Search NASA⌕ Search

SEARCH · Search NASA

Results for “Equilibria”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 145 records · Page 8

Nonrandom two‐liquid activity coefficient model with association theory

Abstract Considered one of the most versatile and widely used classical thermodynamic models to correlate phase equilibria behavior of nonideal systems, the nonrandom two‐liquid (NRTL) theory does not explicitly account for specific chemical associations such as hydrogen bonding. This deficiency has been recognized as the cause for unsatisfactory representation of association systems like methanol–alkanes binaries. This work presents a practical approach to integrate Wertheim's perturbation theory for association contribution with the classical NRTL model. Specifically, the association contribution is calculated from pre‐determined molecule‐specific association strengths while the physical interaction contribution is captured with NRTL binary interaction parameters. The resulting association NRTL model correlates fluid phase equilibria of association systems with few adjustable parameters and offers improved predictive capability for higher order systems.

Hao, Yifan↗

Estimation of isosteric heat of adsorption from generalized Langmuir isotherm

Simulation and design of adsorptive separation units demand accurate estimation of thermodynamic properties. Isosteric heat of adsorption as calculated from generalized Langmuir (gL) isotherm coupled with Clausius-Clapeyron expression for pure component and mixed-gas adsorption equilibria is presented in this work. The estimated isosteric heat of adsorption as functions of surface loading and composition is validated against the experimental data for various adsorption systems. Furthermore, the gL results are compared against classical Langmuir (cL) and Toth isotherm for pure components and with Ideal Adsorbed Solution Theory (IAST) for mixed-gas adsorption equilibria. Furthermore, the comparison highlights that gL outperforms cL and Toth for pure component adsorption and IAST for mixed-gas adsorption, and gL reliably captures the loading dependence and the composition dependence for isosteric heat of adsorption.

42 ENGINEERING↗

The influence of cooling rates on strain phase diagrams and domain structures of ferroelectric thin films: A case study of PbTiO 3

Strain engineering has been established as an effective approach to control phase equilibria, domain configurations, and functional properties of ferroelectric thin films. Temperature-strain phase diagrams have been used as powerful tools for providing insights into strain engineering. However, almost all existing phase diagrams established using the phase-field approach assume quenching conditions without considering actual cooling rates during the post-deposition annealing process of ferroelectric thin films. Within this work, we systematically investigate the influence of cooling rates on domain structures and the strain-phase diagram of ferroelectric thin films using phase-field simulations, taking PbTiO 3 thin films as a model system. We found that both the position of phase boundaries in the strain phase diagrams and the domain morphology are significantly influenced by the cooling rates. It is revealed that while the paraelectric-ferroelectric phase boundary remains invariant, the phase boundaries between single-phase and multi-phase regions tend to shift toward the corresponding multi-phase region as the cool rate reduces. Slow cooling generally leads to more ordered domain structures with increased domain size. Using the obtained equilibrium domain structures, we calculated effective thermal conductivities and found significant variations that can be tuned by the cooling rates. In conclusion, this work reveals an underexplored yet critical impact of cooling rates on phase equilibria and domain structures in ferroelectric thin films, which may inspire further fine-tuning of domains and domain walls in low-dimensional ferroelectrics for multifunctional applications.

Domain structures↗

Thermodynamic modeling of calcium carbonate scale precipitation: aqueous Na + -Ca 2+ -Cl – -HCO 3 – -CO 3 2– -CO 2 system

