Intensity of Low-Energy, Rare Isotope Ion Beams (Final Technical Report)

This final technical report summarizes the work of the Michigan State University (MSU) team supported by grant # DE-SC0021423 awarded by the Office of Nuclear Physics, Department of Energy. Objectives: The successful fulfillment of the FRIB science mission hinges on ensuring the availability of fast, stopped, and reaccelerated beams consisting of rare isotopes. This project's research and development focus was dedicated to supporting the advancement and creation of a cutting-edge linear gas stopper. The primary aim is to efficiently convert the high-intensity fast beams of rare isotopes provided by FRIB into high-quality, low-energy beams. These beams are essential for conducting stopped beam experiments or for subsequent reacceleration. The overarching goal is to advance technology, aiming to increase the beam rate capability of the linear gas stopper for medium-to-heavy-mass rare isotopes by more than tenfold compared to the currently most effective gas stopper in operation, and to improve the purity of the delivered beams. Project Description: The existing technology employed in gas stopping devices designed for low-energy, rare-isotope beams presents limitations in both the purity of extracted beams and the intensities of injected beams. These limitations are incompatible with the requirements of the recently commissioned rare isotope beam facility, FRIB. Our research and development efforts, aligned with the previously outlined objectives, focused on addressing the most critical aspects for enhancing beam-rate capability and purity. Specifically, advanced particle-in-cell simulations were developed and integrated into a simulation pipeline to explore the efficacy of multi-layer RF carpets on increasing ion transport efficiency with high incoming beam rates that generate space charge fields which can limit it. We also explored the possibility of using a collision-induced-dissociation (CID) gas cell to break up molecular contaminant ions that are generated during the stopping process. A prototype CID gas cell was constructed and tested with beams from an offline ion source, validating the concept with the successful demonstration of breaking of molecular ions. The outcome of this research enabled the formulation a conceptual design for a next-generation linear gas stopping device specifically tailored for FRIB. This device is envisioned to deliver rare-isotope-ion beams at a rate of 10 8 particles per second or higher, accompanied by advancements in purity. Methods employed: This project leverages advancements in technologies initially designed for the Advanced Cryogenic Gas Stopper (ACGS), the current state-of-the-art linear gas stopper, through the use of new simulations and beam purification via collision-induced-dissociation. The methods include: 1. Development of a prototype low-energy, low-pressure CID gas stopper. This prototype features a thin, approximately 20 nm, Si 3 N 4 entrance window designed for dissociating stable and rare-isotope molecular ions. The goal is to enhance beam purification and overall efficiency. 2. Creation of Particle-in-cell (PIC) simulations to assess the advantages of multi-layer RF carpets and multi-point extraction for ion transport efficiency. These simulations rely on the 3DCylPIC package, specifically designed for studying devices of this nature. The goal is to quantify and mitigate ion transport losses due to space charge generated in the stopping process of large numbers of ions. 3. Perform ion transport simulations across an RF carpet using an 8-phase travelling wave and evaluate its performance. Compared to the 4-phase RF carpets used in ACGS, the 8-phase carpets will double the wavelength of the generated traveling wave allowing for larger maximum RF amplitudes that could result in improved ion transport efficiency for high-intensity incoming beams when large space charge fields are present. Impact: Tackling the primary challenges associated with transforming high-energy projectile fragment beams into low-energy beams—specifically, addressing efficiency and purity—holds significant promise for advancing FRIB science. This advancement will particularly impact precision mass measurements, laser spectroscopy of short-lived nuclei, and studies in astrophysics and nuclear reactions using reaccelerated beams. These domains play a crucial role in addressing key questions outlined in the 2023 NSAC long-range plan, spanning nuclear structure, nuclear astrophysics, and fundamental symmetries. Additionally, they contribute to addressing 10 out of the 17 benchmarks identified by the NRC RISAC. The development of a next-generation gas stopping device capable of delivering low-energy, rare-isotope beams at a rate of 10 8 particles per second, or more, with high purity holds the potential to unlock experiments that would otherwise be unfeasible. Furthermore, it is expected to reduce the time required for experiments at FRIB, thereby maximizing scientific output. The research and development activities performed as part of this project bolstered essential competencies at FRIB in beam physics and ion source technologies, provided valuable training opportunities for junior scientists.

