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At least 739 records · Page 41

Real-space observation of ergodicity transitions in artificial spin ice

Abstract Ever since its introduction by Ludwig Boltzmann, the ergodic hypothesis became a cornerstone analytical concept of equilibrium thermodynamics and complex dynamic processes. Examples of its relevance range from modeling decision-making processes in brain science to economic predictions. In condensed matter physics, ergodicity remains a concept largely investigated via theoretical and computational models. Here, we demonstrate the direct real-space observation of ergodicity transitions in a vertex-frustrated artificial spin ice. Using synchrotron-based photoemission electron microscopy we record thermally-driven moment fluctuations as a function of temperature, allowing us to directly observe transitions between ergodicity-breaking dynamics to system freezing, standing in contrast to simple trends observed for the temperature-dependent vertex populations, all while the entropy features arise as a function of temperature. These results highlight how a geometrically frustrated system, with thermodynamics strictly adhering to local ice-rule constraints, runs back-and-forth through periods of ergodicity-breaking dynamics. Ergodicity breaking and the emergence of memory is important for emergent computation, particularly in physical reservoir computing. Our work serves as further evidence of how fundamental laws of thermodynamics can be experimentally explored via real-space imaging.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Microstructure and properties of additively manufactured Al–Ce–Mg alloys

Additive manufacturing of aluminum alloys is largely dominated by a near-eutectic Al-Si compositions, which are highly weldable, but have mechanical properties that are not competitive with conventional wrought Al alloys. In addition, there is a need for new Al alloys with improved high temperature properties and thermal stability for applications in the automotive and aerospace fields. In this work, we considered laser powder bed fusion additive manufacturing of two alloys in the Al–Ce–Mg system, designed as near-eutectic (Al–11Ce–7Mg) and hyper-eutectic (Al–15Ce–9Mg) compositions with respect to the binary L → Al + Al 11 Ce eutectic reaction. The addition of magnesium is used to promote solid solution strengthening. A custom laser scan pattern was used to reduce the formation of keyhole porosity, which was caused by excessive vaporization due to the high vapor pressure of magnesium. The microstructure and tensile mechanical properties of the alloys were characterized in the as-fabricated condition and following hot isostatic pressing. The two alloys exhibit significant variations in solidification structure morphology. These variations in non-equilibrium solidification structure were rationalized using a combination of thermodynamic and thermal modeling. Both alloys showed higher yield strength than AM Al-10Si-Mg for temperatures up to 350 °C and better strength retention at elevated temperatures than additively manufactured Scalmaloy.

36 MATERIALS SCIENCE↗

Quantum sensing of paramagnetic analytes by nanodiamonds in levitated microdroplets and aqueous solutions

Nanodiamonds (ND) hosting negatively charged nitrogen-vacancy (NV-) color centers have received attention for applications in magnetic field, electric field, chemical, and bio-sensing. The versatility of these probes is their excellent room-temperature optical and spin properties, along with their small size, functionalized surfaces and resistance to bleaching, making them ideal as nanoscopic sensors in picoliter volumes (e.g. single cells, but also microcompartments and aerosols). For quantitative ND-NV- sensing of paramagnetic analytes in such contexts, however, there remains an incomplete understanding of how factors related to the aqueous phase environment control detection efficiency. To address this, optically detected magnetic resonance (ODMR) is measured in bulk macroscale solutions and single levitated microdroplets as a function of Gd+3 concentration (340 nM to 1.5 mM), nanodiamond size, pH, competitor ions, and ligands. The ODMR response to [Gd+3] is found to be nonlinear, and pH, ND and sample volume dependent; indicating the detection of Gd+3 requires efficient adsorption of the analyte to the diamond surface. Langmuir adsorption isotherms embedded in a quantitative photophysical model links the ODMR response to adsorption thermodynamics of Gd+3. The equilibrium constant for Gd+3 adsorption to a carboxylated ND surface is determined to be (1 ± 0.5) x 105 M-1 corresponding to a free energy of adsorption of (-28 ± 1) kJ mol-1. These results provide general insight into how complex aqueous and microscale environments impact nanodiamond based quantum sensing modalities, and portend their application as quantitative chemical sensors in microenvironments.

