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Site heterogeneity and broad surface-binding isotherms in modern catalysis: Building intuition beyond the Sabatier principle

Learning the science of heterogeneous catalysis and electrocatalysis always starts with the simple case of a flat, uniform surface with an ideal adsorbate. It has of course been recognized for a century that real catalysts are more complicated. For the increasingly complex catalysts of the 21st century, this Perspective argues that surface heterogeneity and non-ideal binding isotherms are central features, and their implications need to be incorporated in current thinking. A variety of systems are described herein where catalyst complexity leads to broad, non-Langmuirian surface isotherms for the binding of hydrogen atoms – and this occurs even for ideal, flat Pt(111) surfaces. Modern catalysis employs nanoscale materials whose surfaces have substantial step, edge, corner, impurity, and other defect sites, and they increasingly have both metallic and non-metallic elements M n X m , including metal oxides, chalcogenides, pnictides, carbides, doped carbons, etc. The surfaces of such catalysts are often not crystal facets of the bulk phase underneath, and they typically have a variety of potential active sites. Catalytic surfaces in operando are often non-stoichiometric, amorphous, dynamic, and impure, and often vary from one part of the surface to another. Understanding of the issues that arise at such nanoscale, multi-element catalysts is just beginning to emerge. Yet these catalysts are widely discussed using Brønsted/Bell-Evans-Polanyi (BEP) relations, volcano plots, Tafel slopes, the Butler-Volmer equation, and other linear free energy relations (LFERs), which all depend on the implicit assumption that the active sites are “similar” and that surface adsorption is close to ideal. These assumptions underly the ubiquitous intuition based on the Sabatier Principle, that the fastest catalysis will occur when key intermediates have free energies of adsorption that are not too strong nor too weak. Current catalysis research often aims to minimize the complexity of non-ideal isotherms through experimental and computational design (e.g., the use of single crystal surfaces), and these studies are the foundation of the field. In contrast, this Perspective argues that the heterogeneity of binding sites and binding energies is an inherent strength of these catalysts. Here, this diversity makes many nanoscale catalysts inherently a high-throughput screen wrapped in a tiny package. Only by making the heterogeneity part of the foundation of catalysis models, sorting the types of active sites and dissecting non-ideal binding isotherms, will modern catalysis learn to harness the inherent diversity of real catalysts. Controlling and exploiting diversity rather than avoiding it will help to optimize complex modern catalysts and catalytic conditions.

Mayer, James M.↗

Understanding Solvent-Induced Glass Transition in Polymer Thin Films Using Absorption–Desorption Isotherms

The fundamental thermodynamic and mechanical underpinnings of polymer thin films exposed to solvent vapor are critical for the development of advanced nanolithography and high-performance coatings. This work investigates the solvent− polymer interactions of glassy thin films by using the solvent absorption−desorption isotherms. An analogous relationship to the Flory−Fox equation was observed between solvent−induced glass transition, swelling, Flory−Huggins interaction parameter, and molecular weight. Isothermal swelling measurements revealed that the glass transition trends are more robust in the absorption curve compared to desorption, contrary to previous reports. Excess osmotic pressure analysis of the isotherm provides a measure of the degree of physical aging in thin films annealed below the glass transition. This is further validated in the ordering of block copolymer (BCP) films annealed at low solvent activity. In agreement with the thermal analysis, free-surface plasticization effects become the most prominent below 100 nm. However, solvent annealing is largely dependent on solvent mass transport, as made evident by the strong dependence on solvent viscosity. From these observations, four general types of isotherms are identified that graphically capture distinct solvent−polymer interaction regimes. More broadly, these results inform solvent vapor annealing-induced self-assembly, sequential infiltration synthesis, membrane-based separations, adsorptive processes, and swelling-based responsive materials design.

