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At least 847 records · Page 47

DECOVALEX-2023: Task F1 Final Report

DECOVALEX-2023 Task F is a comparison of models and methods for post-closure performance assessment (PA) of a deep geologic repository for radioactive waste. The general aims of Task F are to build confidence in the models, methods, and software used for PA and to stimulate additional research and development in PA methodologies. The task objectives are to motivate development of PA modelling skills and capabilities, to examine the influence of model choices on calculated repository performance, and to compare the uncertainties introduced by model choices to other sources of uncertainty. Task F involves no actual experiment or site. It is a PA modelling exercise that requires the conceptual development of hypothetical repository designs and geologic settings. Because three of the teams were interested in salt and the rest of the teams were interested in crystalline rock, Task F was split into two branches: Task F1 for crystalline rock and Task F2 for salt. This report is for Task F1, crystalline rock. Teams from seven countries (Canada, Czech Republic, Germany, Korea, Sweden, Taiwan, and United States) participated in Task F1. The teams worked together to define the features, events, and processes of the reference case repository and established a set of performance measures. In addition, they defined a set of benchmark problems designed to test and compare modelling capabilities for fracture flow and transport at different scales. The repository design and benchmark problems are documented in a Task Specification that evolved over time as the group honed the specifications. The benchmark problems verified that each team can aptly model flow and transport in fractured media in 1-, 2-, and 3-dimensions. Two general approaches were used for the 3-dimensional benchmarks: discrete fracture network (DFN) and equivalent continuous porous medium (ECPM). DFN modelling involves explicit meshing of each fracture while ECPM modelling aims to capture the effective porosity and directional permeability of each cell in a space-filling mesh as affected by intersecting fractures. In some models, a combination of the two is used, i.e., DFN for large known fractures and ECPM for the rest of the domain. Transport is solved by using either the advection-dispersion equation or particle tracking. Although some variation is observed among model breakthrough curves in the benchmark problems, there is strong agreement in breakthrough behaviour up to at least the 75 th percentile for all benchmarks. At the 90 th percentile, breakthrough results show larger differences, suggesting several models retain substantially higher fractions of tracer in regions of slower moving water. In addition to the flow and transport benchmarks, several teams completed the source term benchmark, verifying capabilities for modelling radionuclide decay and ingrowth, waste package breach, instant release fractions, fuel matrix degradation rates, and radionuclide solubility limitations. The reference case is conceptualized as a generic spent fuel repository at a depth of 450 m in fractured crystalline rock. The repository has 50 parallel backfilled drifts, each with 50 deposition holes 6 m apart. Each deposition hole contains a 4-PWR waste package and bentonite buffer. The rock domain is 5 km in length, 2 km in width, and 1 km in depth. It has 6 deterministic fractured deformation zones and a multitude of stochastic fractures. Teams generally used the ECPM approach for the entire rock or a hybrid approach in which the deterministic fracture zones are modelled with a DFN and the rest of the rock is modelled by ECPM. Of the reference case problems specified, only the results of the initial reference case problem are compared in this report. The initial problem focuses on transport from the deposition holes to the surface, i.e., it neglects waste package performance. Tracers are released at all waste package locations at time zero and tracked for their releases to the near field and ground surface. The water fluxes calculated at the ground surface entry and exit regions of the domain are similar for all models except for two that have considerably lower fluxes. For tracer transport, large differences are observed among models in the magnitude of tracer transported. Much of the difference appears to be due to how the repository is implemented and hence the different degrees of repository simplification. Models that exclude the drifts, buffer, and backfill from the domain tend to show greater release of tracers and radionuclides from the repository. The initial study presented here indicates that major differences in modelling important processes within the repository (e.g., diffusion through buffer and backfill) can produce broadly different release and transport results, especially when those processes are excluded. Even for the models that included all specified features, events, and processes, the results show significant differences and demonstrate the importance of examining multiple modelling approaches in performance assessment. The differences in results observed in this study are expected to motivate teams to either increase complexity in future versions of the reference case models or to improve methods to account for the effects of simplified features and processes. Either way, future improvements in these models are expected to produce results that more closely agree.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

