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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 145 records · Page 8
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Toxicity of hydraulic fracturing wastewater from black shale natural-gas wells influenced by well maturity and chemical additives

Hydraulic fracturing of deep shale formations generates large volumes of wastewater that must be managed through treatment, reuse, or disposal. Produced wastewater liberates formation-derived radionuclides and contains previously uncharacterized organohalides thought to be generated within the shale well, both posing unknown toxicity to human and ecological health. Here, we assess the toxicity of 42 input media and produced fluid samples collected from four wells in the Utica formation and Marcellus Shale using two distinct endpoint screening assays. Broad spectrum acute toxicity was assessed using a bioluminescence inhibition assay employing the halotolerant bacterium Aliivibrio fischeri, while predictive mammalian cytotoxicity was evaluated using a N-acetylcysteine (NAC) thiol reactivity assay. The acute toxicity and thiol reactivity of early-stage flowback was higher than later produced fluids, with levels diminishing through time as the natural gas wells matured. Acute toxicity of early stage flowback and drilling muds were on par with the positive control, 3,5-dichlorophenol (6.8 mg L -1 ). Differences in both acute toxicity and thiol reactivity between paired natural gas well samples were associated with specific chemical additives. Samples from wells containing a larger diversity and concentration of organic additives resulted in higher acute toxicity, while samples from a well applying a higher composition of ammonium persulfate, a strong oxidizer, showed greater thiol reactivity, predictive of higher mammalian toxicity. Both acute toxicity and thiol reactivity are consistently detected in produced waters, in some cases present up to nine months after hydraulic fracturing. These results support that specific chemical additives, the reactions generated by the additives, or the constituents liberated from the formation by the additives contribute to the toxicity of hydraulic fracturing produced waters and reinforces the need for careful consideration of early produced fluid management.

03 NATURAL GAS↗
DOE OSTI2021

Dual functionality of over-lithiated NMC for high energy silicon-based lithium-ion batteries

Owing to their high specific capacity and suitably low operating potential, silicon-based anodes are an attractive alternative to graphite in next-generation lithium-ion batteries. However, silicon anodes suffer from low initial coulombic efficiency and fast capacity decay, limiting their widespread application. Pre-lithiation strategies are highly appealing to compensate for irreversible active lithium loss and to boost the cell energy density. In this work, we maximize the cell energy density by direct pre-lithiation of the NMC (LiNi 0.5 Mn 0.3 Co 0.2 O 2 ) cathode to Li 1+x NMCO 2 without introducing inactive deadweight to either electrode. First, we demonstrate that Li 1+x NMCO 2 can be synthesized chemically, via reaction between NMC and lithium napthalide, and electrochemically. The NMC cathode is tolerant of a one-time over-lithiation up to 60 mA h g NMC -1 , giving capacity retention on par with untreated NMC in half cell electrochemical cycling. Using synchrotron X-ray absorption spectroscopy (ex situ) and diffraction (in situ), we demonstrate that higher amounts of over-lithiation lead to local structure distortion – driven by transition metal reduction to Jahn–Teller active Mn 3+ and Co 2+ – as well as bulk structural hysteresis during over-lithiation and layer “buckling” that increases the amount of lithium extracted from the structure in the charged state. The Li 1+x NMCO 2 with low-to-moderate over-lithiation capacity (23, 46, and 70 mA h g NMC -1 ) is proven to be a highly effective dual-purpose lithium source and cathode material in full cell tests with a commercially relevant Si–graphite anode. These cells show higher capacity, superior cycle life, and improved coulombic efficiencies when compared to those with stoichiometric NMC cathodes. Finally, this study introduces a new and simple method to pre-lithiate layered transition metal oxide cathodes, opening up new possibilities for the development of high energy density lithium-ion batteries with next-generation anodes.

