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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 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Generalized Brunauer–Emmett–Teller Isotherm for Mixed-Gas Multilayer Adsorption Equilibria

Here, this work presents a rigorous thermodynamic framework to calculate mixed-gas multilayer adsorption equilibria from single-component isotherms and vapor–liquid equilibria. Named the generalized Brunauer–Emmett–Teller (gBET) isotherm, the newly formulated isotherm considers adsorbent surface heterogeneity, competitive adsorption on the monolayer, condensation–evaporation on the subsequent layers, and adsorbed phase nonideality for the monolayer and the subsequent layers. The monolayer adsorbed phase nonideality is tracked by using an area-based adsorption nonrandom two-liquid activity coefficient model. The adsorbed phase composition and corresponding nonideality in the subsequent layers are calculated at the dew point condition of the mixed gas with either an equation of state or an activity coefficient model for the vapor–liquid equilibria. The proposed model is validated with six single and three binary multilayer adsorption equilibrium systems, and the model results are compared against those from the classical BET isotherm for single-component adsorption and ideal adsorbed solution theory for mixed-gas adsorption equilibria.

09 BIOMASS FUELS↗
DOE OSTI2023

Molecular Simulation of Lithium Carbonate Reactive Vapor–Liquid Equilibria Using a Deep Potential Model

We developed a first-principles machine learning model for the reactive vapor–liquid phase behavior of molten Li 2 CO 3 . The model was trained on ab initio electronic density functional theory data using the Deep Potential (DP) methodology, and its accuracy was evaluated by comparing model predictions of density and viscosity to experimental measurements. Direct coexistence simulations with the DP model over time scales of tens of nanoseconds were used to observe equilibrium dissociation of Li 2 CO 3 into CO 2 residing primarily in the vapor phase and Li 2 O which remains dissolved in the liquid. The simulations covered a range of temperatures, overall system sizes, and vapor-to-liquid volume ratios. Results were analyzed in terms of the observed chemical composition of the liquid and vapor phases, product structure, and CO 2 partial pressures. In addition, we calculated equilibrium constants for the dissociation reaction by assuming ideal-solution behavior for the liquid. As expected on the basis of thermodynamic arguments and prior experiments for this system, the observed partial pressure of CO 2 in the gas phase depends on both the temperature and the ratio of vapor to liquid volumes, while the calculated equilibrium constants only depend on temperature. DP model predictions for the equilibrium constant of the reaction are generally consistent with the available experimental measurements. Furthermore, the present study establishes the validity of the DP methodology for the description of reactive, multiphase equilibria from first principles, with possible applications to many other systems of scientific and technological interest even in the absence of relevant experimental measurements.

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

Microstability of β ~ 1 tokamak equilibria

High-power-density tokamaks offer a potential solution to design cost-effective fusion devices. One way to achieve high power density is to operate at a high β value (the ratio of thermal to magnetic pressure), i.e. β~1 . However, a β~1 state may be unstable to various pressure- and current-driven instabilities or have unfavourable microstability properties. To explore these possibilities, we generate β~1 equilibria and investigate their stability. First, we demonstrate the generation of high-β equilibria with the computer code VMEC. We then analyse these equilibria to determine their stability against the infinite-n ideal-ballooning mode. We follow that by engaging in a detailed microstability study using the GS2 code, beginning with assessments of electrostatic ion-temperature-gradient and trapped election mode instabilities. We observe interesting behaviour for the high-β equilibria – stabilization of these modes through two distinct mechanisms – large negative local shear and reversal of electron precession drift. Finally, we perform electromagnetic gyrokinetic simulations and observe enhanced stability in the outer core of high-β equilibria and absence of kinetic ballooning modes in the negative-triangularity, high-β equilibria. The enhanced outer-core stability of high-β equilibria is different from their lower-β counterparts and offers an alternative, potentially favourable regime of tokamak operation.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Theory of strain phase equilibria and diagrams

Chemical phase equilibria and phase diagrams are well established and have served as indispensable guides for designing materials through chemical tuning. However, a general thermodynamic theory for strain phase equilibria remains elusive despite extensive studies which have revealed dramatic impacts of mechanical strain on the stability of phases and domain states in solid-state materials. Here, we establish the thermodynamic theory of strain equilibria and a general framework for efficiently constructing multidomain and multiphase diagrams of arbitrarily strained solids under incoherent conditions. As examples, we obtain temperature-strain phase diagrams of ferroelectric PbTiO 3 , strongly correlated VO 2 , and unconventional ferroelectric Hf 0.5 Zr 0.5 O 2 . We reveal the analogs of the Gibbs phase rules, multiple- and multi-critical points, common-tangent construction, and level rule in strain equilibria to those in the familiar chemical phase equilibria. Finally, our strain equilibria theory offers a powerful framework for predicting the thermodynamic stability of structural phases and domains in strained solids and for guiding the strain engineering of their functional properties.