Brown, Emily K↗

Field, frequency, and temperature dependencies of the surface resistance of nitrogen diffused niobium superconducting radio frequency cavities

We investigate the rf performance of several single-cell superconducting radio-frequency cavities subjected to low temperature heat treatment in nitrogen environment. The cavities were treated at temperature 120 – 165 ° C for an extended period of time (24–48 h) either in high vacuum or in a low partial pressure of ultrapure nitrogen. The improvement in Q 0 with a Q rise was observed when nitrogen gas was injected at ∼ 300 ° C during the cavity cooldown from 800 ° C and held at 165 ° C , without any degradation in accelerating gradient over the baseline performance. The treatment was applied to several elliptical cavities with frequency ranging from 0.75 to 3.0 GHz, showing an improved quality factor as a result of low temperature nitrogen treatments. The Q rise feature is similar to that achieved by nitrogen alloying Nb cavities at higher temperature, followed by material removal by electropolishing. The surface modification was confirmed by the change in electronic mean free path and tuned with the temperature and duration of heat treatment. The decrease of the temperature-dependent surface resistance with increasing rf field, resulting in a Q rise, becomes stronger with increasing frequency and decreasing temperature. The data suggest a crossover frequency of ∼ 0.95 GHz above that the Q rise phenomenon occurs at 2 K. Some of these results can be explained qualitatively with an existing model of intrinsic field-dependence of the surface resistance with both equilibrium and nonequilibrium quasiparticle distribution functions. The change in the Q slope below 0.95 GHz may result from masking contribution of trapped magnetic flux to the residual surface resistance. Published by the American Physical Society 2024

43 PARTICLE ACCELERATORS↗

Observability of negative capacitance of a ferroelectric film: Theoretical predictions

Here, we theoretically explore mechanisms that can potentially give rise to the steady-state and transient negative capacitance in a uniaxial ferroelectric film stabilized by a dielectric layer. The analytical expressions for the steady-state capacitance of a single-domain and polydomain states are derived within the Landau-Ginzburg-Devonshire approach and used to study the state stability vs the domain splitting as a function of dielectric layer thickness. Analytical expressions for the critical thickness of the dielectric layer, polarization amplitude, equilibrium domain period, and susceptibility are obtained and corroborated by finite element modeling. Furthermore we explore the possible effects of nonlinear screening by two types of screening charges at the ferroelectric-dielectric interface and show that if at least one of the screening charges is very slow, the total polarization dynamics can exhibit complex time- and voltage-dependent behaviors that can be interpreted as an observable negative capacitance. In this setting, the transient negative capacitance effect is accompanied by almost zero dielectric susceptibility in a wide voltage range and low frequencies. These results may help to elucidate the observation of the transient negative capacitance in thin ferroelectric films, and identify materials systems that can give rise to the behavior.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Outcomes and Insights From Simplified Analytic Trajectory Optimization for a Tethered Underwater Kite

This letter formulates and solves a periodic trajectory optimization problem for a tethered underwater kite. The goal is to maximize the average mechanical power harvested by the kite. The type of kite considered in this letter extracts electricity from ocean currents by moving cross-current as its reel away from its base station, and consumes electricity to reel back. The problem of optimizing this kite’s trajectory is challenging due to the high dimensionality and nonlinearity of its dynamics. To tackle this challenge, the literature often separates the problem into two subproblems focusing on optimizing the cross-current and the reel-in/reel-out components of the trajectory, respectively, which may be sub-optimal. In contrast, this letter solves for the combined cross-current and reel-in/reel-out trajectory by linearizing the dynamics of the kite around a zero-power reference equilibrium trajectory in spherical coordinates. This allows the trajectory optimization problem to be solved analytically for simple sinusoidal input perturbations from equilibrium. Here we use linear quadratic regulation to enable the nonlinear kite model to track the optimized trajectory. The result is a computationally efficient approach that achieves an attractive Loyd factor of 19.9%, while providing important insights into the nature of the optimal trajectory.