25 ENERGY STORAGE↗
DOE OSTI2022

Interplay of structural fluctuations and charge carrier dynamics is key for high performance of hybrid lead halide perovskites

The ability of methylammonium lead triiodide (MAPbI 3 ) to achieve photoelectric conversion efficiency that is on par with crystalline silicon has led to a surge of interest in perovskite photovoltaics. However, an in-depth understanding of how the ubiquitous coupling between the fast rovibrational movements of the organic cations and the phonon vibrations of the inorganic framework affects the relaxation and recombination of hot carriers remains largely elusive. Access to such knowledge is critical to guide design and increase efficiency of new classes of perovskite solar cells. In this report, we report a time-domain ab initio investigation of temperature dependent excited state dynamics in MAPbI 3 , with particular emphasis on nuclear anharmonic effects. The observed strong anharmonicity is attributed to softness of the material and unusual dynamical coupling between the organic and inorganic components. At an elevated temperature, the hydrogen bonding between MA and iodines is weakened, enhancing rotation of MA cations, which become more dynamically disordered. As a result, thermal vibrations of the inorganic Pb–I sublattice are suppressed, and the lattice anharmonicity is decreased. Thermal fluctuations of the electronic energy levels are found to follow the trend of anharmonic motions of Pb and I atoms, with holes relaxing faster to the band edges than electrons, due to higher density of the hole states. While elevated temperature accelerates intraband carrier cooling, it slows nonradiative carrier recombination. The latter result is important for performance, since solar cells and other devices heat up during operation. The reported signatures of coupled structural dynamics of the organic cations and inorganic framework unravel the interplay between anomalous structural fluctuations and charge carrier dynamics, which is of particular importance for fundamental understanding of the structure–property relationships in hybrid metal halide perovskites.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Synthesizing and formulating metal oxide nanoparticle inks for perovskite solar cells

The perovskite solar cell has commercial potential due to the low-cost of materials and manufacturing processes with cell efficiencies on par with traditional technologies. Nanomaterials have many properties that make them attractive for the perovskite devices, including low-cost inks, low temperature processing, stable material properties and good charge transport. In this feature article, the use of nanomaterials in the hole transport and electron transport layers are reviewed. Specifically, SnO 2 and NiO x are the leading materials with the most promise for translation to large scale applications. Here, the review includes a discussion of the synthesis, formulation, and processing of these nanoparticles and provides insights for their further deployment towards commercially viable perovskite solar cells.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Electrodialysis and nitrate reduction (EDNR) to enable distributed ammonia manufacturing from wastewaters

Underutilized wastewaters containing dilute levels of reactive nitrogen (Nr) can help rebalance the nitrogen cycle. This study describes electrodialysis and nitrate reduction (EDNR), a reactive electrochemical separation architecture that combines catalysis and separations to remediate nitrate and ammonium-polluted wastewaters while recovering ammonia. By engineering operating parameters (e.g., background electrolyte, applied potential, electrolyte flow rate), we achieved high recovery and conversion of Nr in both simulated and real wastewaters. The EDNR process demonstrated long-term robustness and up-concentration that recovered >100 mM ammonium fertilizer solution from agricultural runoff that contained 8.2 mM Nr. EDNR is the first reported process to our knowledge that remediates dilute real wastewater and recovers ammonia from multiple Nr pollutants, with an energy consumption (245 MJ per kg NH 3 –N in simulated wastewater, 920 MJ per kg NH 3 –N in agricultural runoff) on par with the state-of-the-art. Demonstrated first at proof-of-concept and engineered to technology readiness level (TRL) 4–5, EDNR shows great promise for distributed wastewater treatment and sustainable ammonia manufacturing.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Rapid spatial analysis of surrogate TRISO fuel particles using laser-induced breakdown spectroscopy image analysis