B—N–Bond–Embedded Triplet Terpolymers with Small Singlet–Triplet Energy Gaps for Suppressing Non–Radiative Recombination and Improving Blend Morphology in Organic Solar Cells

Suppressing the photon energy loss (E loss ), especially the non-radiative loss, is of importance to further improve the device performance of organic solar cells (OSCs). However, typical π-conjugated semiconductors possess a large singlet–triplet energy gap (ΔE ST ), leading to a lower triplet state than charge transfer state and contributing to a non-radiative loss channel of the photocurrent by the triplet state. Herein, a series of triplet polymer donors are developed by introducing a BNIDT block into the PM6 polymer backbone. Further, the high electron affinity of BNIDT and the opposite resonance effect of the B—N bond in BNIDT results in a lowered highest occupied molecular orbital (HOMO) and a largely reduced ΔE ST . Moreover, the morphology of the active blends is also optimized by fine-tuning the BNIDT content. Therefore, non-radiative recombination via the terminal triplet loss channels and morphology traps is effectively suppressed. The PNB-3 (with 3% BNIDT):L8-BO device exhibits both small ΔE ST and optimized morphology, favoring more efficient charge transfer and transport. Finally, the simultaneously enhanced V oc of 0.907 V, J sc of 26.59 mA cm –2 , and FF of 78.86% contribute to a champion PCE of 19.02%. Therefore, introducing B—N bonds into benchmark polymers is a possible avenue toward higher-performance of OSCs.

36 MATERIALS SCIENCE↗

Benchmark Study Matrix for Microreactor Geometries Relevant to Multiple Developers

A benchmark study was developed that include design, development, manufacturing, and performance measurement of agnostic reactor relevant geometries to support industry’s adoption of advanced manufacturing in a variety of structures. A matrix of five microreactor component geometries, specifically based on the recent feasibility study on a Marvel microreactor liner, was developed and the Pacific Northwest National Laboratory team initiated one material/process combination, namely 316H using laser powder directed energy deposition (DED). Although the benchmark starts initially with simplistic cubical and cylindrical forms, it builds up to a mock-up of a non-proprietary design that can demonstrate a variety of features potentially useful for presenting knowledge to specific designers of microreactors and for the matter also for other reactor type designers. The initial cubical and cylindrical forms are initial steps to obtain surface features and dimensional responses to the identified process parameters to be used in the non-proprietary design mockup.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Verification of the Uniformly-Ordered Binary Decision Algorithm in Correlated-Benchmark Whisper Calculations

Whisper is a nuclear criticality safety code package that aids analysts in validation exercises by computing upper subcritical limits (USL) for applications of interest. To obtain statistically meaningful, significant, and conservative USLs, the analyst must ensure that Whisper selects a sufficient number of benchmarks that are neutronically similar to the application. Many of the available benchmarks are correlated but are currently treated as independent, leading to an artificially small sample size, as their individual information contributions will be overestimated. To aid the analyst in obtaining a sufficient sample size, prior work [2] demonstrated application of the Uniformly-Ordered Binary Decision (UOBD) algorithm in adjusting benchmark weights to account for benchmark correlations. This work provides verification of the Whisper implementation and considers the impact of updated benchmark correlations compared to those available previously. We demonstrate that the UOBD algorithm performs as expected with an analytic example. With HEU-SOL-THERM-001 cases 1 through 10 as the applications, we compare the USLs computed with benchmark correlations available in the Whisper 1.1 release only to those computed with additional benchmark correlations from DICE 2023 and demonstrate substantive differences.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Development of Innovative Non-Concentrated Alloy (NCA) Fuel Cladding for Advanced Nuclear Reactors

