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BATPAC--VERSION 5.0

Argonne National Laboratory has worked on electrochemical energy storage for several decades. The focus on lithium-ion chemistries started in the early 1990s, developing new materials, synthesis methods, and performance characterizations. Sponsored by the U.S. Department of Energy, Energy Efficiency and Renewable Energy, Vehicle Technologies Office (DOE-EERE-VTO), Argonne has led with many advances. The experimental activities were complemented with multi-scale modeling that ranged from the atomic to the system (manufacturing processes and automobiles) level. The Battery Performance and Cost (BatPaC) model is a calculation method based on Microsoft¿ Office Excel spreadsheets that have been developed at Argonne for estimating the performance and manufacturing cost of lithium-ion batteries for electric-drive vehicles including hybrid-electrics (HEV), plug-in hybrids (PHEV) and pure electrics. The effort is being funded by the Vehicle Technology Office (VTO), which is part of the Energy Efficiency and Renewable Energy (EERE) office of the U.S. Department of Energy (USDOE). BatPaC was first developed in 2007, was subsequently peer-reviewed, and it has served Argonne researchers and the greater battery community in studying the impact of material properties on performance at the pack level. With further developments, the model now allows the design of cells and battery packs for automotive applications, to meet performance requirements (power, energy, recharge time), and estimates the cost of manufacturing the designed batteries. Since the cost depends on the materials he design, and the manufacturing process, this bottom-up model/tool enables the user to study their effects. Designed or the lithium-ion cell and battery researcher, BatPaC helps answer many questions by being 1.Transparent in the assumptions made and the method of calculation 2.Capable of designing a battery specifically for the requirements of an application 3.Constrained by the physical limitations that govern battery performance 4. A bottom-up calculation approach to account for every cost factors. BatPaC predicts the impact of promising materials (and their properties) on the performance metrics relevant for the different applications. Researchers can use the specific capacities and the half-cell voltages of a particular set of electrode materials to calculate the mass and volume of a cell to develop a model incorporating the properties of all the other materials in the cell and the design of the cell enclosure. These calculations not only reveal the impact of an improved material but also enable researchers to calculate the material properties that would be needed to meet the performance criteria of a full battery pack. With this information, researchers can provide he battery industry with realistic expectations that will help it more successfully advance novel battery technologies an Applications.

AHMED, SHABBIR↗

Node Monitoring as a Fault Detection Countermeasure against Information Leakage within a RISC-V Microprocessor

Advanced, superscalar microprocessors (μP) are highly susceptible to wear-out failures because of their highly complex, densely packed circuit structure and extreme operational frequencies. Although many types of fault detection and mitigation strategies have been proposed, none have addressed the specific problem of detecting faults that lead to information leakage events on I/O channels of the μP. Information leakage can be defined very generally as any type of output that the executing program did not intend to produce. In this work, we restrict this definition to output that represents a security concern, and in particular, to the leakage of plaintext or encryption keys, and propose a counter-based countermeasure to detect faults that cause this type of leakage event. Fault injection (FI) experiments are carried out on two RISC-V microprocessors emulated as soft cores on a Xilinx multi-processor System-on-chip (MPSoC) FPGA. The μP designs are instrumented with a set of counters that records the number of transitions that occur on internal nodes. The transition counts are collected from all internal nodes under both fault-free and faulty conditions, and are analyzed to determine which counters provide the highest fault coverage and lowest latency for detecting leakage faults. We show that complete coverage of all leakage faults is possible using only a single counter strategically placed within the branch compare logic of the μPs.

42 ENGINEERING↗

Transition Metal Blocking Microporous Polymer Separators for Energy-Dense and Long-Lived Li-ion Batteries

A revolution in electric-powered mobility is imminent, catalyzed by breakthroughs in Li-ion battery technology that have dramatically lowered the $/kWh price tag of electrochemical energy storage. Increases in production have also enabled greater penetration in key markets. World-wide registration of new plug-in hybrid electric and battery-only electric vehicles (PHEV and BEV) increased by 70% from 2014 to 2015, and sales of PHEVs and BEVs are predicted to be 35% of all vehicle sales by 2040, reaching 41 million units per year—a 90-fold increase from 2015.1,2 In stride with industry giants such as Tesla, EV manufacturers rely on Li-ion cell Original Equipment Manufacturers (OEMs) for relentless improvements in Li-ion battery technology necessary to drive this bullish market penetration outlook. Advancing energy and power density is critical to alleviating EV-customer range anxiety. Furthermore, strategies to extend battery-pack life beyond 1000 cycles—particularly when operating under aggressive duty cycles—requires fresh perspectives and innovation in cell components.