43 PARTICLE ACCELERATORS↗

Experimental Validation of Subsystem Models for a Novel Variable Displacement Hydraulic Motor

A novel, variable displacement, low-speed high-torque hydraulic motor is being developed that is expected to be highly efficient across a broad operating range. To ensure the final hardware achieves the expected performance, the models used in the development of the motor must be experimentally validated and revised, as necessary. The specific focus in this work is on mechanical energy loss models that were used to guide the design of a single-cylinder motor prototype and on experimental tests used for model validation. Ideally each model, whether friction loss in a piston/cylinder interface or energy loss due to leakage in a valve , would be individually validated by an independent test. This granular approach would remove any question of where the error lies and result in highly accurate models. However, many motor components have multiple forms of energy loss, creating difficulty in validating individual losses. Additionally, it is not physically realizable to divide many components into an individual model equivalent test. Testing the motor as a full assembly is possible, but pinpointing the source of discrepancies between the model and the hardware becomes difficult with dozens of models potentially being partially responsible. A compromise was found by separating the motor into functional component groups that are characterized by the type of loss and ability to test each subcomponent independently. By checking for correlation between test observations and model predictions, revisions could be implemented into the models. This allows future solutions to be more accurately predicted in the design phase to drive the design of better machines.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Ultra-Compact High Efficiency Multi-Level Gan-Based PV Inverter

This project developed the key technology for a scalable, high-density photovoltaic (PV) inverter, based on gallium-nitride (GaN) power semiconductors, and advanced digital control. Specifically, we explored the feasibility of a flying-capacitor multi-level inverter for 1.5 kV PV installations, through the development of hardware prototypes utilizing low-inductance commutation loop designs, robust digital control and signaling, and low-cost heatsink integration.

14 SOLAR ENERGY↗

The CMS Phase-2 Fast Beam Condition Monitor prototype test with beam

The Fast Beam Condition Monitor (FBCM) is a standalone luminometer for the High Luminosity LHC (HL-LHC) program of the CMS Experiment at CERN. The detector is under development and features a new, radiation-hard, front-end application-specific integrated circuit (ASIC) designed for beam monitoring applications. The achieved timing resolution of a few nanoseconds enables the measurement of both the luminosity and the beam-induced background. The ASIC, called FBCM23, features six channels with adjustable shaping times, enabling in-field fine-tuning. Each ASIC channel outputs a single binary asynchronous signal encoding time-of-arrival and time-over-threshold information. The FBCM is based on silicon-pad sensors, with two sensor designs presently being considered. This paper presents the results of tests of the FBCM detector prototype using both types of silicon sensors with hadron, muon, and electron beams. Irradiated FBCM23 ASICs and silicon-pad sensors were also tested to simulate the expected conditions near the end of the detector's lifetime in the HL-LHC radiation environment. Based on test results, direct bonding between the sensor and ASIC was chosen, and an optimal bias voltage and ASIC threshold for FBCM operation were proposed. The current design of the front-end test board was validated following the beam test and is now being used for the first front-end module, which is expected to be produced in summer 2025. These results represent a major step forward in validating the FBCM concept, first version of the firmware and establishing a reliable design path for the final detector.

Beam-line instrumentation (beam position and profi↗

Tethered from the Head and from the Tail: The Structure of Hydroxyl-Functionalized Ionic Liquids

Ionic liquids with special functionalities are synthesized with the specific purpose of creating new patterns of interaction in the condensed phase. This Letter discusses the case of alcohol-functionalized ILs, the so-called HFILs, which are part of the larger cohort of task-specific ionic liquids. We find that this small chemical modification can cause massive changes in the liquid landscape when the cationic tails are longer. For prototypical ionic liquids, larger alkyl tails act as separators of charge networks, but in the case of HFILs these become physical charge network linkers. The OH functionality adds a large repertoire of interactions and correlations that were mostly unavailable to traditional ILs.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Anisotropic, multiband, and strong-coupling superconductivity of the Pb 0.64 ⁢Bi 0.36 alloy