Hendeniya, Nayanathara [Iowa State Univ., Ames, IA↗

Isothermal solidification for high-entropy alloy synthesis

Kinetically trapping the high-temperature states through rapid cooling solidification is widely used for the synthesis of high-entropy alloys (HEAs), especially those with intrinsically immiscible elemental combinations. However, strategies need to be developed to overcome the fundamental limitations of rapid cooling solidification in controlling the crystallinity, structure and morphology of HEAs. Here, in this study, we introduce an isothermal solidification strategy for the synthesis of HEAs by rapidly altering the metal alloy composition through liquid–liquid interface reactions at low temperatures, for example, from 25 °C to 80 °C. We use gallium (Ga)-based metal as the sacrificial reagent and mixing medium. By directing the reactions to the interfaces between the Ga-based liquid metal and an aqueous metal ion solution, the foreign metal ions can be reduced at the interfaces and incorporated into the liquid metal quickly. HEAs with various crystallinity (single crystal, mesocrystal, polycrystal and amorphous), morphology (zero, two and three dimensions) and compositions can be achieved through the isothermal solidification. Ga can be completely consumed, resulting in Ga-free HEAs. If desired, Ga can be one of the metal elements in the final products. In situ liquid phase transmission electron microscopy (TEM) studies and theoretical analysis show the isothermal solidification mechanisms. Our direct observations show the enhanced mixing of liquid metal elements and the solidification process with fluctuating nucleation dynamics. The isothermal solidification marks a powerful strategy for HEA synthesis through an unexplored pathway of kinetically trapping the high-entropy states.

Zhang, Qiubo [Lawrence Berkeley National Laborator↗

Measurement of Palladium Hydride and Palladium Deuteride Isotherms Between 130 K and 393 K

The data collected in the present work extend the measured phase diagram for palladium hydride and palladium deuteride to a region that has been sparsely reported in open literature. Absorption isotherms were measured using a 2.5-g bed of palladium powder at temperatures between 130 K and 393 K and pressures less than 1.3 x 10 5 Pa. Such low-pressure and low-temperature measurements are useful for characterizing palladium beds used for tritium pumping and storage. For tritium storage, pressures are kept below a few millibar for safety reasons. Low temperatures increase the tritium storage capacity of palladium. The measured absorption isotherms show the well-documented, two-phase behavior for this system: two solubility regions and a mixed, hydride-forming region. The isotherms show that an increased quantity of hydride is formed at lower temperatures, as marked by an increase in the hydride-forming region. This region exceeds hydrogen to metal ratios of 0.75 for T ≤ 273 K. Equilibrium pressures in the mixed region decrease with decreasing temperatures until a critical temperature is reached for each isotope. Below these critical temperatures, the rate of pressure decrease with decreasing temperature is significantly reduced. This change in trend suggests hydrogen isotopes are adsorbed onto the palladium surface, rather than forming a hydride. Using the equilibrium pressures recorded at temperatures between 236 K and 393 K for protium and between 211 K and 354 K for deuterium, the van’t Hoff constants were calculated to be A = –36 ± 1 kJ/mol and B = 88 ± 3 J/K for protium and A = -32 ± 2 kJ/mol and B = 88 ± 9 J/K for deuterium. As a result, these constants agree favorably with literature in the range where the temperatures of the measured isotherms overlap.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Generalized definition of the isothermal compressibility in (2+1)-flavor QCD

We introduce a generalized definition of the isothermal compressibility ($𝜅_{𝑇,𝜎{^2_𝑄}}$) calculable by keeping net conserved charge fluctuations rather than total number densities constant. We present lattice QCD results for this isothermal compressibility, expressed in terms of fluctuations of conserved charges that are related to baryon (𝐵), electric charge (𝑄), and strangeness (𝑆) quantum numbers. This generalized isothermal compressibility is compared with hadron resonance gas model calculations as well as with heavy-ion collision data obtained at RHIC and the LHC. We find $𝜅_{𝑇,𝜎{^2_𝑄}}$ = 13.8⁢(1.3) fm 3 /GeV at $𝑇_{\textrm{pc},0}$ =156.5⁢(1.5) MeV and $\hat{𝜇}_𝐵$ = 0. This finding is consistent with the rescaled result of the ALICE Collaboration, where we replaced the number of charged hadrons (𝑁 ch ) by the total number of hadrons (𝑁 tot ) at freeze-out. Normalizing this result with the QCD pressure (𝑃) we find that the isothermal compressibility on the pseudocritical line stays close to that of an ideal gas, i.e., $𝑃⁢𝜅_{𝑇,𝜎{^2_𝑄}} ≃$ 1.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Liquid Piston with Spray Cooling Near-Isothermal Compressor