As the nuclear energy sector advances toward next-generation reactors, the need for high-performance fuel cladding materials has become increasingly urgent. Traditional alloys like zirconium and stainless steel are reaching their performance limits under higher temperatures, more corrosive coolants, and extended irradiation. This report presents the development of a new class of fuel cladding materials based on Non-Concentrated Alloys (NCAs) ? multi-element systems designed to deliver enhanced mechanical strength, corrosion resistance, and radiation tolerance. Through a combination of computational modeling (Computer Coupling of Phase Diagrams and Thermochemistry: CALPHAD), simulation-guided alloy selection, and experimental fabrication via arc melting and spark plasma sintering (SPS), three strategic alloy design paths were explored: (1) FeCrAl-based NCAs, (2) refractory-lean neutron-efficient alloys, and (3) equimolar high-entropy compositions. Microstructural analysis confirmed the formation of stable body-centered cubic BCC_A2 phases, while mechanical testing demonstrated hardness values significantly exceeding those of conventional cladding materials. The results highlight the tunability of NCA systems and their potential for balancing strength and ductility ? a critical consideration for in-reactor performance. Looking forward, future work will focus on thermomechanical optimization, CALPHAD refinement, and benchmarking against industry standards to enable scalable deployment. This work not only advances the science of nuclear materials but also supports broader goals in nuclear safety, performance, and nuclear energy innovation.

36 - MATERIALS SCIENCE↗

Defining and applying an electricity demand flexibility benchmarking metrics framework for grid-interactive efficient commercial buildings

Building demand flexibility (DF) research has recently gained attention. To unlock building DF as a predictable grid resource, we must establish a quantitative understanding of the resource size, performance variability, and predictability based on large empirical datasets. Researchers have proposed various sets of theoretical metrics to measure this performance. Some metrics have been applied to simulation results, but most fall short of exploring the complexities in real building applications. There are practical metrics used in individual demand response field studies but they alone cannot fulfil the job of DF benchmarking across a diverse group of buildings. The electrical grid's geographically diverse and changing nature presents challenges to comparing building DF performance measured under different conditions (i.e., benchmarking DF). To address this challenge, a novel DF benchmarking framework focused on load shedding and shifting is presented; the foundation is a set of simple, proven single-event metrics with attributes describing event conditions. These enable benchmarking and visualization in different dimensions for identifying trends that represent how these attributes influence DF. To test its feasibility and scalability, the DF framework was applied to two case studies of 11 office buildings and 121 big-box retail buildings with demand response participation data. Furthermore, these examples provided a pathway for using both building level benchmarking and aggregation to extract insights into building DF about magnitude, consistency, and influential factors. Potential applications of the framework and real-world values have been identified for grid and building stakeholders.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Computing Bottleneck Structures at Scale for High-Precision Network Performance Analysis

The Theory of Bottleneck Structures is a recently-developed framework for studying the performance of data networks. It describes how local perturbations in one part of the network propagate and interact with others. This framework is a powerful analytical tool that allows network operators to make accurate predictions about network behavior and thereby optimize performance. Previous work implemented a software package for bottleneck structure analysis, but applied it only to toy examples. In this work, we introduce the first software package capable of scaling bottleneck structure analysis to production-size networks. Here, we benchmark our system using logs from ESnet, the Department of Energy's high-performance data network that connects research institutions in the U.S. Using the previously published tool as a baseline, we demonstrate that our system achieves vastly improved performance, constructing the bottleneck structure graphs in 0.21 s and calculating link derivatives in 0.09 s on average. We also study the asymptotic complexity of our core algorithms, demonstrating good scaling properties and strong agreement with theoretical bounds. These results indicate that our new software package can maintain its fast performance when applied to even larger networks. They also show that our software is efficient enough to analyze rapidly changing networks in real time. Overall, we demonstrate the feasibility of applying bottleneck structure analysis to solve practical problems in large, real-world data networks.

benchmark↗

Adaptive variational quantum minimally entangled typical thermal states for finite temperature simulations

Scalable quantum algorithms for the simulation of quantum many-body systems in thermal equilibrium are important for predicting properties of quantum matter at finite temperatures. Here we describe and benchmark a quantum computing version of the minimally entangled typical thermal states (METTS) algorithm for which we adopt an adaptive variational approach to perform the required quantum imaginary time evolution. The algorithm, which we name AVQMETTS, dynamically generates compact and problem-specific quantum circuits, which are suitable for noisy intermediate-scale quantum (NISQ) hardware. We benchmark AVQMETTS on statevector simulators and perform thermal energy calculations of integrable and nonintegrable quantum spin models in one and two dimensions and demonstrate an approximately linear system-size scaling of the circuit complexity. We further map out the finite-temperature phase transition line of the two-dimensional transverse field Ising model. Finally, we study the impact of noise on AVQMETTS calculations using a phenomenological noise model.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Preliminary Chlorine Worth Study Benchmark Evaluation