This paper presents theoretical and experimental studies on the superconductivity of Pb ⁢0.64 ⁢Bi 0.36 alloy, which is a prototype of strongly coupled superconductors and exhibits one of the strongest coupling under ambient pressure among the materials studied so far. The critical temperature, the specific heat in the superconducting state, and the magnetic critical fields are experimentally determined. Deviations from the single-gap s-wave BCS-like behavior are observed. The electronic structure, phonons, and electron-phonon interactions are analyzed in relation to the metallic Pb, explaining why the Pb-Bi alloy exhibits such a large value of the electron-phonon coupling parameter λ ≃ 2. Superconductivity is studied using the isotropic Eliashberg formalism as well as the anisotropic density functional theory for superconductors. Here, we find that while Pb is a two-gap superconductor with well-defined separate superconducting gaps, in the Pb-Bi alloy an overlapped three-gap-like structure is formed with a strong anisotropy. Furthermore, the chemical disorder, inherent to this alloy, leads to strong electron scattering, which is found to reduce the critical temperature.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Performance of a second generation of the Fermilab Constant Fraction Discriminator ASIC for time-stamping long-strip AC-LGAD sensors.

We present the design and performance characterization results of the second generation of the novel Fermilab Constant Fraction Discriminator ASIC (FCFD) developed to readout AC-coupled low gain avalanche detector (AC-LGAD) sensors. This study presents the performance of the ASIC which was optimized specifically for reading out strip AC-LGAD sensors designed for ePIC experiment at EiC. Performance was measured using charge injection and particle beams with prototype AC-LGAD sensors wirebonded to the FCFD ASIC.

Apresyan, A.↗

Ride Pingo to Transit

In this project, we developed an on-demand microtransit first- and last-mile service. To integrate the service with fixed-route transit, we developed a feature called Transit Connect that prioritized riders’ on-time arrival at the transit station over other service requirements. We first prototyped service and related algorithms in a simulated environment, and then piloted the service in the city of Kent, Washington. Our algorithm incorporates request-specific hard drop-off deadlines to ensure timely arrivals for transit transfers. In the pilot, these constraints were obtained from GTFS Realtime data to accurately determine the schedule of the transit and the location of the stations. This approach introduced the ability to accept or decline new requests based on the timing of transit connections for these new requests and connection status of onboarding customers. The pilot (called “Ride Pingo to Transit”) deployed a fleet of three 14-person vans, ran from September 2021 to March 2023, and served a total of 21,329 trips. Transit Connect was offered for drop-offs at both Kent Station and the Kent Valley hub. In total, 2,844 such trips were completed. This dataset was collected from our pilot, which includes the following: - Requests: List of all trip requests, including those that were actually served and those not materialized. - Fleet: Daily vehicle service logs. - Service details: Daily vehicle stop logs (boarding and alighting). - Trip types: First mile, last mile, or point-to-point. ![pingo to transit](pingo-to-transit.jpg)

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Cummins R-SOFC System Development

The overall purpose of this project was to reduce the Reversible-Solid Oxide Fuel Cell (R-SOFC) system cost by developing two technologies, an improved cell design and the incorporation of an ejector in the fuel recycle loop instead of a blower. A Simulink model of the baseline SOFC system was developed and calibrated with experimental test data. The R-SOFC system model was built by integrating GT Suite developed models of the steam generation components into the baseline Simulink SOFC system model. The ability to run the stack in SOEC operating mode was also added to the model. The system model was used to explore the ability of the R-SOFC system to meet operational constraints on Steam/Carbon ratio and H2 concentration on the fuel side electrode. A CFD ejector model was developed and used to explore a range of ejector design parameters, leading to the final ejector design that was prototyped for testing. A prototype steam ejector was first tested in a laboratory environment using room temperature air. The steam ejector was subsequently tested using the full hot recycle loop with all relevant heat exchangers and steam generation components. The test conditions utilized temperatures, pressures, and flow rates expected in an R-SOFC application. Throughout the experimental testing work, ejector performance test data was used to improve and then validate the CFD ejector model. A CFD cell model was developed and used to optimize thermal gradients, voltage, and cost of a new cell substrate design. A CFD comparison of co-flow and cross-flow cell designs informed the decision to use a co-flow design for the new cell substrate. Multiple rounds of CFD simulation were used to improve the cell design to minimize the variation in air and fuel distribution across cell channels and to minimize the variation in air and fuel distribution across different cells in the stack. A few prototypes of the new cell substrate design were produced and validated in a laboratory environment by thermally spraying and verifying that they met established manufacturing specifications. The cell manufacturing process was adjusted in order to bring these metrics within acceptable tolerances. Cummins’ internal calculations show that the new cell design reduces cost ~50% compared to the baseline cell, while the ejector + superheater/boiler concept reduces cost of the recycle loop by ~40%. The impact of these cost reductions on the cost of producing H2 will depend on the specific system where they are applied. Therefore, a Techno-Economic Analysis was completed using system cost as a variable, and showing how the NREL Current and Future system costs translate into H2 production cost.