The goal of this project was to prototype and characterize the performance of a liquid-piston spray-cooled gas compressor. The working principle of the compressor enables optimized high-efficiency operation over a very wide range of operating conditions, unlike conventional compressors that are optimized for a narrow range of operating conditions. The compressor technology is suitable for many applications, such as gas pipeline transport, gas storage, and commercial and residential heat pumps. Both physical testing and computational fluid dynamics (CFD) modeling of the processes using the Oak Ridge National Laboratory high-performance computing center were completed. The experimental and CFD studies focused on a near-isothermal liquid-piston compressor (LPC) that uses propylene glycol to compress CO 2 . The first prototype demonstrated isothermal operation during several sequentially executed cycles of CO 2 compression and raised the temperature of the compressed CO 2 by only 2 K, compared with approximately 6 K when the gas was compressed non-isothermally. Isothermal operation was demonstrated at CO 2 flow rates of up to 2 L/min. The second prototype was designed with two compression chambers to allow continuous flow of high-pressure CO 2 . However, the design of the valve train to direct flow between the compression chambers was not sufficient to allow demonstration of CO 2 compression. Numerical simulations of the LPC in which the compression chamber was filled with propylene glycol injected from the bottom inlet were performed using large eddy simulation (LES) with the wall-adapting local eddy-viscosity subgrid-scale model coupled with the multiphase volume of fluid (VOF) model to simulate the transient interface between gas and liquid and to capture the heat and mass transfers within the compression chamber. In this effort, the effects of boundary conditions applied to the LES-VOF calculations (i.e., no wall, an adiabatic wall, and a wall with a heat flux subscribed) on the overall pressure and temperature of the CO 2 gas as well as the transient evolution of flow and heat transfer within the compression chamber were investigated and are discussed in this report. The LES calculation with no wall showed no dynamical flow patterns, and the volume-averaged temperature of CO 2 increased from 305 to 392.7 K, whereas LES calculations with a constant wall temperature or a wall heat flux had similar increases of CO 2 temperatures. The results of the LES simulation using a wall heat flux showed different stages in the compression process and revealed dynamical formation and interaction of CO 2 gas layers and circulation flow patterns within the chamber that contributed to the overall heat transfer between the solid wall, gas, and liquid surface in the compressor. Though an industrial partnership for commercializing the compressor was not secured, the technology was attractive for an industrial partner to use in two research proposals in response to US Department of Energy funding opportunity announcements.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

The physical implications of an isothermal model for the hot intracluster medium

HEAO-1 A-2 and Einstein Observatory IPC observations of 15 clusters of galaxies have been used to measure the isothermal beta-model parameters, and the parameters are compared with those derived from model fits to the X-ray images. The physical constraints imposed on this model by existing optical data, the implied gas mass, and the gas contribution to the binding cluster mass are addressed. Values of beta less than unity are obtained, consistent with results from X-ray imaging data. This is interpreted to imply that the gas extends out to 8-10 core radii, about 2-3 Mpc. The isothermal gas mass can be as large as 60 percent of the virial mass for some clusters. This contradicts the fundamental assumption that the cluster potential is determined by an unseen mass which is given by the King approximation to an isothermal sphere, and it is concluded that the isothermal model is a nonphysical model.