42 ENGINEERING↗

Linking Community‐Climate Disequilibrium to Ecosystem Function

Turnover in species composition often lags behind the pace of climate change, resulting in mismatches between climate and communities. However, the impact of these community‐climate disequilibria on ecosystem functions is rarely considered, and current methods for measuring disequilibria assume that species ranges were, until recently, in equilibrium with climate. Here, in this work, we develop a simple theoretical model to address both of these problems by linking community‐climate disequilibrium with ecosystem functioning. We show how disequilibrium can impair functioning in the near‐term even when climate change is expected to enhance functioning in the long‐term. Responses are most likely to change over time in communities where turnover is slow, the impact of disequilibrium counteracts the direct effects of climate on ecosystem function, and pre‐existing disequilibrium is large. These findings emphasise the importance of precise and unbiased estimates of community‐climate disequilibria for improving ecological forecasts. By fitting our model to time series of both climate and ecosystem function from a metacommunity simulation, we show the potential for community‐climate disequilibrium to be inferred without direct knowledge about species' distributions or climatic tolerances. We end by outlining a research agenda to apply dynamic disequilibrium concepts and test novel hypotheses across diverse ecosystems.

climate change↗

Theoretical Understanding of the Linear Relationship between Convective Updrafts and Cloud-Base Height for Shallow Cumulus Clouds. Part II: Continental Conditions

This is the Part II of a two-part study that seeks a theoretical understanding of an empirical relationship for shallow cumulus clouds: subcloud updraft velocity covaries linearly with the cloud-base height. This work focuses on continental cumulus clouds that are more strongly forced by surface fluxes and more deviated from equilibrium than those over oceans (Part I). We use a simple analytical model for shallow cumulus that is well tested against a high-resolution (25 m in the horizontal) large-eddy simulation model. Consistent with a conventional idea, we find that surface Bowen ratio is the key variable that regulates the covariability of both parameters: under the same solar insolation, a drier surface allows for stronger buoyancy flux, triggering stronger convection that deepens the subcloud layer. We find that the slope of the Bowen-ratio-regulated relationship between the two parameters (defined as λ) is dependent on both the local time and the stability of the lower free atmosphere. The value of λ decreases with time exponentially from sunrise to early afternoon and linearly from early afternoon to sunset. The value of λ is larger in a more stable atmosphere. In addition, continental λ in the early afternoon more than doubles the oceanic λ. Validation of the theoretical results against ground observations over the Southern Great Plains shows a reasonable agreement. Physical mechanisms underlying the findings are explained from the perspective of different time scales at which updrafts and cloud-base height respond to a surface flux forcing.

54 ENVIRONMENTAL SCIENCES↗

Comparative Study of High-Resolution LysB29(Nε-myristoyl) des(B30) Insulin Structures Display Novel Dynamic Causal Interrelations in Monomeric-Dimeric Motions

The treatment of insulin-dependent diabetes mellitus is characterized by artificial supplementation of pancreatic β-cell ability to regulate sugar levels in the blood. Even though various insulin analogs are crucial for reasonable glycemic control, understanding the dynamic mechanism of the insulin analogs may help to improve the best-protracted insulin analog to assist people with type 1 diabetes (T1D) to live comfortably while maintaining tight glycemic control. Here, we present the high-resolution crystal structure of NN304, known as insulin detemir, to 1.7 Å resolution at cryogenic temperature. We computationally further investigated our crystal structure’s monomeric-dimeric conformation and dynamic profile by comparing it with a previously available detemir structure (PDB ID: 1XDA). Our structure (PDB ID: 8HGZ), obtained at elevated pH, provides electrostatically triggered minor movements in the equilibrium between alternate conformational substates compared to the previous structure, suggesting it might induce an intermediate state in the dissociation pathway of the insulin detemir’s hexamer:dihexamer equilibrium. Supplemented with orientational cross-correlation analysis by a Gaussian network model (GNM), this alternate oligomeric conformation offers the distinct cooperative motions originated by loose coupling of distant conformational substates of a protracted insulin analog that has not been previously observed.

59 BASIC BIOLOGICAL SCIENCES↗

Technical note: A modified formulation of dynamic energy budget theory for faster computation of biological growth

Abstract. The mass conservation equation in the presence of boundary fluxes and chemical reactions from non-equilibrium thermodynamics is used to derive a modified dynamic energy budget (mDEB) model. Compared to the standard dynamic energy budget (sDEB) model (Kooijman, 2009), this modified formulation does not place the dilution effect in the mobilization kinetics of reserve biomass, and it maintains the partition principle for reserve mobilization dynamics for both linear and non-linear kinetics. Overall, the mDEB model shares most features with the sDEB model. However, for biological growth that requires multiple nutrients, the mDEB model is computationally much more efficient by not requiring numerical iterations for obtaining the specific growth rate. In an example of modeling the growth of Thalassiosira weissflogii in a nitrogen-limiting chemostat, the mDEB model was found to have almost the same accuracy as the sDEB model while requiring almost half of the computing time of the sDEB model. Since the sDEB model has been successfully applied in numerous studies, we believe that the mDEB model can help improve the modeling of biological growth and the associated ecosystem processes in various contexts.