The Chlorine Worth Studies (CWS) experiments with polyvinyl chloride (PVC with chemical formula (C 2 H 3 Cl) n ), chlorinated polyvinyl chloride (CPVC with chemical formula (C 9 H 11 Cl 7 ) n ), and high density polyethylene (HDPE with chemical formula (CH 2 ) n ) were a series of measurements performed at the National Criticality Experiments Research Center (NCERC). The purpose of the CWS experiments was to perform integral experiments that were highly sensitive to the thermal 35 Cl(n,γ) reaction and matched the sensitivities of aqueous chloride operations at the plutonium facility at Los Alamos National Laboratory (LANL). The CWS experiments were performed on the Planet critical assembly machine at NCERC and utilized weapons grade plutonium (WGPu) plates as fuel. The design process and design of the CWS experiment were discussed previously. This paper discusses the benchmark evaluation of the experiment, intended for the International Criticality Safety Benchmark Evaluation Project (ICSBEP). Criticality calculations were performed with MCNP version 6.3. Results presented here are preliminary, as the benchmark has not yet been submitted to the ICSBEP.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Definitive Assessment of the Accuracy, Variationality, and Convergence of Relativistic Coupled Cluster and Density Matrix Renormalization Group in 100-Orbital Space

Accuracy, variationality, and convergence underpin the reliability of modern electronic structure methods, yet definitive benchmarks in the relativistic regime remain elusive due to the absence of numerically exact full configuration interaction (CI) references. Recent algorithmic advances in the CI framework, enabled by the small-tensor-product (STP) decomposition approach, have dramatically extended the tractable size of the configuration space, making numerically exact CI calculations feasible in large active spaces previously beyond reach. In this paper, we employ the recently developed STP-CI framework to perform large-scale numerically exact CI calculations and directly benchmark relativistic coupled cluster and density matrix renormalization group methods. Definitive benchmarking of approximate relativistic electronic structure methods is ensured through the application of the gap theorem, which provides rigorous error bounds on the CI reference and establishes a controlled standard for assessing accuracy, variationality, and convergence.

Chemical calculations↗

Impacts of benchmarking choices on inferred model skill of the Arctic–Boreal terrestrial carbon cycle

Abstract Land surface models require continuous validation against observations to improve and reduce simulation uncertainty. However, inferred model performance can be heavily influenced by subjective choices made in the selection and application of observational data products. A key area often misrepresented by models is the Arctic–Boreal region, which is a potential tipping point region in Earth’s climate system due to large permafrost carbon stocks that are vulnerable to release with climate warming. We use the International Land Model Benchmarking (ILAMB) framework to evaluate how the model skill of TRENDY-v9 models varies based on the choice of observational-based benchmark and how benchmarks are applied in model evaluation. This analysis uses global datasets integrated into ILAMB and new, regionally-specific observational products from the Arctic–Boreal Vulnerability Experiment. Our results cover the overall time period of 1979–2019 and show that model scores can vary substantially depending on the data product applied, with higher model scores indicating better model performance against observations. The lowest model scores occur when benchmarked against regional, compared to global, datasets. We also evaluate observed and modeled functional relationships between ecosystem respiration and air temperature and between gross primary production and precipitation. Here, we find that the magnitude and shape of the responses are strongly impacted by the choice of observational dataset and the approach used to construct the functional relationship benchmark. These results suggest that model evaluation studies could conclude a false sense of model skill if only using a single benchmark data product or if not applying regional data products when performing a regional model analysis. Collectively, our findings highlight the influence of benchmarking choices on model evaluation and point to the need for benchmarking guidelines when assessing model skill.