36 MATERIALS SCIENCE↗
DOE OSTI2026

From molecular to macroscopic: predicting liquid–liquid phase equilibria and small-angle scattering of mixtures of organic liquids from atomistic simulation using Kirkwood–Buff theory

Macroscopic phase equilibria between solutions define the functionality of many biological and industrial processes, yet they are challenging to predict due to the inherent complexity of liquids containing large molecules. This work introduces an approach for the purely predictive calculation of such phase equilibria in temperature-composition space from molecular dynamics (MD) simulations at one temperature in the single-phase region. We use an approach developed previously to obtain the entropic and enthalpic contributions to the free energy of mixing from the atomic-scale information given by MD simulations via Kirkwood–Buff theory. This allows us to accurately estimate the free energy of mixing as a function of temperature, and thus obtain liquid–liquid phase equilibria, including liquid–liquid critical points, associated binodal and spinodal lines, and composition fluctuations across a region of temperature and composition. Results for binary malonamide–alkane systems are validated by comparison to a direct experimental probe of the fluctuations: the small angle X-ray scattering intensity near zero wavenumber. The MDKB → Phase method demonstrated here provides a significant improvement in predicting liquid–liquid equilibria and free energy as a function of temperature for our systems of interest compared to conventional thermodynamic models. The accurate performance of this purely predictive approach lies in its preservation of atomistic details when determining thermodynamic properties. Furthermore, its inherent extensibility to multi-component systems will likely make the MDKB → Phase approach a valuable general tool for connecting molecular interactions to macroscopic phase equilibria and for the computational screening of materials for targeted thermodynamic behavior.

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

An adjoint-based method for optimising MHD equilibria against the infinite- n , ideal ballooning mode

We demonstrate a fast adjoint-based method to optimise tokamak and stellarator equilibria against a pressure-driven instability known as the infinite-n ideal ballooning mode. We present three finite-β (the ratio of thermal to magnetic pressure) equilibria: one tokamak equilibrium and two stellarator equilibria that are unstable against the ballooning mode. Using the self-adjoint property of ideal magnetohydrodynamics, we construct a technique to rapidly calculate the change in the eigenvalue, a measure of ideal ballooning instability. Using the SIMSOPT optimisation framework, we then implement our fast adjoint gradient-based optimiser to minimise the eigenvalue and find stable equilibria for each of the three originally unstable equilibria.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

A 3D helical filament surrogate model for 3D tokamak equilibria

A novel approach for efficient representation of three-dimensional (3D) tokamak equilibria is investigated, where a set of helical current filaments occupying the plasma region are employed to resolve deviations from the two-dimensional (2D) axi-symmetric state. A discrete set of 3D filaments, located at rational surfaces for a given toroidal mode number n and following the 2D equilibrium field lines (thus forming closed current loops), are found to provide a surrogate model of 3D equilibria with reasonable accuracy. Specifically, application of the filament model to 3D perturbed equilibria, due to the resonant magnetic perturbation (RMP) in DIII-D and MAST-U discharges, reveals that (1) a single helical filament per rational surface is sufficient; (2) 21 such helical filaments are capable of representing the n = 2 3D response field in MAST-U with less than 10% relative error as compared to that computed by a full magnetohydrodynamic code; (3) optimizing currents (both amplitude and phase) flowing in 3D filaments with fixed geometry, the highest accuracy fitting is found to depend on the characteristics of the 3D equilibria such as the coil current phasing of the RMP coils in our case studies. Here, whis filament approach is also applicable for generating surrogate models of other type of 3D tokamak equilibria, including those during the initial phase of the plasma disruption.