Henrichsen, Lars↗

Coupled SAM/Griffin Model of a Reference Pebble Bed High-Temperature Gas Cooled Reactor for Multi-Physics Simulations

An effort has been dedicated to developing a reference model for multi-physics coupled simulation of the pebble bed high-temperature gas-cooled reactor (PB-HTGR) with SAM and Griffin computer codes for safety analysis and licensing purpose. The reference problem of a prototypical reactor design serves as the foundation for the U.S. NRC (Nuclear Regulatory Commission) to verify the adequacy of computer codes and evaluation models for specific reactor types. In this work, a SAM model of the HTR-PM reactor has been developed based on publicly available design information and the multi-dimensional Pronghorn model developed by Idaho National Laboratory. The SAM HTR-PM model includes a multi-dimensional core region and 0- D/1-D fluid components. Additionally, a simplified air RCCS loop is modeled for decay heat removal. The Griffin model is based on a recent work by Idaho National Laboratory. The coupling between the models is achieved through the MOOSE MultiApp system. Both steady-state and transient scenarios were simulated to demonstrate the coupled model’s capability for multi-physics simulations.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

Coupled SAM/Griffin Model of a Reference Fluoride-Salt-Cooled High-Temperature Reactor for Multi-Physics Simulations

A multi-physics coupled simulation model of a reference pebble bed fluoride-salt-cooled high-temperature reactor (PB-FHR) has been developed with SAM and Griffin computer codes for transient safety analysis. The reference problem of a prototypical reactor design serves as the foundation for the U.S. NRC (Nuclear Regulatory Commission) to verify the adequacy of computer codes and evaluation models for specific reactor types. In this work, the previously developed SAM model for PB-FHR primary loop has been updated for the coupled simulation. The updated SAM PB-FHR model includes a 2-D axial symmetric core region and external core components in 0-D/1-D. In addition to the primary loop, a detailed model of the RCCS (reactor cavity cooling system) is added. The 2-D and 1-D domains are tightly coupled using the single-solve approach developed in SAM. In the pebble bed region, the SAM multiscale explicit pebble model is applied to calculate the pebble and TRISO fuel kernel temperatures. The Griffin model used in this work is based on a model developed at Idaho National Laboratory in collaboration with the U.S. NRC. The Griffin neutronics model and SAM thermal hydraulics model is coupled with the Comprehensive Reactor Analysis Bundle (CRAB or alternately BlueCRAB) application. Both steady-state and transient scenarios are simulated to demonstrate the model's suitability for multi-physics simulations of PB-FHR transients.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

Distributed Resilience in High-Energy Physics Data Acquisition

Historical experience in the High-Performance Computing community teaches us that as computing systems grow, the instance of failures goes from rare to a regular occurrence. A survey of the growth in the size and complexity of Data AcQuisition (DAQ) networks in High-Energy Physics (HEP) experiments reveals that these networks are scaling exponentially, trending to a point where automated fault handling should be considered over the current manual practice, especially given the rarity of data such as in DUNE's mission to observe core-collapse supernovae. We propose a general system, DiDAQt, which is designed to provide fault detection and handling in HEP DAQs specifically, through MPI-like primitives that allow it to be added easily to existing systems. We evaluate the scalability and response time of a prototype on the FABRIC national testbed, with results indicating sufficient scalability for current and near-future DAQs as well as practical response times (under 1 microsecond decision time).