Laser-induced breakdown spectroscopy (LIBS) mapping enables rapid elemental and spatial analysis of solid samples. In this work, surrogate TRi-structural ISOtropic (TRISO) particles with various layers consisting of Zr, W, C, and Si were used to demonstrate the use of a new thickness measurement tool developed to analyze elemental images generated from LIBS maps. Zr particles with varying outer-layer thicknesses ranging from 16 to 32 μm were measured with scanning electron microscopy with energy dispersive spectroscopy (SEM-EDS) and LIBS with both a complementary metal-oxide-semiconductor (CMOS) detector and an intensified charged coupled device (ICCD) detector. LIBS maps of particles were completed using CMOS and ICCD spectrometers with effective spatial resolutions of 4 and 2 μm, respectively. The novel thickness measurement tool identified layer regions within a LIBS map and then identified the locations of the boundaries between these layers. The tool then generated up to 1000 random profiles stemming radially from the center region, which were used to measure the layer thickness/radius. This image analysis tool demonstrated LIBS's ability to provide values comparable with SEM-EDS (3.7% relative difference) along with a 95% reduction in measurement time. Furthermore, the precision of these measurements was on par with the SEM-EDS measurements at <15% relative standard deviation. Following the analysis of the Zr particles, W particles with increased complexity (e.g., five versus three layers) were analyzed using both the CMOS and ICCD spectrometers simultaneously. The spatial dimensions were extracted with an average relative difference of 2.7% and an average relative standard deviation of 9%.

Andrews, Hunter B. [Oak Ridge National Laboratory ↗
DOE OSTI2025

Critical role of oxide anchoring groups in organic electron transport layers for perovskite solar cell stability

Charge transport layers (CTLs) play a critical role in the performance and long-term stability of perovskite solar cells (PSCs) by facilitating efficient charge extraction and providing interfacial stabilization. For organic CTLs, different functional groups have been designed to modulate the interactions with the substrate. Anchoring groups are used to establish strong adhesion to transparent conductive oxides (TCOs) but are not routinely incorporated in organic CTL design. In this study, we investigate the influence of anchoring groups in organic electron transport layers (ETLs) on PSC performance and stability by synthesizing and evaluating two naphthalene diimide (NDI)-based ETLs: NDI-(PhPA) 2 , functionalized with polar phenyl phosphonic acid (PhPA) groups, and NDI-(PhBr) 2 , modified with nonpolar bromophenyl (PhBr) groups. X-ray photoelectron spectroscopy confirms that PhPA functionalization leads to NDIs anchored onto fluorine-doped tin oxide (FTO) following chemical bath deposition, while NDI-(PhBr) 2 shows no detectable surface presence after deposition. We show that NDI-(PhPA) 2 deposits as a thin film on FTO, exhibiting strong adhesion, high solvent resistance, and enhanced light and thermal stability, achieving a maximum device efficiency of 14.3%. Stability assessments conducted under continuous illumination at 25 °C for 200 hours and at 65 °C for 100 hours demonstrate performance on par with TiO 2 -based ETLs. In contrast, NDI-(PhBr) 2 , which lacks strong anchoring interactions, fails to adhere to the FTO surface, resulting in a rapid decrease in efficiency over a few hours, comparable to devices without an ETL. These findings highlight the importance of anchoring groups in organic CTLs for achieving long-term PSC stability under operational conditions.

Kim, Sanggyun [Georgia Institute of Technology, At↗
DOE OSTI2026

Synergistic ruthenium single-atom and nanoparticles in nickel as cooperative catalysts for the alkaline hydrogen evolution reaction

Efficient hydrogen evolution reaction (HER) catalysts that reduce the use of noble metals and can be synthesized on a large scale are essential for advancing anion exchange membrane water electrolyzers (AEMWEs) toward commercialization. Herein, we present a composite catalyst in which Ru nanoparticles coexist with Ru single-atom alloys (SAAs) dispersed within Ni nanoparticles (Ru-SAA/Ni), creating a highly active HER electrocatalyst. Using a one-pot and scalable synthesis method, we can tune the material composition from SAA, i.e. materials containing atomically dispersed Ru atoms (with ≤0.4 at% Ru) to composite structures in which SAAs coexist with Ru NPs. Comprehensive characterization using XPS, XAS, and TEM confirms Ru-SAA formation at a low Ru content and composite structures at higher contents. Electrochemical evaluations conducted in a three-electrode setup reveal that Ru-SAA/Ni composites achieve HER performance on par with that of Pt/C. Computational insights suggest that water dissociation is significantly faster at the Ru/Ni interface compared with that on extended surfaces. These active sites are thermodynamically as active as basal planes, preventing the excessive accumulation of reaction intermediates (H*, OH*). All these results highlight the synergistic interaction between Ru SAAs and Ru nanoparticles and their potential for large-scale applications with minimal use of precious metals. Finally, the materials are processed and tested in AEMWEs, achieving 1.85 V at 0.5 A cm −2 with a total noble metal loading of only 0.1 mg cm −2 .