36 MATERIALS SCIENCE↗

An experimentally validated electro-thermal EV battery pack model incorporating cycle-life aging and cell-to-cell variations

Lithium-ion batteries are used in a wide variety of applications. To meet the power and energy demands of these applications battery packs are composed of hundreds to thousands of cells. The electrical and thermal interactions between cells introduce additional complexity in the pack dynamics. To capture these effects, a battery pack model composed of 192 cells based on a first-generation (2012) Nissan Leaf battery pack is developed in MATLAB/Simulink/Simscape. Here, with this model, we simulate the electrical dynamics (using a first-order equivalent-circuit model), the thermal dynamics (using a first-order lumped-parameter thermal model), and the aging dynamics (using a semi-empirical severity factor-based model) of every cell in the pack and we also create a pack thermal model that explicitly captures the heat exchange between the modules, and the cells contained within, during operation. The models are calibrated and validated, both at the cell and pack level, with experimental data. Two different case studies of this pack model are investigated. In the first case study, an initial, normally-distributed, cell-to-cell capacity variation is introduced and its effect on the pack voltage and module temperatures is studied. In the second case study, we deliberately insert cells with lower than nominal capacity into the pack and we investigate how this type of initial cell-to-cell capacity variation affects the pack’s ability to deliver energy over time. Finally, we also study how parallel-connected cells can reduce the effects of cell-to-cell variations at the expense of increased aging of the pack overall.

25 ENERGY STORAGE↗

Drive Cycles, Battery Pack Scaling, and Usage Considerations for Long-Haul and Regional-Haul Electric Trucks

Electrifying Class-8 heavy-duty trucks presents a promising opportunity to enhance energy efficiency and reduce freight transport costs. Battery electric trucks (BETs), once considered niche, are gaining traction due to advancements in battery technology and cost reductions. However, accurately predicting battery lifespan under realistic usage conditions remains a key challenge. Understanding battery failure mechanisms and their links to design, operation, and management is essential for developers and fleet operators. This study introduces a method to develop simplified, lab-testable dynamic stress test (DST) cycles for regional and long-haul Class-8 BETs, derived from real-world diesel truck usage. These DSTs enable benchmarking of battery technologies, identification of aging stressors, and optimization of battery design, life, and cost. The approach supports evaluation of key metrics such as levelized cost of driving and total cost of ownership, aiding fair comparisons and adoption decisions. We also propose feasible battery pack sizes that meet current driving demands with strategic charging, and a method to scale pack-level DSTs to cell-level cycles for lab-based testing. These tools facilitate tradeoff analysis across battery chemistries, pack sizing, and charging strategies, while offering means to get insights into battery aging under realistic conditions-ultimately supporting informed BET deployment decisions.

25 ENERGY STORAGE↗

Large-Area Periodic Arrays of Atomically Flat Single-Crystal Gold Nanotriangles Formed Directly on Substrate Surfaces

The advancement of nanoenabled wafer-based devices requires the establishment of core competencies related to the deterministic positioning of nanometric building blocks over large areas. Within this realm, plasmonic single-crystal gold nanotriangles represent one of the most attractive nanoscale components but where the formation of addressable arrays at scale has heretofore proven impracticable. In this work, a benchtop process is presented for the formation of large-area periodic arrays of gold nanotriangles. The devised growth pathway sees the formation of an array of defect-laden seeds using lithographic and vapor-phase assembly processes followed by their placement in a growth solution promoting planar growth and threefold symmetric side-faceting. The nanotriangles formed in this high-yield synthesis distinguish themselves in that they are epitaxially aligned with the underlying substrate, grown to thicknesses that are not readily obtainable in colloidal syntheses, and present atomically flat pristine surfaces exhibiting gold atoms with a close-packed structure. As such, they express crisp and unambiguous plasmonic modes and form photoactive surfaces with highly tunable and readily modeled plasmon resonances. The devised methods, hence, advance the integration of single-crystal gold nanotriangles into device platforms and provide an overall fabrication strategy that is adaptable to other nanomaterials.