Wolosewicz, A. [IIT, Chicago]↗

Advancing the HERO WEC Through Integrated Modeling, Testing, and Field Deployments

The Hydraulic and Electric Reverse Osmosis Wave Energy Converter (HERO WEC) was developed by the National Laboratory of the Rockies as a modular platform for advancing wave-powered desalination technologies. Designed to operate in either a hydraulic or electric configuration, the system enables direct comparison of mechanical-to-water and electrical-to-water conversion pathways using a single hardware architecture. Deployments in 2022 and 2024 at the Jennette's Pier test site in North Carolina demonstrated freshwater production between 60 and 300 gallons per day, including successful operation in wave heights as low as 0.25 m. A structured evaluation approach combining numerical modeling of hydrodynamic and power take-off response, controlled laboratory testing, and in-ocean field deployments has been used to characterize and refine system performance. Specifically, insights from these efforts are now informing the second-generation HERO WEC (V2) to increase robustness and overall survivability. Changes from the original prototype include improved drivetrain components, refined geometry, enhanced control systems, and design. The HERO WEC platform continues to serve as an open-access research asset supporting broader marine energy and desalination development.

16 TIDAL AND WAVE POWER↗

SMART-COM – Scalable Multi-Agent Adaptive Resolution Tools for Collaborative Outage Management

The purpose of this grant was to conduct scientific research and prototype applications to support NPP outage staff in their adaptive decision-making in efficient scheduling and resource allocation while preventing violation of safety technical specifications. The project contributed to scientific knowledge and engineering methods in (1) user interface design, (2) scheduling optimization and risk estimation, and (2) natural language processing that would benefit the nuclear power plants in minimizing schedule overruns and even unexpected shutdowns. The research team conducted site visits at a test reactor facility and an operating nuclear power plant to gather necessary information and inputs for research and development of a software application to support NPP staff in executing their outages. The final software application consisted of three modules. First, the natural language processing module supports interactive processing of technical documentation to build a database for outage staff to query non-permissible actions on system components. This module can alleviate outage staff from reviewing extensive documentation and minimize violation of technical specifications, especially in time-sensitive situations. Second, the schedule optimization module schedules outage activities and compute risk indices that outperform existing software and current practice. This module can reduce completion time of an outage that typically have too many activities for human to optimize based on current practice that does not apply the latest operations research. Finally, the visualization module presents progress and risk information of the overall outage and individual activities, as well as enabling access to the natural language processing and schedule optimization modules. This module can provide outage staff with situation awareness that are necessary to make risk-informed decisions in response to unexpected events during the execution of an outage.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

The CWS Experiments – An Experimental Study of the Effects of Chlorine on Thermal Neutron Absorption

The Chlorine Worth Study (CWS) experiments consist of layers of Zero Power Physics Reactor plates moderated by high density polyethylene, polyvinyl chloride, and chlorinated polyvinyl chloride with the goal to produce a thermal critical experiment. A thick high density polyethylene reflector surrounds the experiments. Aluminum fuel trays and frames were used to conduct the intrinsic heat generation of the plutonium plates away from the core and out to the top plate and the platen, both acting as heat sinks. The goal of the CWS experiments was to provide benchmark critical experiments that were sensitive to chlorine and matched the sensitivity of criticality safety applications for aqueous chloride operations at PF-4 at Los Alamos National Laboratory. The specific aqueous chloride PF-4 applications were solutions of 30 g/L plutonium, 300 g/L plutonium, and 600 g/L plutonium. The CWS experiments were designed using prototype methods developed by the ARCHIMEDES and EUCLID projects at Los Alamos National Laboratory. The CWS experiments were performed in December of 2021 at the National Criticality Experiments Research Center at the Nevada Nuclear Security Site on the Planet critical assembly. It is intended that the CWS experiments will be evaluated and submitted to the ICSBEP in the future as criticality safety benchmarks.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Design of high-performance guns for the HL-LHC HEL