Khalil, Gaëlle [Université de Paris (France)]↗
DOE OSTI2024

Application of performance portability solutions for GPUs and many-core CPUs to track reconstruction kernels

Next generation High-Energy Physics (HEP) experiments are presented with significant computational challenges, both in terms of data volume and processing power. Using compute accelerators, such as GPUs, is one of the promising ways to provide the necessary computational power to meet the challenge. The current programming models for compute accelerators often involve using architecture-specific programming languages promoted by the hardware vendors and hence limit the set of platforms that the code can run on. Developing software with platform restrictions is especially unfeasible for HEP communities as it takes significant effort to convert typical HEP algorithms into ones that are efficient for compute accelerators. Multiple performance portability solutions have recently emerged and provide an alternative path for using compute accelerators, which allow the code to be executed on hardware from different vendors. We apply several portability solutions, such as Kokkos, SYCL, C++17 std::execution::par, Alpaka, and OpenMP/OpenACC, on two mini-apps extracted from the mkFit project: p2z and p2r. These apps include basic kernels for a Kalman filter track fit, such as propagation and update of track parameters, for detectors at a fixed z or fixed r position, respectively. The two mini-apps explore different memory layout formats. We report on the development experience with different portability solutions, as well as their performance on GPUs and many-core CPUs, measured as the throughput of the kernels from different GPU and CPU vendors such as NVIDIA, AMD and Intel.

Kwok, Ka Hei Martin↗
DOE OSTI2024

Evaluating Performance Portability with the CMS Heterogeneous Pixel Reconstruction code

In the past years the landscape of tools for expressing parallel algorithms in a portable way across various compute accelerators has continued to evolve significantly. There are many technologies on the market that provide portability between CPU, GPUs from several vendors, and in some cases even FPGAs. These technologies include C++ libraries such as Alpaka and Kokkos, compiler directives such as OpenMP, the SYCL open specification that can be implemented as a library or in a compiler, and standard C++ where the compiler is solely responsible for the offloading. Given this developing landscape, users have to choose the technology that best fits their applications and constraints. For example, in the CMS experiment the experience so far in heterogeneous reconstruction algorithms suggests that the full application contains a large number of relatively short computational kernels and memory transfer operations. In this work we use a stand-alone version of the CMS heterogeneous pixel reconstruction code as a realistic use case of HEP reconstruction software that is capable of leveraging GPUs effectively. We summarize the experience of porting this code base from CUDA to Alpaka, Kokkos, SYCL, std::par, and OpenMP offloading. We compare the event processing throughput achieved by each version on NVIDIA and AMD GPUs as well as on a CPU, and compare those to what a native version of the code achieves on each platform.

Andriotis, Nikolaos↗
DOE OSTI2024

Porting ATLAS Fast Calorimeter Simulation to GPUs with Performance Portable Programming Models

FastCaloSim is a parameterized simulation of the particle energy response and of the energy distribution in the ATLAS calorimeter. It is a relatively small and self-contained package with massive inherent parallelism and captures the essence of GPU offloading via important operations like data transfer, memory initialization, floating point operations, and reduction. It was identified by the High Energy Physics Center for Computational Excellence project as a good testbed for evaluating the performance and ease of portability of programming models. In this paper, we will discuss the results of our evaluation of the porting process to Kokkos, SYCL, Alpaka, OpenMP and std::par (nvc++), and compare performance on NVIDIA, AMD and Intel GPUs, as well as multicore CPUs.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Cavitation model of the inflationary stage of Big Bang

In this study, we propose a model for the initial stage of the development of the universe analogous to cavitation in a liquid in a negative pressure field. It is assumed that at the stage of inflation, multiple breaks of the metric occur with the formation of areas of physical vacuum in which the generation of matter occurs. The proposed model explains the large-scale isotropy of the universe without ultrafast inflationary expansion and the emergence of a large-scale cellular (cluster) structure, as a result of the development of cavitation ruptures of a false vacuum. It is shown that the cavitation model can be considered on par with (or as an alternative to) the generally accepted inflationary multiverse model of the Big Bang.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