To allow for accurate calculations of calcium carbonate scaling in highly saline produced waters, we present a comprehensive thermodynamic model based on the electrolyte nonrandom two-liquid (eNRTL) activity coefficient equation for the aqueous Na ⁺ -Ca ²⁺ -Cl – -HCO 3 – -CO 3 ²– -CO 2 system. The eNRTL binary interaction parameters for the H 2 O:(Na ⁺ -CO 3 2– ) pair, the H 2 O:(Na ⁺ -HCO 3 – ) pair, the (Na⁺-Cl–):(Na ⁺ -CO 3 2– ) pair, and the (Na ⁺ -Cl – ):(Na ⁺ -HCO 3 – ) pair are identified in this work via the regression of thermodynamic, calorimetric, and phase equilibria experimental data. The binary interaction parameters associated with the H 2 O:(Na ⁺ -Cl – ) pair, the CO 2 :(Na ⁺ -Cl – ) pair, the H 2 O:(Ca ²⁺ -Cl – ) pair, and the (Na ⁺ -Cl – ):(Ca ²⁺ -Cl – ) pair are retrieved from the literature. The remaining binary interaction parameters are retrieved from Aspen Plus or set to zero. In addition, the solubility product constants are identified for Na 2 CO 3 ·10H 2 O (s) , Na 2 CO 3 · 7H 2 O (s) , Na 2 CO 3 ·H 2 O (s) , Na 2 CO 3 ·NaHCO 3 2H 2 O (s) , Na 2 CO 3 ·3NaHCO 3 (s) , and CaCO 3(s) via regression of solubility data. Here, the model is capable of accurately calculating all phase equilibria and calorimetric properties at temperatures up to 473.15 K and salt concentrations up to saturation.

42 ENGINEERING↗

Experimental investigation and thermodynamic modeling of the binary Pt–Sn system

Here, the thermodynamics of the Pt–Sn system is revisited with attention to phase equilibria involving PtSn 4 , a topological quantum material with interesting physical properties. The phase relationship in the Sn-rich region of the Pt–Sn binary system was investigated by a combination of differential scanning calorimetry and equilibration experiments. Based on the present experiments and a critical evaluation of the available thermodynamic and phase diagram data reported in the literature, thermodynamic assessments of the entire Pt–Sn system were performed using the CALPHAD approach. Two sets of thermodynamic parameters were optimized, where the liquid phase was described using the Bragg-Williams random mixing model and the associate solution model, respectively. The modeling results are compared with the reliable experimental data and are shown to provide good representations of the phase equilibria and thermodynamic properties in this system.

36 MATERIALS SCIENCE↗

Thermodynamic evaluation and modeling of the CeF 3 -LaF 3 -LiF-NaF system

The thermodynamic properties of the LiF-NaF-CeF 3 -LaF 3 pseudo-quaternary system have been evaluated, and models for the relevant phases have been revised or newly developed. The solid solubility of NaF in LaF 3 and CeF 3 was described in the model based on reported phase-equilibria observations and results from density functional theory calculations. The Gibbs energy functions for the NaCeF 4 and NaLaF 4 phases have been updated with recently reported thermochemical measurements. The Gibbs energy functions and model relations for the LiF-NaF-LaF 3 and LiF-NaF-CeF 3 pseudo-ternary systems were successfully optimized based on thermochemical properties and phase equilibria observations.

CALPHAD↗

Thermodynamic modeling of CsF with LiF-NaF-KF for molten fluoride-fueled reactors

Gibbs energy models were developed to describe the thermochemical behavior of CsF in molten FLiNaK (46.5LiF-11.5NaF-42KF mol%), a proposed molten salt reactor (MSR) fuel solvent and coolant, as cesium is of concern due to its high radiotoxicity and volatility. Initially, it was necessary to obtain a more accurate Gibbs energy function for CsF which required fitting parameters to reported vapor pressures over condensed phase CsF. The pseudo-binary systems CsF-LiF, CsF-NaF and CsF-KF were then evaluated utilizing phase equilibria and enthalpy of mixing (Δ mix H) values, together with original differential scanning calorimetry (DSC) measurements performed for the CsF-LiF and CsF-KF systems. The CsF-LiF-NaF, CsF-LiF-KF and CsF-NaF-KF pseudo-ternary system representations were obtained by interpolation of the constituent pseudo-binary systems, with DSC measurements performed for the CsF-LiF-NaF system to corroborate the calculated liquidus temperature. Ultimately, the pseudo-ternary systems were interpolated to obtain Gibbs energy models for the pseudo-quaternary CsF-LiF-NaF-KF system, supported by DSC measurements at low CsF compositions (1–10 mol%), yielding computed equilibria and cesium-containing vapor pressures that compare favorably with reported values. In conclusion, the Molten Salt Thermal Properties Database – Thermochemical (MSTDB-TC) was subsequently expanded to include these Gibbs energy models allowing description of the thermochemical behavior of the CsF-LiF-NaF-KF system.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Thermodynamic properties of ZrCl 4 with LiCl, NaCl, KCl, CsCl, MgCl 2 , and UCl 3 for molten salt reactor applications