The High Luminosity LHC project (HL-LHC) foresees the construction and installation of important new equipment to increase the performance of the LHC machine. The Hollow Electron Lens (HEL) is a promising system to control the beam halo. It improves the beam collimation system of the HL-LHC and mitigates possible equipment damage in case of failure scenarios from halo losses. The halo can store up to 30 MJ energy. The specifications for this new device are quite demanding. The source, an electron gun with an annular shaped cathode, must deliver a current up to 5 A. Additionally, this is five times higher than the current in the existing electron lenses in Fermi and Brookhaven national laboratories. This note describes the programme carried out to design and test high-perveance guns equipped with two types of high-performance scandate cathodes. The size of the final gun for the HL-LHC lenses is now considerably smaller than the one of the first prototype, allowing a reduction of diameter and cost of the superconducting magnet system used to steer the electron beam. The tests carried out at FNAL, BVERI and BJUT demonstrated that the developed cathodes fulfil the specifications and can supply a 5 A fully Space Charge Limited (SCL) current.

43 PARTICLE ACCELERATORS↗

Inspecta Technical Report

Sandia National Laboratories (SNL) is in the process of creating Inspecta (International Nuclear Safeguards Personal Examination and Containment Tracking Assistant), an Artificial Intelligence (AI)-powered smart digital assistant (SDA) with robotic capabilities, aimed at enhancing the effectiveness, efficiency, and safety of international nuclear safeguards inspections. This innovative tool is designed to assist inspectors on-site by supporting or automating tasks that are typically mundane, hazardous, or susceptible to errors. In 2021, the development team established the specifications for Inspecta by analyzing International Atomic Energy Agency (IAEA) documents and consulting with former IAEA inspectors and subject matter experts. This process involved aligning in-field inspection tasks with existing commercial or open-source technologies to outline a roadmap for the initial prototype of Inspecta, while also identifying areas needing further research and development. From 2022 – 2024, the focus has shifted to integrating a critical inspection activity, the examination of seals, into an early version of Inspecta. This has involved developing both the software and hardware capabilities necessary for this task. This report outlines the ongoing advancements in Inspecta's functionalities, specifically those supporting the seal examination process.

97 MATHEMATICS AND COMPUTING↗

Exploring the Influence of Linker Substitution and Ratios on Cooperative Framework Flexibility through the Mixed-Linker Approach

Cooperatively flexible metal–organic frameworks that exhibit step-shaped, or Type V-like, adsorption–desorption profiles can lower requisite pressure–temperature swings and thus energy input, necessary for an array of gas storage, delivery, and separations applications. However, such benefits are lost if the pressure threshold of the adsorption and desorption steps at a given temperature does not match the conditions dictated by the application, such as H 2 storage and delivery or olefin–paraffin separations. Unfortunately, the discovery of cooperatively flexible frameworks remains wholly serendipitous and de novo design remains impossible. Accordingly, there is a great need to further our understanding of flexibility such that we can intuitively derivatize known frameworks and, ultimately, design entirely new ones to meet the requisite conditions of energy-consumptive processes. In this work, we demonstrate that the mixed-linker, or multivariate, approach is a powerful tool for the derivation of a known flexible framework, with variances in linker substitution and ratio giving rise to a family wherein significant changes to the step-shaped adsorption–desorption profiles for multiple adsorbates are observed. Specifically, we report 12 isostructural mixed-linker derivatives of CdIF-13 (sod–Cd(benzimidazolate) 2 ) with six point-modified benzimidazole linkers spontaneously synthesized through prototypical solvothermal conditions. Furthermore, each is shown by PXRD to exhibit similar reversible flexibility to CdIF-13 and by TGA and DSC to be similarly thermally stable. Isothermal gas adsorption measurements with N 2 at 77 K, CO 2 at 195 K, and propane at 298 K demonstrate the wide-ranging, adsorbate-dependent effects of linker substitution and ratio, including dramatic reductions in the adsorption threshold pressure, evolution of multiple steps, and complete absence of observable adsorption. Aided by prior crystallographic characterization of CdIF-13, the observed trends were analyzed in an attempt to resolve the influence of linker substitution and ratios on structural behavior. In total, this work illustrates how the mixed-linker approach enables the synthesis and study of a large catalog of functionally modified frameworks, which can help identify the variables that influence flexibility and sorption behavior.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