High-fidelity kinetic modeling of instabilities and gyromotion physics in nonuniform low-beta plasmas

A fourth-order accurate continuum kinetic Vlasov solver and a systematic method for constructing customizable kinetic equilibria are demonstrated to be powerful tools for the study of nonuniform collisionless low-beta plasmas. The noise-free methodology is applied to investigate two gradient-driven instabilities in 4D (x,y,vx,vy) phase space: the Kelvin–Helmholtz instability and the lower hybrid drift instability. Nonuniform two-species configurations where ion gyroradii are comparable to gradient scale lengths are explored. The approach sheds light on the evolution of the pressure tensor in Kelvin–Helmholtz instabilities and demonstrates that the associated stress tensor deviates significantly from the gyroviscous stress tensor. Even at high magnetization, first-order approximations to finite-gyromotion physics are shown to be inadequate for the Kelvin–Helmholtz instability, as shear scales evolve to become on par with gyromotion scales. The methodology facilitates exploring transport and energy partitioning properties associated with lower hybrid drift instabilities in low-beta plasma configurations. Distribution function features are captured in detail, including the formation of local extrema in the vicinity of particle-wave resonances. Finally, the approach enables detailed targeted investigations and advances kinetic simulation capability for plasmas in which gyromotion plays an important role.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗
DOE OSTI2021

A new and alternative look at nonlinear Alfvénic states

The formulation for studying nonlinear Alfvenic states, sustainable in Hall Magnetohydrodynamics (HMHD), becomes considerably simpler and more tractable when circularly polarized Beltrami vectors (the eigenstates of linear HMHD) are used as the basis functions. Nonlinear HMHD is, then, reduced to a rather simple looking set of scalar equations from which a model problem of three interacting Beltrami modes is formulated and analytically solved. The triplet interactions span a variety of familiar nonlinear processes leading to a redistribution as well as periodic exchange of energy. The energy exchange processes (whose strength is measured by an energy exchange/depletion time) will, perhaps, play a dominant role in determining the spectral content of an eventual Alfvenic state. All nonlinearities (sensitive functions of the interacting wave vectors) operate at par, and none is dominant over any substantial region of k-space; their intricate interplay prevents a “universal” picture from emerging; few generalizations on the processes that may, for instance, lead to a turbulent state, are possible. However, the theory can definitely claim: (1) the energy tends to flow from lower to higher k and (2) the higher k z (in the direction of the ambient magnetic field) components of a mode with a given k are depleted/oscillate faster—in some cases much faster. It is noteworthy that the mode coupling is the strongest (with the shortest depletion time) when the participating wave vectors are nearly perpendicular; perhaps, an expected consequence of the curl (cross product) nonlinearities. Numerical simulations will be necessary to help create a fully reliable picture.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

A new generation of effective core potentials from correlated and spin–orbit calculations: Selected heavy elements

We introduce new correlation consistent effective core potentials (ccECPs) for the elements I, Te, Bi, Ag, Au, Pd, Ir, Mo, and W with 4d, 5d, 6s, and 6p valence spaces. These ccECPs are given as a sum of spin-orbit averaged relativistic effective potential (AREP) and effective spin–orbit (SO) terms. The construction involves several steps with increasing refinements from more simple to fully correlated methods. The optimizations are carried out with objective functions that include weighted many-body atomic spectra, norm-conservation criteria, and SO splittings. Transferability tests involve molecular binding curves of corresponding hydride and oxide dimers. The constructed ccECPs are systematically better and in a few cases on par with previous effective core potential (ECP) tables on all tested criteria and provide a significant increase in accuracy for valence-only calculations with these elements. Our study confirms the importance of the AREP part in determining the overall quality of the ECP even in the presence of sizable spin–orbit effects. The subsequent quantum Monte Carlo calculations point out the importance of accurate trial wave functions that, in some cases (mid-series transition elements), require treatment well beyond a single-reference.