Here, a set of self-consistent Gibbs energy functions has been developed to describe the thermochemical behavior of the major reactive fission product ZrCl 4 with key components in chloride molten salt reactors (MSRs): LiCl–ZrCl 4 , NaCl–ZrCl 4 , KCl–ZrCl 4 , CsCl–ZrCl 4 , MgCl 2 –ZrCl 4 and UCl 3 –ZrCl 4 . Low ZrCl 4 concentration phase equilibria most relevant to MSR applications have been confirmed via differential scanning calorimetry for NaCl–ZrCl 4 , and X-ray diffraction analysis performed on equilibrated samples of NaCl–ZrCl 4 , KCl–ZrCl 4 , MgCl 2 –ZrCl 4 , and UCl 3 –ZrCl 4 . Within the framework of the modified quasi-chemical model in the quadruplet approximation, extrapolations of pseudo-binary models were generated to represent KCl–MgCl 2 –ZrCl 4 , KCl–NaCl–ZrCl 4 , and MgCl 2 –NaCl–ZrCl 4 , which show agreement with phase equilibria data where available without the use of ternary interaction parameters. The optimized thermodynamic descriptions for these systems and others are available in the open-source compendium Molten Salt Thermal Properties Database – Thermochemical (MSTDB–TC).

CALPHAD↗

Leveraging computational thermodynamics to guide SiC-ZrC chemical vapor deposition process development

Here using the CALPHAD approach to understand zirconium carbide deposition, a series of phase equilibria were calculated from a custom thermodynamic database based on a literature source, and the equilibria were used to explore the potential chemical vapor deposition (CVD) processing space in the ZrCl 4 -CH 3 SiCl 3 -CH 4 -H 2 system as a function of pressure, temperature, and gas composition. Several gas ratios were considered. At a given ZrCl 4 :CH 3 SiCl 3 ratio within the range studied, the most important factor was found to be the ratios of CH 4 :ZrCl 4 , wherein the nature of the composition – carbide vs. silicide – could be controlled. A pure binary composition of ZrC and SiC is expected to form by increasing the initial amount of methane and decreasing the amount of hydrogen from values predicted purely based on thermodynamic equilibrium. Rietveld analysis of the x-ray diffractograms from corresponding experimental depositions confirmed that increasing the CH 4 :ZrCl 4 ratio increased the fraction of carbon-containing species (SiC, ZrC) and decreased the fraction of non-carbides (ZrSi, ZrSi 2 , etc.), as predicted from the CALPHAD results.

36 MATERIALS SCIENCE↗

The DESC stellarator code suite. Part 2. Perturbation and continuation methods

A new perturbation and continuation method is presented for computing and analysing stellarator equilibria. The method is formally derived from a series expansion about the equilibrium condition $\boldsymbol {F} \equiv \boldsymbol {J}\times \boldsymbol {B} - \boldsymbol {\nabla } p = 0$ , and an efficient algorithm for computing solutions to second- and third-order perturbations is developed. The method has been implemented in the DESC stellarator equilibrium code, using automatic differentiation to compute the required derivatives. Examples are shown demonstrating its use for computing complicated equilibria, perturbing a tokamak into a stellarator and performing parameter scans in pressure, rotational transform and boundary shape in a fraction of the time required for a full solution.