Henriksen, M. J.↗

Calculation of thermomechanical fatigue life based on isothermal behavior

The isothermal and thermomechanical fatigue (TMF) crack initiation response of a hypothetical material was analyzed. Expected thermomechanical behavior was evaluated numerically based on simple, isothermal, cyclic stress-strain - time characteristics and on strainrange versus cyclic life relations that have been assigned to the material. The attempt was made to establish basic minimum requirements for the development of a physically accurate TMF life-prediction model. A worthy method must be able to deal with the simplest of conditions: that is, those for which thermal cycling, per se, introduces no damage mechanisms other than those found in isothermal behavior. Under these assumed conditions, the TMF life should be obtained uniquely from known isothermal behavior. The ramifications of making more complex assumptions will be dealt with in future studies. Although analyses are only in their early stages, considerable insight has been gained in understanding the characteristics of several existing high-temperature life-prediction methods. The present work indicates that the most viable damage parameter is based on the inelastic strainrange.

Halford, Gary R.↗

Calculation of thermomechanical fatigue life based on isothermal behavior

The isothermal and thermomechanical fatigue (TMF) crack initiation response of a hypothetical material was analyzed. Expected thermomechanical behavior was evaluated numerically based on simple, isothermal, cyclic stress-strain-time characteristics and on strainrange versus cyclic life relations that have been assigned to the material. The attempt was made to establish basic minimum requirements for the development of a physically accurate TMF life-prediction model. A worthy method must be able to deal with the simplest of conditions: that is, those for which thermal cycling, per se, introduces no damage mechanisms other than those found in isothermal behavior. Under these assumed conditions, the TMF life should be obtained uniquely from known isothermal behavior. The ramifications of making more complex assumptions will be dealt with in future studies. Although analyses are only in their early stages, considerable insight has been gained in understanding the characteristics of several existing high-temperature life-prediction methods. The present work indicates that the most viable damage parameter is based on the inelastic strainrange.

Halford, G. R.↗

Isothermal and nonisothermal fatigue behavior of a metal matrix composite

The isothermal and nonisothermal fatigue resistance of a metal matrix composite (MMC) consisting of Ti-15V-3Cr-3Al-3Sn (Ti-15-3) matrix reinforced by 33 vol pct continuous SiC fibers was investigated. The fibers were nominally oriented parallel to the specimen axis. Isothermal fatigue tests were performed in air at 300 and 550 C. The MMC had good isothermal fatigue resistance at low cyclic stress, with fatigue cracks initiating from fiber-matrix interfaces and foil laminations. At high cyclic stresses, stress relaxation in the matrix reduced isothermal composite fatigue resistance at 550 C. Nonisothermal fatigue loading substantially degraded composite fatigue resistnce. This degradation was produced by a thermomechanical fatigue damage mechanism associated with the fiber-matrix interfaces.

Gabb, T. P.↗

An analysis of isothermal, bithermal, and thermomechanical fatigue data of Haynes 188 and B1900+Hf by energy considerations

The low-cycle fatigue behavior of Haynes 188 and B1900+Hf under isothermal, bithermal, and thermomechanical loading conditions has been analyzed on the basis of the total hysteresis energy expended per cycle. It has been observed that in the case of isothermal fatigue the total hysteresis energy correlates well with the fatigue life. In the case of bithermal 'high rate' fatigue, for a given total hysteresis energy per cycle, the fatigue life is equal to or greater than the isothermal fatigue life at the maximum bithermal temperature. This observation could be used to establish a lower bound on life for design purposes. In one case of bithermal creep-fatigue and in thermomechanical fatigue, the life is shorter than that corresponding to the isothermal life at the maximum temperature. The energy supplied, per se, may not always give a systematic correlation with the fatigue life in the cases where time-dependent creep and environmental effects are encountered. Thus, in bithermal creep-fatigue and thermomechanical fatigue, the role of creep and environment and their dependence on the energy supplied have to be properly accounted for before the energy term can be used for life prediction.