MARS-F↗
DOE OSTI2020

Energy-Casimir, dynamically accessible, and Lagrangian stability of extended magnetohydrodynamic equilibria

The formal stability analysis of Eulerian extended magnetohydrodynamics (XMHD) equilibria is considered within the noncanonical Hamiltonian framework by means of the energy-Casimir variational principle and the dynamically accessible stability method. Specifically, we find explicit sufficient stability conditions for axisymmetric XMHD and Hall MHD (HMHD) equilibria with toroidal flow and for equilibria with arbitrary flow under constrained perturbations. The dynamically accessible, second-order variation of the Hamiltonian, which can potentially provide explicit stability criteria for generic equilibria, is also obtained. Moreover, we examine the Lagrangian stability of the general quasineutral two-fluid model written in terms of MHD-like variables, by finding the action and the Hamiltonian functionals of the linearized dynamics, working within a mixed Lagrangian-Eulerian framework. Upon neglecting electron mass, we derive a HMHD energy principle, and in addition, the perturbed induction equation arises from Hamilton’s equations of motion in view of a consistency condition for the relation between the perturbed magnetic potential and the canonical variables.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Generalization of thermodynamic Langmuir isotherm for mixed‐gas adsorption equilibria

Abstract This work presents a comprehensive thermodynamic model for both pure component isotherms and mixed‐gas adsorption equilibria. A generalization of thermodynamic Langmuir isotherm, the proposed model assumes competitive adsorption of multiple adsorbates on adsorbent surface for mixed‐gas adsorption equilibria, and it applies an area‐based adsorption nonrandom two‐liquid activity coefficient model in the activity coefficient calculations for the adsorbate phase. The resulting generalized Langmuir isotherm properly captures both surface loading dependence and adsorbate phase composition dependence for mixed‐gas adsorption equilibria. The model is validated with accurate representations of gas adsorption equilibrium data for varieties of unary, binary, and ternary gas systems. The model results are further compared with those calculated from extended Langmuir isotherm and Ideal Adsorbed Solution Theory.

Hamid, Usman↗
DOE OSTI2025

Stable isotope equilibria in the dihydrogen-water-methane-ethane-propane system. Part 1: Path-integral calculations with CCSD(T) quality potentials

Isotopic compositions of alkanes are typically assumed to be kinetically controlled, but recently is has been proposed that alkanes can isotopically equilibrate for both C and H isotopes during natural gas generation. Evaluation of this requires knowledge of the isotopic equilibrium between alkanes and other common hydrogen and carbon bearing species. Here, in this study, we calculate isotopic equilibria within and between gaseous dihydrogen (H 2 ), water (H 2 O), methane (CH 4 ), ethane (C 2 H 6 ) and propane (C 3 H 8 ), including isotope fractionation among molecules, clumped isotope effects, as well as among sites of propane (i.e., the site-specific isotope effects) from 0°C to 500°C using a path-integral method paired with high-level descriptions of molecular potentials and the diagonal correction to the Born Oppenheimer approximation. While path-integral calculations with high- level CCSD(T) potentials are available for the isotopic equilibria involving methane, the path-integral calculations for ethane and propane have only been performed based on lower-level descriptions of the molecular potentials. We analyze the relative importance of various approximations that are commonly employed when isotopic equilibria are evaluated. We find that clumped isotope effects can be calculated to the same accuracy using computationally inexpensive combination of the Bigeleisen-Mayer-Urey model with the molecular potential from density functional theory. In contrast, fractionation and site preferences of both deuterium and carbon-13 benefit from the use of the higher level CCSD(T) potentials and accounting for anharmonic effects. Additionally, for fractionation and site preference of deuterium corrections to Born-Oppenheimer approximation can also be important.

03 NATURAL GAS↗
DOE OSTI2021

Gradient-based optimization of 3D MHD equilibria

Using recently developed adjoint methods for computing the shape derivatives of functions that depend on magnetohydrodynamic (MHD) equilibria (Antonsen et al. , J. Plasma Phys. , vol. 85, issue 2, 2019; Paul et al. , J. Plasma Phys. , vol. 86, issue 1, 2020), we present the first example of analytic gradient-based optimization of fixed-boundary stellarator equilibria. We take advantage of gradient information to optimize figures of merit of relevance for stellarator design, including the rotational transform, magnetic well and quasi-symmetry near the axis. With the application of the adjoint method, we reduce the number of equilibrium evaluations by the dimension of the optimization space ( ${\sim }50\text {--}500$ ) in comparison with a finite-difference gradient-based method. We discuss regularization objectives of relevance for fixed-boundary optimization, including a novel method that prevents self-intersection of the plasma boundary. We present several optimized equilibria, including a vacuum field with very low magnetic shear throughout the volume.