Conlin, Rory (ORCID:0000000183662111)↗

Magnetic fields with general omnigenity

Omnigenity is a desirable property of toroidal magnetic fields that ensures confinement of trapped particles. Confining charged particles is a basic requirement for any fusion power plant design, but it can be difficult to satisfy with the non-axisymmetric magnetic fields used by the stellarator approach. Every ideal magnetohydrodynamic equilibrium previously found to approximate omnigenity has been either axisymmetric, quasi-symmetric or has poloidally closed contours of magnetic field strength $B$ . However, general omnigenous equilibria are a much larger design space than these subsets. A new model is presented and employed in the DESC stellarator optimization suite to represent and discover the full parameter space of omnigenous equilibria. Although exact omnigenity aside from quasi-symmetry is impossible, these results reveal that excellent particle confinement can be achieved in practice. Examples far from quasi-symmetry with poloidally, helically and toroidally closed $B$ contours are attained with DESC and shown to have low neoclassical collisional transport and fast particle losses.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Intramolecular Electrostatic Effects on O 2 , CO 2 , and Acetate Binding to a Cationic Iron Porphyrin

Noncovalent electrostatic interactions are important in many biological and chemical reactions, especially those that involve charged intermediates. There has been a growing interest in using electrostatic ligand designs—placing charges in the second coordination sphere—to improve molecular reactivity, catalysis, and electrocatalysis. For instance, an iron porphyrin bearing four cationic ortho -trimethylanilinium groups, Fe( o -TMA), has been reported to be an exceptional electrocatalyst for both the carbon dioxide reduction reaction (CO 2 RR) and the oxygen reduction reaction (ORR). These reactions involve many different steps, and it is not evident which steps are affected by the four positive charges, or why. By comparing Fe( o -TMA) with the related iron-tetraphenylporphyrin, this work examines how covalently positioned charged groups affect substrate binding and other key pre-equilibria of both the ORR and CO 2 RR, specifically acetate, dioxygen, and carbon dioxide binding. This study is among the first to directly measure the effects of electrostatics on ligand-binding. The results show that adding electrostatic groups to a catalyst design often results in a complex interplay of multiple effects, including changes in pre-equilibria prior to substrate binding, combinations of through-space and inductive contributions, and effects of ionic strength and solution dielectric. The inverse half-order dependence of binding constant on ionic strength is proposed as a clear marker for an electrostatic effect. Overall, the conclusions provide guidance for the increasingly popular electrostatic ligand designs in catalysis and other reactivity.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

On the Thermodynamic Condition for Adsorption Azeotropes

Adsorption azeotropy is a common phenomenon in mixed-gas adsorption equilibria. Since the first literature report of binary adsorption azeotropes in 1933, numerous studies investigated the thermodynamic conditions for adsorption azeotropes but failed to reach definitive conclusions. Based on the generalized Langmuir isotherm model for multicomponent adsorption equilibria which takes into account the vacant site as part of the adsorbed phase, this study presents the thermodynamic condition for adsorption azeotropes as derived from the generalized Langmuir isotherm to be the equality of the ratios of adsorbed phase activity coefficient γi and adsorption equilibrium constant $K$$^{o}_{i}$ for the two adsorbates in the binary 1–2 adsorption system, i.e., γ 1 /$K$$^{o}_{1}$ = γ 2 /$K$$^{o}_{2}$. This adsorption azeotropic condition is analogous to the vapor–liquid equilibrium azeotropic condition, i.e., the equality of the products of liquid phase activity coefficient and saturation vapor pressure Pisat for the two components, i.e., γ 1 $P$$^{sat}_{1}$ = γ 2 $P$$^{sat}_{2}$. We validated the thermodynamic condition for adsorption azeotropes with 14 azeotrope-forming adsorption systems in this study. As a result, we investigated the effects of the pressure, temperature, and adsorbed phase nonideality on azeotrope formation.

42 ENGINEERING↗

A Novel Method to Train Classification Models for Structure Detection in In Situ Spacecraft Data

We present a method for creating spacecraft-like data which can be used to train Machine Learning (ML) models to detect and classify structures in in situ spacecraft data. First, we use the Grad-Shafranov equation to numerically solve for several magnetohydrostatic equilibria which are variations on a known analytic equilibrium. These equilibria are then used as the initial conditions for Particle-In-Cell simulations in which the structures of interest are observed and labeled. We then take one-dimensional slices through the simulations to replicate what a spacecraft collecting data from the simulation would observe. This sliced data then can be used as training data for the initial training of ML models intended for use on spacecraft data. We demonstrate the method applied to the problem of detecting small-scale plasmoids in the magnetotail, which is important for understanding complex magnetotail reconnection dynamics. The simple 1D classifier we train is able to detect more than 70% of the plasmoid points in the data set but also produces a large number of false positives. Our further work on this example problem is detailed, and further potential uses of the method are discussed.