Radhakrishnan, V. M.↗

On the Isothermality of Solar Plasmas

Recent measurements have shown that the quiet unstructured solar corona observed at the solar limb is close to isothermal, at a temperature that does not appear to change over wide areas or with time. Some in dividual active loop structures have also been found to be nearly iso thermal both along their axis and across their cross-section. Even a complex active region observed at the solar limb has been found to be composed of three distinct isothermal plasmas. If confirmed, these r esults would pose formidable challenges to the current theoretical understanding of the thermal structure and heating of the solar corona. For example, no current theoretical model can explain the excess dens ities and lifetimes of many observed loops if the loops are in fact i sothermal. All of these measurements are based on the so-called emiss ion measure (EM) diagnostic technique that is applied to a set of opt ically thin lines under the assumption of isothermal plasma. It provi des simultaneous measurement of both the temperature and EM. However, no study has ever been carried out to quantify the uncertainties in the technique and to rigorously assess its ability to discriminate bet ween isothermal and multithermal plasmas. Such a study is the topic o f the present work. We define a formal measure of the uncertainty in the EM diagnostic technique that can easily be applied to real data. We here apply it to synthetic data based on a variety of assumed plas ma thermal distributions, and develop a method to quantitatively asse ss the degree of multithermality of a plasma.

Landi, E.↗

Simulating Thermal Cycling and Isothermal Deformation Response of Polycrystalline NiTi

A microstructure-based FEM model that couples crystal plasticity, crystallographic descriptions of the B2-B19' martensitic phase transformation, and anisotropic elasticity is used to simulate thermal cycling and isothermal deformation in polycrystalline NiTi (49.9at% Ni). The model inputs include anisotropic elastic properties, polycrystalline texture, DSC data, and a subset of isothermal deformation and load-biased thermal cycling data. A key experimental trend is captured.namely, the transformation strain during thermal cycling is predicted to reach a peak with increasing bias stress, due to the onset of plasticity at larger bias stress. Plasticity induces internal stress that affects both thermal cycling and isothermal deformation responses. Affected thermal cycling features include hysteretic width, two-way shape memory effect, and evolution of texture with increasing bias stress. Affected isothermal deformation features include increased hardening during loading and retained martensite after unloading. These trends are not captured by microstructural models that lack plasticity, nor are they all captured in a robust manner by phenomenological approaches. Despite this advance in microstructural modeling, quantitative differences exist, such as underprediction of open loop strain during thermal cycling.

Manchiraju, Sivom↗

On the validity and limitations of 1D model for heat and mass transfer performance evaluation in a multilayer binder-free desiccant dehumidifier: isothermal dehumidification with internal cooling

Efficient humidity control is essential for maintaining indoor thermal comfort, yet conventional vapor-compression-based dehumidifiers are energy-intensive. Employing separate sensible and latent cooling through desiccant-coated heat exchangers (DCHEs) combined with evaporative coolers offers energy savings of up to 80 % compared to conventional systems. However, the dehumidification performance of DCHEs remains limited due to the use of polymer binders for coating desiccant materials onto heat exchange surfaces. In our previous study, we developed a multilayer fixed-bed binder-free desiccant dehumidifier (MFBDD) that demonstrated high dehumidification capacity and low pressure drop compared to rotary desiccant wheels. Nevertheless, its potential for further enhancement through internal cooling and the use of step-shaped adsorption isotherms has not been explored. In this study, a physics-based one-dimensional (1D) transient model is developed and validated to capture the coupled heat and mass transfer processes in the MFBDD and extended to simulate internal cooling using a high-capacity composite metal–organic framework, MIL-101/GO-6 (water uptake ≈1.6 g/g within 35–47 % RH). The model enables detailed analysis of local air and bed temperature dynamics and quantifies how internal cooling affects the dehumidification performance under a wide range of operating conditions. Results show that integrating internal cooling and using MIL-101/GO-6 enhance mass adsorbed, moisture removal capacity, and dehumidification effectiveness by 50 %–99 % compared with the M.S. Gel baseline. The study further reveals that achieving near-isothermal operation requires simultaneous enhancement of the convective heat transfer coefficient and heat exchange surface area. In conclusion, this work provides the first detailed physical insight into the interplay between internal cooling and step-shaped isotherms in a binder-free desiccant device and establishes a validated modeling framework for scaling up and system-level performance evaluation of next-generation energy-efficient dehumidification systems.