Tang, Jinyun↗

Acceleration of Thermochemistry Solves in MOOSE and Pronghorn

This work focuses on the development and implementation of strategies to accelerate thermochemical calculations within MOOSE-based multiphysics simulations, particularly for applications in MSRs. We highlight the inherent complexity of nuclear materials, which require a multiscale approach to accurately model their behavior across various physical domains, including mechanical, chemical, and thermal phenomena. Thermochemical equilibrium calculations are crucial for predicting material properties and enhancing the fidelity of these simulations. The integration of Thermochimica, a Gibbs energy minimizer, into MOOSE allows for the direct minimization of Gibbs energy at every point on the mesh. However, the computational cost of such integration is significant. To address this, we explored acceleration strategies such as multi-threading support and the use of a thermodynamic ValueCache to reduce redundant calculations. Additionally, we investigated modifications to Thermochimica to enable phase constraints and improve its coupling with phase-field models, which are essential for simulating microstructural evolution and corrosion in MSR. These efforts aim to optimize the computational efficiency and accuracy of multiphysics simulations, thereby supporting the development of reliable and efficient nuclear materials for next-generation reactor technologies.

36 - MATERIALS SCIENCE↗

Transient Modeling and Simulation of a Generic Stable Salt Reactor

A SAM system-level model of a generic stable salt reactor has been developed to investigate thermal-hydraulic behavior and safety performance under steady and transient conditions. The model integrates information generated from a reactor physics analysis using PROTEUS and PERSENT, and a computation fluid dynamics (CFD) analysis using STAR-CCM+. A loose, iterative coupling scheme between PROTEUS and SAM is implemented to calculate the equilibrium power and temperature distributions in the steady-state critical core condition. The converged steady-state model is then used in PERSENT to calculate the four reactivity feedback temperature coefficients (Doppler, fuel density, coolant density, and core radial expansion) and kinetic parameters that are needed in SAM to model the temperature feedback effects in transient simulations. Within the fully enclosed liquid fuel pins, natural convection is the dominant heat transfer mechanism. The STAR-CCM+ model of the fuel pin considers conjugate heat transfer from the liquid fuel salt to the pin cladding and external reactor coolant. The CFD results of the axial and radial temperature profiles are used to empirically determine an effective fuel salt thermal conductivity in the SAM fuel pin model so that the temperatures predicted by the SAM model match as closely as possible the CFD results. In the central region of the fuel pin, the effective thermal conductivity is as high as similar to 60 times the physical fuel salt thermal conductivity. The whole-plant SAM model is then used to simulate an unprotected station blackout transient. The results of this simulation showed that the large negative fuel axial expansion reactivity feedback reduces fission power to similar to 2.4% nominal power. The core is cooled by natural circulation, which removes heat in the core to the emergency heat removal system, and ultimately, to the ambient. However, peak fuel salt and cladding temperatures can potentially reach as high as 1500 K, albeit briefly, if the shutdown mechanism fails to operate.

stable salt reactor; transient simulations; system↗

Rotational excitations in rare-earth nuclei: A comparative study within three cranking models with different mean fields and treatments of pairing correlations