79 ASTRONOMY AND ASTROPHYSICS↗

Computational remodeling of an enzyme conformational landscape for altered substrate selectivity

Structural plasticity of enzymes dictates their function. Yet, our ability to rationally remodel enzyme conformational landscapes to tailor catalytic properties remains limited. Here, we report a computational procedure for tuning conformational landscapes that is based on multistate design of hinge-mediated domain motions. Using this method, we redesign the conformational landscape of a natural aminotransferase to preferentially stabilize a less populated but reactive conformation and thereby increase catalytic efficiency with a non-native substrate, resulting in altered substrate selectivity. Steady-state kinetics of designed variants reveals activity increases with the non-native substrate of approximately 100-fold and selectivity switches of up to 1900-fold. Structural analyses by room-temperature X-ray crystallography and multitemperature nuclear magnetic resonance spectroscopy confirm that conformational equilibria favor the target conformation. Our computational approach opens the door to targeted alterations of conformational states and equilibria, which should facilitate the design of biocatalysts with customized activity and selectivity.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Dynamic metal-linker bonds in metal–organic frameworks

Metal-linker bonds serve as the “glue” that binds metal ions to multitopic organic ligands in the porous materials known as metal–organic frameworks (MOFs). Despite ample evidence of bond lability in molecular and polymeric coordination compounds, the metal-linker bonds of MOFs were long assumed to be rigid and static. Given the importance of ligand fields in determining the behaviour of metal species, labile bonding in MOFs would help explain outstanding questions about MOF behaviour, while providing a design tool for controlling dynamic and stimuli-responsive optoelectronic, magnetic, catalytic, and mechanical phenomena. Here, in this work, we present emerging evidence that MOF metal-linker bonds exist in dynamic equilibria between weakly and tightly bond conformations, and that these equilibria respond to guest–host chemistry, drive phase change behavior, and exhibit size-dependence in MOF nanoparticles.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Global geodesic acoustic mode in an ideal magnetohydrodynamic tokamak plasma

A concise and transparent second order ordinary differential equation (ODE) describing the radial structure of the global geodesic acoustic mode (GAM) is analytically presented in a low-β tokamak plasma. The large-aspect-ratio and circular cross section are assumed to linearize the ideal magnetohydrodynamic equations. We show clearly how finite β-dependent terms affect the global GAM frequency and radial mode structure. Here, a typical Wentzel–Kramers–Brillouin form of solution is found for some reversed shear equilibria. For some other equilibria with lower β, even also in a reversed shear tokamak, the GAM continuum is upraised by the high order β-dependent terms so that its maximum is beyond ω G , where ω G is the classical local frequency of GAM. As a result, no self-consistent solution to the ODE can be found.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DESC: A stellarator equilibrium solver

In this paper, the new code DESC is presented to solve for fixed-boundary ideal magnetohydrodynamic equilibria in stellarators. The approach directly solves the equilibrium force balance as a system of nonlinear equations in the form f(x) = 0. The independent variables x represent nested magnetic flux surfaces expressed in the inverse representation with toroidal flux coordinates, and the equations f(x) quantify equilibrium force balance errors at discrete points in real space. Discretizing with global Fourier–Zernike basis functions properly treats the magnetic axis and minimizes the number of coefficients needed to describe the flux surfaces. The pseudospectral method provides great flexibility in where the errors are evaluated, and the system of equations is efficiently solved with a Newton–Raphson iteration. Equilibria are computed and compared against VMEC for both axisymmetric and non-axisymmetric examples. The results show fast convergence rates and solutions with low errors throughout the plasma volume.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