42 ENGINEERING↗

Experimental and Computational Analysis of NEAMS Pebble Bed Reactors

The Advanced High-Temperature Pebble Bed Reactor concept leverages a particle-based fuel format consisting of discrete spherical graphite pebbles arrayed in a packed bed architecture. Thermal regulation achieved via flow of gas (e.g., helium) or liquid (e.g., molten salt) coolants through the void spaces between pebbles in the bed (characteristic pebble diameters: ~ 6 cm, gas cooled; ~ 3 cm, liquid cooled). This design is of interest owing to inherent advantages including passive safety features and highly efficient heat transfer characteristics that enable high power densities to be achieved. Fully leveraging these advantages requires a fundamental understanding of the complex coolant flow structure within the pebble-shaped fuel bed. Unfortunately, complexities associated with non-invasively probing the micro-scale flow phenomena within the complex network of void spaces between pebbles have hindered efforts to characterize the underlying transport phenomena. Without this fundamental foundation, it becomes challenging to rationally construct macroscopic transport models based upon volume averages of micro-scale parameters that accurately capture the observed flow behavior. Consequently, this lack of fundamental knowledge has limited previous work to coarse comparisons between theory and extremely limited experimental data. Moreover, these comparisons have been made only in terms of integral or macroscopic results. Therefore, multipoint measurements with a high level of spatial and temporal resolution are critically needed to fully map the complex flow patterns and to provide data at high spatial density to permit accurate volume averaging in the pebble bed. For this project, we performed a coordinated experimental and computational effort to quantitatively map the full-field velocity and temperature fields in the interstitial spaces within the pebble bed. The major accomplishments of this project included the important knowledge acquired for the flow mixing and heat transfer in the interstitial pore scales, the effects of flow mixing in the near-wall and far-wall regions, and the by-pass flows of pebble bed systems. The produced high-resolution experimental data (not broadly available in existing literature) were then used for the numerical studies enabling the refinement and validation of standard simulation tools (Nek5000).

42 ENGINEERING↗

Enhancement of Carbon Capture Reactor Performance (Final Technical Report)

Significant challenges are still present in post-combustion CO 2 capture and new technologies and advanced components are needed to significantly advance the deployment of CO 2 capture for natural gas combined cycle (NGCC) plants. Critical elements of CO 2 capture that still need to be addressed include how to increase CO 2 mass transfer in the absorber column with liquid to gas ratios of <1.2, while reducing the size of the absorber column to reduce capital costs. Research involving chemical mechanism with design, synthesis, and assembly of materials with targeted functionally were combined with advanced additive manufacturing techniques towards development of enhanced CO 2 capture reactors that can lead to safe, reliable, and low-cost carbon capture technologies. The objective of the project was to develop and test novel carbon capture materials and reactor components that contribute to increased CO 2 mass transfer through increased turbulent gas-liquid interface and improved solvent wetting within the absorber. A technoeconomic analysis (TEA) was completed showing how the proposed technology decreases capital costs by reducing the size of the absorber column and the amount of packing required for high CO 2 capture rates. A technology maturation plan (TMP) was also developed to describe the current technology readiness levels (TRL) and outline additional research and development (R&D) needed to further develop these advanced components for NGCC CO 2 capture plants. The successful completion of this project has shown a pathway to reduce the absorber size and associated construction costs of post-combustion NGCC CO 2 capture systems at 97% capture and promote the utilization of abundant natural gas for production of reliable electricity.