High-spin rotational bands in rare-earth Er (Z = 68), Tm (Z = 69), and Yb (Z = 70) isotopes are investigated by three different nuclear models. These are (i) the cranked relativistic Hartree-Bogoliubov (CRHB) approach with approximate particle number projection by means of the Lipkin-Nogami (LN) method, (ii) the cranking covariant density functional theory (CDFT) with pairing correlations treated by a shell-model-like approach (SLAP) or the so-called particle-number conserving (PNC) method, and (iii) cranked shell model (CSM) based on the Nilsson potential with pairing correlations treated by the PNC method. A detailed comparison between these three models in the description of the ground-state rotational bands of even-even Er and Yb isotopes is performed. The similarities and differences between these models in the description of the moments of inertia, the features of band crossings, and equilibrium deformations and pairing energies of the even-even nuclei under study are discussed. These quantities are considered as a function of rotational frequency and proton and neutron numbers. The changes in the properties of the first band crossings with increasing neutron number in this mass region are investigated. On average, a comparable accuracy of the description of available experimental data is achieved in these models. However, the differences between model predictions become larger above the first band crossings. Because of the time-consuming nature of numerical calculations in the CDFT-based models, a systematic study of the rotational properties of both ground-state and excited-state bands in odd-mass Tm nuclei is carried out only by the PNC-SCM. With few exceptions, the rotational properties of experimental 1-quasiparticle and 3-quasiparticle bands in 165,167,169,171 Tm are reproduced reasonably well. As a result, the appearance of backbendings or upbendings in these nuclei is well understood from the analysis of the variations of the occupation probabilities of the single-particle states and their contributions to total angular momentum alignment with rotational frequency.

150 ≤ A ≤ 189↗

Secondary organic aerosols derived from intermediate-volatility n-alkanes adopt low-viscous phase state

Abstract. Secondary organic aerosol (SOA) derived from n-alkanes, as emitted from vehicles and volatile chemical products, is a major component of anthropogenic particulate matter, yet the chemical composition and phase state are poorly understood and thus poorly constrained in aerosol models. Here we provide a comprehensive analysis of n-alkane SOA by explicit gas-phase chemistry modeling, machine learning, and laboratory experiments to show that n-alkane SOA adopts low-viscous semi-solid or liquid states. Our study underlines the complex interplay of molecular composition and SOA viscosity: n-alkane SOA with a higher carbon number mostly consists of less functionalized first-generation products with lower viscosity, while the SOA with a lower carbon number contains more functionalized multigenerational products with higher viscosity. This study opens up a new avenue for analysis of SOA processes, and the results indicate few kinetic limitations of mass accommodation in SOA formation, supporting the application of equilibrium partitioning for simulating n-alkane SOA formation in large-scale atmospheric models.

54 ENVIRONMENTAL SCIENCES↗

In Situ Insights into Cathode Calcination for Predictive Synthesis: Kinetic Crystallization of LiNiO 2 from Hydroxides

Abstract Calcination is a solid‐state synthesis process widely deployed in battery cathode manufacturing. However, its inherent complexity associated with elusive intermediates hinders the predictive synthesis of high‐performance cathode materials. Here, correlative in situ X‐ray absorption/scattering spectroscopy is used to investigate the calcination of nickel‐based cathodes, focusing specifically on the archetypal LiNiO 2 from Ni(OH) 2 . Combining in situ observation with data‐driven analysis reveals concurrent lithiation and dehydration of Ni(OH) 2 and consequently, the low‐temperature crystallization of layered LiNiO 2 alongside lithiated rocksalts. Following early nucleation, LiNiO 2 undergoes sluggish crystallization and structural ordering while depleting rocksalts; ultimately, it turns into a structurally‐ordered layered phase upon full lithiation but remains small in size. Subsequent high‐temperature sintering induces rapid crystal growth, accompanied by undesired delithiation and structural degradation. These observations are further corroborated by mesoscale modeling, emphasizing that, even though calcination is thermally driven and favors transformation towards thermodynamically equilibrium phases, the actual phase propagation and crystallization can be kinetically tuned via lithiation, providing freedom for structural and morphological control during cathode calcination.