Physics↗
DOE OSTI2025

Metastability of stratified magnetohydrostatic equilibria and their relaxation

Motivated by explosive releases of energy in fusion, space and astrophysical plasmas, we consider the nonlinear stability of stratified magnetohydrodynamic equilibria against two-dimensional interchanges of straight magnetic-flux tubes. We demonstrate that, even within this restricted class of dynamics, the linear stability of an equilibrium does not guarantee its nonlinear stability: equilibria can be metastable. We show that the minimum-energy state accessible to a metastable equilibrium under non-diffusive two-dimensional dynamics can be found by solving a combinatorial optimisation problem. These minimum-energy states are, to good approximation, the final states reached by our simulations of destabilised metastable equilibria for which turbulent mixing is suppressed by viscosity. To predict the result of fully turbulent relaxation, we construct a statistical mechanical theory based on the maximisation of Boltzmann's mixing entropy. This theory is analogous to the Lynden-Bell statistical mechanics of collisionless stellar systems and plasma, and to the Robert–Sommeria–Miller theory of two-dimensional vortex turbulence. Our theory reproduces well the results of our numerical simulations for sufficiently large perturbations to the metastable equilibrium.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Strain-Dependent Surface Defect Equilibria of Mixed Ionic-Electronic Conducting Perovskites

We report understanding the surface defect chemistry and its strain dependency is essential in developing next-generation electrochemical devices. However, due to their nanoscale dimensions, surface defects cannot be accessed by conventional techniques used in bulk defect studies. Here, we constructed the strain-dependent surface defect equilibria (i.e., the Brouwer diagram) of mixed ionic-electronic conducting perovskite oxides with near ambient pressure X-ray absorption spectroscopy. Using coherently strained thin-film La 0.6 Sr 0.4 Fe O3 (LSF) as model systems, we probed their surface defect equilibria at 400 °C in oxygen partial pressures between 1 to 10 -5 Torr. We found that the electron holes on the LSF surfaces have strong oxygen character, regardless of the strain states. Nevertheless, tensile strain makes the LSF surface more reducible than the compressed counterpart. These two observations were then validated using first-principles calculations. Finally, with the aid of thermodynamic analyses, we showed that the strain-dependent surface defect equilibria of LSF can be captured by bulk-like ideal solution defect models with shifted oxygen chemical potentials. The findings and methodology presented in this study enable quantitative determination of the surface defect chemistry, which is crucial to understanding and designing functional surfaces for efficient conversions of energy and fuels.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Computational investigation of hysteresis and phase equilibria of n-alkanes in a metal-organic framework with both micropores and mesopores

Abstract Adsorption hysteresis is a phenomenon related to phase transitions that can impact applications such as gas storage and separations in porous materials. Computational approaches can greatly facilitate the understanding of phase transitions and phase equilibria in porous materials. In this work, adsorption isotherms for methane, ethane, propane, and n-hexane were calculated from atomistic grand canonical Monte Carlo (GCMC) simulations in a metal-organic framework having both micropores and mesopores to better understand hysteresis and phase equilibria between connected pores of different size and the external bulk fluid. At low temperatures, the calculated isotherms exhibit sharp steps accompanied by hysteresis. As a complementary simulation method, canonical (NVT) ensemble simulations with Widom test particle insertions are demonstrated to provide additional information about these systems. The NVT+Widom simulations provide the full van der Waals loop associated with the sharp steps and hysteresis, including the locations of the spinodal points and points within the metastable and unstable regions that are inaccessible to GCMC simulations. The simulations provide molecular-level insight into pore filling and equilibria between high- and low-density states within individual pores. The effect of framework flexibility on adsorption hysteresis is also investigated for methane in IRMOF-1.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Numerical minimization of neoclassical poloidal viscosity for supersonic equilibria in tokamak geometry

Extensive experimental evidence has shown that the presence of poloidal flow in tokamaks can dramatically improve transport properties. However, theory indicates that poloidal flows are damped by poloidal viscosity, thus necessitating external drivers, such as neutral beam injection or radio frequency heating. In this work, ideal magnetohydrodynamic equilibria are calculated via the FORTRAN code FLOW [Guazzotto et al., Phys. Plasmas 11, 604 (2004)] and a postprocessor is used to estimate the neoclassical poloidal viscosity. The equilibrium inputs, which correspond to intuitive physical quantities, are then numerically optimized to reduce a viscosity figure of merit. We present supersonic equilibria in tokamak geometry with minimized neoclassical poloidal viscosities for various velocity free function inputs, plasma aspect ratios, and collisionality regimes. Benchmarks are made against an analytic theory as well as a classical expression of poloidal viscosity. Numerical confirmation of the analytic theory is obtained in the high aspect ratio and high collisionality limit. Good agreement is also seen near the plasma core and edge, with discrepancies arising in the intermediate region. Outside of these limits, rotation input function profiles are found that provide ∼order of magnitude improvements over the analytic theory, with additional progress being made toward predictions for tokamak-relevant equilibria.

Physics↗