20 FOSSIL-FUELED POWER PLANTS↗

Singlet fission

Singlet fission (SF) is a process whereby a photo-excited singlet exciton spontaneously splits into lower energy triplet excitons. This process has been known to occur in select organic materials for over 50 years but in the past was viewed as a curiosity and not as a problem worthy of focused attention. Over the past decade, this viewpoint has changed as the promising use of SF to improve photovoltaic efficiency has spurred vast activity, which has revealed the richness of the phenomenon. Currently, our understanding of the role played by various bright and dark states and their couplings to vibrations and to each other and by chemical composition and packing, among other factors, has enabled a large increase in the number of viable SF systems as well as a far deeper understanding of the process itself. These advances have allowed for the demonstration of proof-of-concept increases in the solar cell efficiency via the use of SF materials in simple tandem cells and as sensitizers in conjunction with conventional photovoltaics. Indeed, concepts surrounding the field have now invaded other fields, with a prominent example being the use of photon upconversion associated with triplet–triplet fusion (the inverse process to SF) in organic chemistry and photocatalysis. The 23 research articles in this special topic showcase recent cutting-edge advances in the field and highlight the diverse new directions being explored in the field of SF.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Distributed sustainable metals production: opportunities for intensifying separations & alternative feedstocks

Meeting the increased demand for rare earth elements and beyond primary mined ore. Secondary sources like phosphogypsum, coal fly ash, used nuclear fuel, and electronic waste are concentrated sources of critical minerals. One strategy for a resilient supply chain is to decentralize sourcing and hydrometallurgical processing of metals. Rotating packed beds (RPBs) for solid-phase extraction and liquid-liquid extraction are gaining momentum for their ability to increase process throughput by 5-10x the state of the art. In conclusion, this review discusses advances in hydrometallurgical RPB processes and opportunities for implementation in distributed metals production.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Simulation of the supercritical CO 2 recompression Brayton power cycle with a high-temperature regenerator

The supercritical carbon dioxide (sCO 2 ) recompression Brayton cycle promises higher efficiency and lower capital cost than traditional steam Rankine power cycles. However, achieving high efficiency requires large, highly effective recuperators. Regenerators may be a low-cost alternative to printed circuit and micro-tube heat exchangers for recuperation in sCO 2 power cycles. Regenerators are a periodic heat exchanger in which thermal energy is extracted from the hot stream, stored in solid media, and then released to the cold stream at a later time. Fixed bed regenerators with valves to direct fluid are the preferred method for implementing regenerators in power cycles, but the inherently transient nature of these systems has not been characterized for this application. This study presents the simulation of a high-temperature regenerator within a 10 MWe sCO 2 recompression Brayton cycle. A transient, one-dimensional regenerator model presented in a previous study is used to simulate the regenerator. Dynamic heat exchanger models are also developed for the precooler, low-temperature recuperator, and primary heat exchanger, and the compressors and the turbine are modeled with off-design performance maps. We assess two regenerator-valve design options; one for fast switching, and one for reduced flow rate fluctuations. System simulation finds that both designs see significant fluctuations in turbomachinery flow rate, turbomachinery and system power, and regenerator discharge process outlet temperature. While designing the regenerator-valve subsystem for lower fluctuations is possible, the regenerator cold discharge temperature and net power still fluctuate by ±77.6°C and 6%, respectively. Increasing buffer volume is not effective at sufficiently reducing these fluctuations, but adding a packed bed in between the regenerator and the primary heat exchanger can reduce regenerator discharge process outlet temperature fluctuations to 6.4°C. Further reductions could be possible by increasing the size of this packed bed.

42 ENGINEERING↗

Early Detection of Li-Ion Battery Thermal Runaway Using Commercial Diagnostic Technologies

The rate of electric vehicle (EV) adoption, powered by the Li-ion battery, has grown exponentially; largely driven by technological advancements, consumer demand, and global initiatives to reduce carbon emissions. As a result, it is imperative to understand the state of stability (SoS) of the cells inside an EV battery pack. That understanding will enable the warning of or prevention against catastrophic failures that can lead to serious injury or even, loss of life. The present work explores rapid electrochemical impedance spectroscopy (EIS) coupled with gas sensing technology as diagnostics to monitor cells and packs for failure markers. These failure markers can then be used for onboard assessment of SoS. Experimental results explore key changes in single cells and packs undergoing thermal or electrical abuse. Rapid EIS showed longer warning times, followed by VOC sensors, and then H 2 sensors. While rapid EIS gives the longest warning time, with the failure marker often appearing before the cell vents, the reliability of identifying impedance changes in single cells within a pack decreases as the pack complexity increases. This provides empirical evidence to support the significant role that cell packaging and battery engineering intricacies play in monitoring the SoS.