Heat and mass transfer↗

Addressing spreading pressure dependence of real adsorbed solution theory with generalized Langmuir isotherm

This work addresses spreading pressure dependence of Real Adsorbed Solution Theory (RAST) for mixed-gas adsorption equilibria using generalized Langmuir (gL) isotherm. Considering vacant sites as an integral part of competitive multicomponent adsorption on a constant adsorbent surface area, the gL isotherm properly accounts for surface heterogeneity and loading, adsorbate composition, and temperature dependence. We show the spreading pressure dependence of adsorbate activity coefficient expression in the RAST framework can be generated from the gL isotherm. The procedure is illustrated with a spreading pressure dependent adsorption Nonrandom Furthermore, two-Liquid activity coefficient model, and the results are validated for ten binary mixed-gas adsorption equilibria systems including two highly nonideal azeotropic systems.

42 ENGINEERING↗

A review on nearly isothermal compression technology

Compressors can be described as the heart of a vapor compression refrigeration system, circulating the working fluid in the system. Significant benefits can be gained from improving its efficiency since energy consumption is responsible for almost the entire system's power input. An effort has been made to achieve isothermal compression through liquid refrigerant injection or inter-stage cooling in refrigeration systems. In recent years, much effort has been invested into isothermal compression technology for air compressors or compressed air energy storage systems with the rise of renewable energy. Here, this work has explored the advancements made in this area and categorized them to discuss the benefits, limitations, and tradeoffs. Evidently, increasing heat transfer area is a significant aid in improving heat transfer, resulting in better isothermal compression. However, liquid pistons open more avenues for this to be pursued, and therefore, are limited to air compression applications. In addition, water injection proved to be the most effective among the methods. Finally, there is a need for more experimental research on refrigeration applications and the field is still in its infancy.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

CO 2 Sorption in Moisture Swing Anion Exchange Resins for Direct Air Capture: Experimental Isotherm Determination and Modeling

Moisture swing (MS) sorption is a promising direct air capture (DAC) technology to achieve negative CO 2 emissions and counter global warming. Here, in this study, MS CO 2 sorption in a model MS sorbent, IRA900, was investigated. IRA900 is a macroporous commercial strong-base anion exchange resin (AER) with quaternary ammonium functional groups. A rigorous CO 2 desorption process was developed to desorb all CO 2 from the sample and obtain CO 2 sorption isotherms as a function of relative humidity, CO 2 partial pressure, and temperature. CO 2 sorption increased with decreasing relative humidity, decreasing temperature, and increasing CO 2 partial pressure. Remarkably, the total CO 2 uptake from the sorption isotherms matched the ion exchange capacity (IEC) of the material, suggesting a stoichiometry of one CO 2 molecule reacting per active site. An isotherm model for CO 2 sorption starting with empty sorption sites (i.e., with the AER in the OH – form) described the experimental data well, supporting the hypothesis that the bicarbonate-loaded AER fully unloaded to the OH – state following rigorous CO 2 desorption. CO 2 sorption kinetics were studied, and carbon diffusion coefficients were estimated as a function of %RH and CO 2 partial pressure. Overall, this study provides a roadmap for the systematic evaluation of MS CO 2 DAC materials.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Isotherm measurements of high-pressure metal hydrides for hydrogen compressors

Hydrogen absorption and desorption isotherms have been measured for several metal hydride alloys identified as possible candidates in the high-pressure (i.e. >80 MPa) stage of a two-stage hydrogen compressor. The isotherms were obtained using two independent Sieverts volumetric test systems built specifically for measuring hydrogen absorption and desorption parameters from 0.10 to 100 MPa. The results obtained enabled us to identify the alloy Ti 0.8 Zr 0.2 Fe 1.6 V 0.4 as the most viable of the candidates investigated for use in the high-pressure stage of a prototype two-stage 80+ MPa compressor, as it produced the highest desorption pressures at moderate temperatures. Issues and challenges in determining reliable isotherms at pressures >50 MPa are also described.

08 HYDROGEN↗