36 MATERIALS SCIENCE↗

Fluoride-Cooled High-Temperature Pebble-Bed Reactor Reference Plant Model

In this report we present work performed in Fiscal Year 2022 that demonstrates the modeling and simulation of a fully coupled neutronics thermal hydraulics reference plant model for a fluoride-cooled high-temperature pebble-bed reactor. The multiphysics model is developed on the Nuclear Regulatory Commission’s Comprehensive Reactor Analysis Bundle (BlueCRAB) available on the Idaho National Laboratory’s high-performance computer, which natively and seamlessly couples Griffin, Pronghorn, and the BISON Multiphysics Object-Oriented Simulation Environment based applications. Griffin provides reactor physics capabilities, including depletion to the equilibrium core, k-eigenvalue, adjoint, and transient. The unique direct equilibrium core capability in Griffin is based on a streamline methodology to spatially deplete the pebbles into burnup groups. Pronghorn solves the porous medium equations for the fluid regions and conduction in the solid regions and incorporates a fluidic diode model to simulate the transition from forced to natural convection during accident scenarios. MOOSE modules solves thermal conduction problems for the pebbles and tristructural isotropic in the pebble-bed core, thus providing the fuel and moderator spatial fields for each pebble burnup group. The neutronics feedback relies primarily on fuel, moderator, and reflector temperatures as as well as the FLiBe salt density. Here, we present results for the uncoupled equilibrium core and perform comparisons to equivalent Monte Carlo models. The power distributions and kinetic parameters obtained with Griffin are consistent with those computed with Griffin. We demonstrate a noticeable improvement with the use of discrete ordinates method (SN) transport. The coupled steady-state equilibrium core provides the initial condition for two time-dependent problems: a control rod withdrawal event and an unprotected loss of flow event. In both cases, the reactor design is self-stabilizing and the solutions are consistent with the expected physics. Although this model is prototypical regarding BlueCRAB’s capabilities, its results are consistent with published work by Kairos Power and other research entities. Significant improvements to the model are planned in future work.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Global X-Ray Properties of the Vela and Puppis A Supernova Remnants

The Vela and Puppis A supernova remnants (SNRs) comprise a large emission region of ∼8° diameter in the soft X-ray sky. The HaloSat CubeSat mission provides the first soft X-ray (0.4–7 keV) observation of the entire Vela SNR and Puppis A SNR region with a single pointing and moderate spectral resolution. HaloSat observations of the Vela SNR are best fit with a two-temperature thermal plasma model consisting of a cooler component with kT{sub 1}=0.19{sub −0.01}{sup +0.01} keV in collisional ionization equilibrium and a hotter component with kT{sub 2}=1.06{sub −0.27}{sup +0.45} keV in nonequilibrium ionization. Observations of the Puppis A SNR are best fit with a single-component plane-parallel shocked plasma model with kT=0.86{sub −0.05}{sup +0.06} keV in nonequilibrium ionization. For the first time, we find the total X-ray luminosities of both components of the Vela SNR spectrum in the 0.5–7 keV energy band to be L{sub X}=4.4{sub −1.4}{sup +1.4}×10{sup 34} erg s{sup −1} for the cooler component and L{sub X}=4.1{sub −1.5}{sup +1.8}×10{sup 34} erg s{sup −1} for the hotter component. We find the total X-ray luminosities of the Vela and Puppis A SNRs to be L{sub X}=8.4×10{sup 34} erg s{sup −1} and L{sub X}=6.7{sub −0.9}{sup +1.1}×10{sup 36} erg s{sup −1}.

79 ASTRONOMY AND ASTROPHYSICS↗

Configuration Space Integration for Adsorbate Partition Functions: The Effect of Anharmonicity on the Thermophysical Properties of CO–Pt(111) and CH 3 OH–Cu(111)

A method for computing anharmonic thermophysical properties for adsorbates on metal surfaces has been extended to include libration, or frustrated rotation. Classical phase space integration is used with Monte Carlo sampling of the configuration space to obtain the partition function of CO on Pt(111) and CH 3 OH on Cu(111). A minima-preserving neural network potential energy surrogate is used within the integration routines. Direct state counting using discrete variable representation is used to benchmark the results. We find that the phase space integration approach is in excellent agreement with the direct state counting results. Comparison with standard models such as the harmonic oscillator indicates that anharmonicity contributes significantly to the thermodynamic properties of CH 3 OH on Cu(111). We find that there is also a considerable difference between the harmonic oscillator and phase space integration for CO on Pt(111), although the discrepancy can largely be attributed to the presence of multiple binding sites within the unit cell. We demonstrate that a multisite harmonic oscillator model might be sufficient for CO-Pt(111). A more thorough description of the potential energy surface, which can be achieved with phase space integration, is necessary for weakly bound adsorbates such as CH 3 OH. In conclusion, the thermophysical properties were used to calculate free energies of adsorption on the respective metals, and subsequently the equilibrium constants and Langmuir isotherms in relevant temperature ranges. The results show that the choice of model to obtain partition functions greatly affects the resulting surface coverages in kinetic models.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