25 ENERGY STORAGE↗

< c+a > dislocations in {101 - 2} twins in Mg: A kinematic and energetic requirement

Consideration of published TEM and molecular dynamics studies of interactions between matrix dislocations and {101¯2} twin boundaries (TB) in hexagonal close packed metals inspires a hypothesis regarding the formation of dislocations with < c+a > Burgers vectors inside the twins. It was previously reported that when basal < a > dislocations from the matrix are swept by an advancing TB, they are converted into partial dislocations bounding basal I 1 stacking faults (SFs) within the twin. In the present work, we show that this dislocation configuration near TB renders it energetically favorable for a pair of partial dislocations to constrict into a dislocation within the twin. New in situ TEM observations confirm this hypothesis by revealing long < c+a > dislocation dipoles terminated by the TB at one end and by I1 SFs within the twin at the other end. Finally, the resulting near-screw < c+a > dislocation dipoles are observed to be glissile, enabling self-annihilation in some circumstances. Thus, rather than requiring a high energy dislocation pile-up to press two < a > dislocations through a TB into a single < c+a > dislocation, it is demonstrated that < c+a > dislocations naturally form, within {101¯2} twins in Mg, as TB migrates into a matrix, which inevitably contains dislocations with < a > Burgers vectors. Furthermore, these observations help to explain how the twins themselves may subsequently deform and why they may be particularly vulnerable to plastic, shear localization.

36 MATERIALS SCIENCE↗

Modeling Advanced Strippers for CO2 Capture from Gas-Fired Power Plants using Aqueous Piperazine

Energy performance of 5 m piperazine was evaluated with an advanced stripper at the pilot scale, accounting for heat loss. Modeling studies indicated that heat loss at locations other than the heat source impacted the heat duty. For strippers with excess packing, the column was the most important source of heat loss, and values as low as 0.03 GJ/hr can cause pinch and reabsorption of CO2. Solvents like 5 m PZ are more affected by heat loss in the column due to a top-side temperature pinch at high lean loading. Heat loss impacts NGCC CO2 capture more than coal-based CO2 capture. Surface temperature measurements pilot plants showed that heat loss was 50-75% controlled by natural convection. Measured heat loss was correlated with steam flowrate and wind speed and ranged from 8126 to 219668 Btu/hr, representing 35% of the measured heat rate on average. Net heat duty linearly varied with CO2 removal at low lean loading and was similar for coal and NGCC conditions at fixed removal. At 90% removal, net heat duty was about 2.5 GJ/t with 4 and 12% CO2 in the flue gas. 7 At NGCC conditions, strippers with finite packing can benefit from a flashing feed to the top of the column by using a hot bypass. A flashing feed was linked to a reduction in irreversibility of the stripper from temperature driving forces. It also reduces heat duty by up to 6% at fixed packing height and reduces packing requirement for a fixed steam heater size compared to a warm bypass. Lean loading and lean solvent rate were effective handles to maximize profitability of a fixed stripper design at low gas price. High ambient temperature operation can benefit from low pressure stripping to about 0.18 lean loading at 150 ℃ to maintain the cyclic capacity at reduced rich loading. At low gas price, the capture plant was able to maximize profitability even with a high heat duty of 2.7-3.1 GJ/t at a lean loading of 0.2-0.22 mol/mol. Heat recovery by partial water vapor condensation in a gas-liquid exchanger can be replaced by a direct contact condenser (DCC). The DCC improved gas cooling and reduced heat duty compared to the CO2 exchanger at 0.2 lean loading. The DCC when used with a 150 ℃/5.5 bar stripper can reduce the cost of capture compared to the base case by $3- 4/tonne at 15 ft of packing (optimum) but increases cost of capture by $6/tonne with a 120 ℃/2 bar stripper and 10 ft of packing (optimum). The DCC can work effectively with a solvent with a high heat of absorption and thermal stability.