Wang, Guangming (ORCID:0000000231327925)↗
DOE OSTI2022

Deep level defects in low-pressure chemical vapor deposition grown (010) β-Ga 2 O 3

This study provides the full-bandgap evaluation of defect state distributions in beta phase gallium oxide (β-Ga 2 O 3 ) grown by low-pressure chemical vapor deposition (LPCVD) on (010) β-Ga 2 O 3 substrates at high growth of up to 20 µm/h. Deep-level optical spectroscopy and deep-level transient spectroscopy measurements applied to Ni/β-Ga 2 O 3 Schottky diodes revealed the presence of a previously unreported defect state at E C -3.6 eV, which dominated the overall trap distribution in LPCVD grown material. However, states at E C -0.8 eV, E C -2.0 eV, and E C -4.4. eV were also detected, similar to prior studies on β-Ga 2 O 3 grown by other methods, with similar or lower concentrations for the LPCVD samples. The E C -0.8 eV and E C -2.0 eV states were previously connected to residual Fe impurities and gallium vacancies, respectively. The total concentration of traps in the LPCVD material was on par with or lower than the state-of-the-art metal–organic chemical vapor deposition-grown materials despite the much higher growth rate, and the distribution of states showed negligible dependence on SiCl 4 flow rate and doping concentration. These results demonstrate that the high growth rate of LPCVD-grown β-Ga 2 O 3 is very promising for achieving thick, low defect density, and high-quality layers needed for multi-kV device applications.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Synergy of semiempirical models and machine learning in computational chemistry

Catalyzed by enormous success in the industrial sector, many research programs have been exploring data-driven, machine learning approaches. Performance can be poor when the model is extrapolated to new regions of chemical space, e.g., new bonding types, new many-body interactions. Another important limitation is the spatial locality assumption in model architecture, and this limitation cannot be overcome with larger or more diverse datasets. The outlined challenges are primarily associated with the lack of electronic structure information in surrogate models such as interatomic potentials. Given the fast development of machine learning and computational chemistry methods, we expect some limitations of surrogate models to be addressed in the near future; nevertheless spatial locality assumption will likely remain a limiting factor for their transferability. Here, we suggest focusing on an equally important effort—design of physics-informed models that leverage the domain knowledge and employ machine learning only as a corrective tool. In the context of material science, we will focus on semi-empirical quantum mechanics, using machine learning to predict corrections to the reduced-order Hamiltonian model parameters. The resulting models are broadly applicable, retain the speed of semiempirical chemistry, and frequently achieve accuracy on par with much more expensive ab initio calculations. These early results indicate that future work, in which machine learning and quantum chemistry methods are developed jointly, may provide the best of all worlds for chemistry applications that demand both high accuracy and high numerical efficiency.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Molecular hydrodynamic theory of the velocity autocorrelation function

The velocity autocorrelation function (VACF) encapsulates extensive information about a fluid’s molecular-structural and hydrodynamic properties. We address the following fundamental question: How well can a purely hydrodynamic description recover the molecular features of a fluid as exhibited by the VACF? To this end, we formulate a bona fide hydrodynamic theory of the tagged-particle VACF for simple fluids. Our approach is distinguished from previous efforts in two key ways: collective hydrodynamic modes and tagged-particle self-motion are modeled by linear hydrodynamic equations; the fluid’s spatial velocity power spectrum is identified as a necessary initial condition for the momentum current correlation. This formulation leads to a natural physical interpretation of the VACF as a superposition of products of quasinormal hydrodynamic modes weighted commensurately with the spatial velocity power spectrum, the latter of which appears to physically bridge continuum hydrodynamical behavior and discrete-particle kinetics. The methodology yields VACF calculations quantitatively on par with existing approaches for liquid noble gases and alkali metals. Furthermore, we obtain a new, hydrodynamic form of the self-intermediate scattering function whose description has been extended to low densities where the Schmidt number is of order unity; various calculations are performed for gaseous and supercritical argon to support the general validity of the theory. Excellent quantitative agreement is obtained with recent MD calculations for a dense supercritical Lennard-Jones fluid.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