Poe, Jeralyn (ORCID:0000000318495278)↗

High-Resolution Simulations of Geological CO 2 Injection: Application to the SPE11 Benchmark

Geological carbon sequestration (GCS) will play a critical role in decarbonization and in facilitating the transition to clean energy systems. Because CO 2 is highly mobile, ensuring its safe and permanent injection into subsurface geological formations involves monitoring over larger spatial domains and longer time periods than is typical for hydrocarbon reservoirs. This can benefit from simulation tools capable of modeling key CO 2 trapping mechanisms, particularly those optimized for speed and scalability on high-performance computing systems. Using isothermal versions of the SPE11B and SPE11C benchmark cases, we conduct a mesh refinement study simulating CO 2 injection into kilometer-scale rock formations at centimeter resolution with the GEOS open-source simulation framework. We focus on how mesh refinement improves the accuracy of convective mixing in both 2D and 3D simulations. The computational costs associated with achieving a converged solution highlight the need for predictive upscaling techniques. A systematic performance scaling analysis—including both central processing unit (CPU) and graphics processing unit (GPU) architectures—complements the “Results” section.

Geosciences↗

Validation Data for Benchmarking Wire Arc Additive Manufacturing Process Simulations

Residual stresses cause geometric distortion and affect mechanical performance of additively manufactured structures, yet they are notoriously difficult to assess and predict. Distortion (warpage) can drive parts outside dimensional tolerance limits, leading to part rejection or rework. For parts that meet tolerance, locked-in residual stress fields can affect structural integrity during operation, particularly subcritical cracking by fatigue, creep, or corrosion. This work develops benchmark data for a common additive manufacturing process (Wire Arc Additive Manufacturing) that can be applied for calibration and validation of physical process models that predict residual stress fields. The work includes design of two different samples of differing geometry, detailed manufacturing records for a set of physical samples, and an extensive set of residual stress measurement data developed using two diverse techniques (the contour method and neutron diffraction). An initial application of the work is also reported, where a modeling challenge was issued to secure residual stress model predictions from two independent laboratories that were blind to residual stress measurement data. These initial blind residual stress predictions show significant discrepancies relative to the measurement data, illustrating the potential value of the underlying validation data. An open repository for this work, including the sample designs, manufacturing process records, and the residual stress data, is also provided for future application in non-blind validation efforts.

36 MATERIALS SCIENCE↗

Reduced order modeling for flow and transport problems with Barlow Twins self-supervised learning

Abstract We propose a unified data-driven reduced order model (ROM) that bridges the performance gap between linear and nonlinear manifold approaches. Deep learning ROM (DL-ROM) using deep-convolutional autoencoders (DC–AE) has been shown to capture nonlinear solution manifolds but fails to perform adequately when linear subspace approaches such as proper orthogonal decomposition (POD) would be optimal. Besides, most DL-ROM models rely on convolutional layers, which might limit its application to only a structured mesh. The proposed framework in this study relies on the combination of an autoencoder (AE) and Barlow Twins (BT) self-supervised learning, where BT maximizes the information content of the embedding with the latent space through a joint embedding architecture. Through a series of benchmark problems of natural convection in porous media, BT–AE performs better than the previous DL-ROM framework by providing comparable results to POD-based approaches for problems where the solution lies within a linear subspace as well as DL-ROM autoencoder-based techniques where the solution lies on a nonlinear manifold; consequently, bridges the gap between linear and nonlinear reduced manifolds. We illustrate that a proficient construction of the latent space is key to achieving these results, enabling us to map these latent spaces using regression models. The proposed framework achieves a relative error of 2% on average and 12% in the worst-case scenario (i.e., the training data is small, but the parameter space is large.). We also show that our framework provides a speed-up of $$7 \times 10^{6}$$ 7 × 10 6 times, in the best case, and $$7 \times 10^{3}$$ 7 × 10 3 times on average compared to a finite element solver. Furthermore, this BT–AE framework can operate on unstructured meshes, which provides flexibility in its application to standard numerical solvers, on-site measurements, experimental data, or a combination of these sources.

97 MATHEMATICS AND COMPUTING↗

Simulating energy performance of buildings: a study using eQUEST and Energy Star ® portfolio manager