Suresh Babu, Athreya↗

Advances in Singlet Fission Chromophore Design Enabled by Vibrational Spectroscopies

Singlet fission leads to the formation of two separate triplet T 1 excitons from an initial singlet S1 exciton through 1 (TT) and 1 (T...T), multiexcitonic intermediates that retain singlet character. Its ability to achieve external quantum efficiencies higher than 100% made it an attractive candidate for optoelectronic device applications. However, singlet fission has not been applied widely despite having been investigated by a myriad of spectroscopic methods, in part due to our poor understanding of how to optimize molecular structure and packing in chromophores well-suited to large-scale production. Vibrational spectroscopies provide a solution, because they directly probe nuclear motions, allowing us to monitor evolving structural changes in molecules undergoing singlet fission, thus providing us with roadmaps to design molecules suitable for optoelectronic applications. Furthermore, this Perspective reviews the contributions and analyzes the future directions of vibrational spectroscopies to the advancement in our knowledge about the mechanisms and rational designing of chromophores undergoing efficient singlet fission.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

New Constraints on the Melting Temperature and Phase Stability of Shocked Iron up to 270 GPa Probed by Ultrafast X-Ray Absorption Spectroscopy

Studying the properties and phase diagram of iron at high-pressure and high-temperature conditions has relevant implications for Earth’s inner structure and dynamics and the temperature of the inner core boundary (ICB) at 330 GPa. Also, a hexagonal-closed packed to body-centered cubic (bcc) phase transition has been predicted by many theoretical works but observed only in a few experiments. The recent coupling of high-power laser with advanced x-ray sources from synchrotrons allows for novel approaches to address these issues. Here, we present a study on shock compressed iron up to 270 GPa and 5800 K probed by single-pulse (100 ps FWHM) x-ray absorption spectroscopy (XAS). Based on the analysis of the XAS spectra, we provide structural identification and bulk temperature measurements along the Hugoniot up to the melting. These results rule out the predicted transition to a high-temperature bcc phase and allow one to discriminate among existing equations of state models and melting curves. In particular, we report the first bulk temperature measurement in shock compressed iron on the melting plateau at 240(20) GPa and 5345(600) K. The melting curve resulting from our work extrapolates to a temperature of 6202(514) K at 330 GPa and represents a refined upper bound for the ICB temperature. Published by the American Physical Society 2024

Balugani, S.↗

Battery Performance and Cost Model (BatPaC) Version 6.0

SF-26-016 The Battery Performance and Cost model (BatPaC) is a calculation method based on Microsoft Excel spreadsheets that has been developed at Argonne for estimating the performance and manufacturing cost of lithium-ion batteries for electric-drive vehicles including hybrid-electrics (HEV), plug-in hybrids (PHEVs) and pure electrics. BatPaC was first developed in 2007, was subsequently peer reviewed, and it has served Argonne researchers and the greater battery community in studying the impact of material properties on performance at the pack level. BatPaC has been updated and re-released multiple times since its original public release in 2011. This current version is BatPaC 6.0, which contains additional functionality needed to handle advances in automotive batteries, like the use of lithium metal and silicon anodes and the need to accommodate cell expansion and apply high levels of pressure.

KNEHR, KEVIN [Argonne National Laboratory (ANL), A↗

State-of-the-Art Organic- and Inorganic-Based Hollow Fiber Membranes in Liquid and Gas Applications: Looking Back and Beyond

The aggravation of environmental problems such as water scarcity and air pollution has called upon the need for a sustainable solution globally. Membrane technology, owing to its simplicity, sustainability, and cost-effectiveness, has emerged as one of the favorable technologies for water and air purification. Among all of the membrane configurations, hollow fiber membranes hold promise due to their outstanding packing density and ease of module assembly. Herein, this review systematically outlines the fundamentals of hollow fiber membranes, which comprise the structural analyses and phase inversion mechanism. Furthermore, illustrations of the latest advances in the fabrication of organic, inorganic, and composite hollow fiber membranes are presented. Key findings on the utilization of hollow fiber membranes in microfiltration (MF), nanofiltration (NF), reverse osmosis (RO), forward osmosis (FO), pervaporation, gas and vapor separation, membrane distillation, and membrane contactor are also reported. Moreover, the applications in nuclear waste treatment and biomedical fields such as hemodialysis and drug delivery are emphasized. Subsequently, the emerging R&D areas, precisely on green fabrication and modification techniques as well as sustainable materials for hollow fiber membranes, are highlighted. Last but not least, this review offers invigorating perspectives on the future directions for the design of next-generation hollow fiber membranes for various applications. As such, the comprehensive and critical insights gained in this review are anticipated to provide a new research doorway to stimulate the future development and optimization of hollow fiber membranes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