Commercial buildings consume significant energy in the United States and exhibit high potential for energy use reduction through retrofits. Benchmarking and energy simulation are well established tools in the industry to identify potential improvements and measure performance. Analysis to identify most sensitive retrofit parameters to energy performance can optimize investment and available energy savings. Presented study demonstrates methodology using a static model to determine sensitivity of building design and retrofit parameters with respect to energy performance. Calibrated simulation energy models (eQUEST) of two distribution centers (A, B) are presented. A fractional factorial analysis is conducted on retrofit parameters of efficiency measures targeting the highest energy consumers, and the results are benchmarked using Energy Star® Portfolio Manager. A custom Microsoft Excel® based simulation model is created to simulate occupancy levels, lighting, plug loads, and other equipment used in various spaces throughout the day. For Building A, efficient lighting was the most influential parameter for energy savings, carbon savings and benchmarking score; whereas, for Building B, HVAC efficiency was most influential for energy and demand controlled ventilation and economizers was most influential for benchmarking score. While retrofit projects can save energy and carbon emissions, variation in source-site ratios and state grid emissions, benchmarking scores may not always reflect equivalent improvement. State grid emissions factors, natural gas composition are difficult to model and hence not considered in this study. In conclusion, the synergistic analysis presented, emphasizes the importance of benchmarking and efficiency retrofits in promoting sustainable building practices to reduce energy consumption.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

Graphene-Based Interconnect Exploration for Large SRAM Caches for Ultrascaled Technology Nodes

Graphene-based interconnects are considered promising replacements for traditional copper (Cu) interconnect due to their great electric properties. In this article, an interconnect-memory co- design framework is developed to efficiently optimize various graphene-based interconnect technologies. Four interconnect materials and heterogeneous design schemes are benchmarked against their traditional Cu counterparts to optimize large cache-level SRAM performance in terms of delay and energy per access, energy-delay product (EDP), and energy-delay-area product (EDAP). Here, a large design space exploration is performed based on realistic subarray design and device technology. Various interconnect- and array-level design parameters are studied to quantify the true potential of graphene-based wires for optimal memory performance.

42 ENGINEERING↗

Benchmarking Cylindrical Blast Wave Theory Against the OSIRIS-REx Sample Return Capsule Reentry

Weak shock theory based on cylindrical blast waves has been used to interpret meteor infrasound, but it has not been systematically benchmarked against a non-ablating hypersonic source with independently known parameters. The objective of this study is not to propose a new theoretical framework, but to evaluate the operational validity of the existing suite of blast radius formulations against a high-fidelity ground truth dataset. The OSIRIS-REx Sample Return Capsule reentry on 24 September 2023 provides such a benchmark because the capsule geometry, trajectory, and infrasound emission points are constrained from mission data and ray tracing, reducing source-side uncertainty associated with ablation. Using observations from 39 infrasound stations, this benchmarking study evaluates six published blast radius (${R}_{0}$ ) formulations and three weak-shock transition coefficients ( C ) within a stratified atmospheric propagation model to predict signal period and peak overpressure. The benchmarking identifies the Sakurai formulation as the best-performing formulation for non-ablating bodies, with the Jones/Plooster formulation performing comparably when a physically appropriate C is adopted. Sakurai and Jones/Plooster yield linear-period median absolute percentage residuals of 9% and 11%, respectively. The period predictions show only weak sensitivity to C at these propagation distances. The Mach-diameter approximation commonly used in meteor studies overestimates ${R}_{0}$ by more than a factor of 3 in the absence of ablation. Finally, these results establish a performance baseline for applying cylindrical blast wave theory to effectively non-ablating hypersonic bodies and demonstrate that the signal period is a robust observable for constraining ${R}_{0}$.

atmospheric entry↗

Breaking the trade-off between selectivity and adsorption capacity for gas separation

It is generally recognized that porous solids (sorbents) with high selectivity and high adsorption capacity offer potential for energy-efficient gas separations. Unfortunately, there is generally a trade-off between capacity and selectivity, which represents a roadblock to the utility of sorbents in key industrial processes. For example, acetylene (C 2 H 2 ), an important fuel and chemical intermediate, is produced with CO 2 as an impurity, and the similar physicochemical properties of C 2 H 2 and CO 2 mean that most sorbents are poorly selective. Hybrid ultramicroporous materials (HUMs) are candidates for gas separations as they exhibit benchmark selectivity for several key gas pairs. Unfortunately, existing HUMs are handicapped by low capacity. Here, we report a new HUM, SIFSIX-21-Ni, that addresses the trade-off between selectivity and capacity that has plagued sorbents, as its high uptake and high selectivity renders it the new benchmark for C 2 H 2 /CO 2 separation performance.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