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The thermodynamic properties of oxygen and nitrogen. Part 1: Thermodynamic properties of nitrogen from 115 R to 3500 R with pressures to 150000 psia

An equation of state is presented for liquid and gaseous nitrogen for temperatures from 115 R to 3500 R and pressures to 150,000 psia. All of the pressure-density-temperature data available from the published literature have been reviewed, and appropriate corrections have been identified and applied to bring experimental temperatures into accord with the International Practical Temperature Scale of 1968. Comparisons of property values calculated from the equation of state to measured values are included to illustrate the accuracy of the equation in representing the data. The coefficients of the equation of state were determined by a weighted least squares fit to selected published data and, simultaneously, to constant volume data determined by corresponding states analysis from oxygen data, and to data which define the phase equilibrium criteria for the saturated liquid and saturated vapor. The methods of weighting the various data for simultaneous fitting are presented and discussed. The equation of state is estimated to be accurate to within 0.5 percent in the liquid region, to within 0.1 percent for supercritical isotherms up to 15,000 psia, and to within 0.3 percent from 15,000 to 150,000 psia.

Stewart, R. B.↗

The thermodynamic properties of oxygen and nitrogen. Part 2: Thermodynamic properties of oxygen from 100 R to 600 R with pressure to 5000 psia

An equation of state is presented for liquid and gaseous oxygen for temperatures from 100 R to 600 R and pressures to 5000 psia. The pressure-density-temperature data available from the published literature have been reviewed, and appropriate corrections have been applied to bring experimental temperatures into accord with the International Practical Temperature Scale of 1968. Representative comparisons of property values calculated from the equation of state to measured values are included to illustrate the accuracy of the equation of state. The coefficients of the equation of state were determined by a weighted least squares fit to selected published data, and simultaneously to isochoric heat capacity data, and to data which define the phase equilibrium for the saturated liquid and saturated vapor. The equation of state is estimated to be accurate for the liquid to within 0.1 percent in density, to within 0.2 percent for the vapor below the critical temperature and for states above the critical temperatures to 250 K, and within 0.1 percent for supercritical states at temperatures from 250 K to 300 K. The vapor pressure equation is accurate to within + or - 0.01 K between the triple point and the critical point.

Stewart, R. B.↗

Computational thermodynamics and its applications

Thermodynamics is a science concerning the state of a system, whether it is stable, metastable or un- stable, when interacting with the surroundings. In this overview, fundamentals of thermodynamics are briefly reviewed through the combination of first and second laws of thermodynamics for open and nonequilibrium systems to demonstrate that the reversible equilibrium and irreversible nonequilibrium thermodynamics can be integrated to enhance the power and utilities of thermodynamics. The recent progresses in computational thermodynamics, the remaining challenges, and potential impacts in broad scientific fields are discussed here. It is shown that computational thermodynamics enables the modeling of thermodynamics of a state as a function of both external and internal variables and quantitative calculations of a broad range of properties of a multicomponent system in terms of first and second derivatives of energy, including not only equilibrium states when there are no driving forces for any internal processes and but also non-equilibrium states with driving forces for internal processes. Consequently, external constraints such as fixed strain and internal degree of freedoms such as ordering and defects can be described in a coherent framework and applied to materials design. Furthermore, two important but largely overlooked aspects in thermodynamics will be discussed, i.e. the rigorous application of statistical thermodynamics with the probability of configurations and their contributions to system properties, and the applications of second derivatives of energy with respect to either two extensive variables or two potentials or a mixture of them in terms of understanding and predicting emergent behaviors, critical phenomena, kinetic coefficients, and mechanical properties.

36 MATERIALS SCIENCE↗

Extended quasilocal Thermodynamics of Schwarzchild–anti de Sitter black holes

Highlights: •A Hamiltonian approach to the quasilocal SAdS Thermodynamics is introduced. •The cosmological constant is considered a function on phase space. •The quasilocal SAdS Thermodynamics is extended. •A new equation of state for the quasilocal SAdS Thermodynamics is constructed. •The role of homogeneity and stability in the SAdS Thermodynamics is studied. -- Abstract: In this work we study a homogeneous and quasilocal Thermodynamics associated to the Schwarzschild–anti de Sitter black hole. The usual thermodynamic description is extended within a Hamiltonian approach with the introduction of the cosmological constant in the thermodynamic phase space. The macroscopic treatment presented is consistent in as much as it respects the laws of black hole Thermodynamics and accepts the introduction of any thermodynamic potential. We are able to construct new equations of state that characterize the Thermodynamics. Novel phenomena can be expected from the proposed setup.

79 ASTRONOMY AND ASTROPHYSICS↗

Thermodynamics and its prediction and CALPHAD modeling: Review, state of the art, and perspectives

Thermodynamics is a science concerning the state of a system, whether it is stable, metastable, or unstable, when interacting with its surroundings. The combined law of thermodynamics derived by Gibbs about 150 years ago laid the foundation of thermodynamics. In Gibbs combined law, the entropy production due to internal processes was not included, and the 2nd law was thus practically removed from the Gibbs combined law, so it is only applicable to systems under equilibrium, thus commonly termed as equilibrium or Gibbs thermodynamics. Gibbs further derived the classical statistical thermodynamics in terms of the probability of configurations in a system in the later 1800's and early 1900's. With the quantum mechanics (QM) developed in 1920's, the QM-based statistical thermodynamics was established and connected to classical statistical thermodynamics at the classical limit as shown by Landau in the 1940's. In 1960's the development of density functional theory (DFT) by Kohn and co-workers enabled the QM prediction of properties of the ground state of a system. On the other hand, the entropy production due to internal processes in non-equilibrium systems was studied separately by Onsager in 1930's and Prigogine and co-workers in the 1950's. In 1960's to 1970's the digitization of thermodynamics was developed by Kaufman in the framework of the CALculation of PHAse Diagrams (CALPHAD) modeling of individual phases with internal degrees of freedom. CALPHAD modeling of thermodynamics and atomic transport properties has enabled computational design of complex materials in the last 50 years. Our recently termed zentropy theory integrates DFT and statistical mechanics through the replacement of the internal energy of each individual configuration by its DFT-predicted free energy. The zentropy theory is capable of accurately predicting the free energy of individual phases, transition temperatures and properties of magnetic and ferroelectric materials with free energies of individual configurations solely from DFT-based calculations and without fitting parameters, and is being tested for other phenomena including superconductivity, quantum criticality, and black holes. Those predictions include the singularity at critical points with divergence of physical properties, negative thermal expansion, and the strongly correlated physics. Furthermore, those individual configurations may thus be considered as the genomic building blocks of individual phases in the spirit of the materials genome®. This has the potential to shift the paradigm of CALPHAD modeling from being heavily dependent on experimental inputs to becoming fully predictive with inputs solely from DFT-based calculations and machine learning models built on those calculations and existing experimental data through newly developed and future open-source tools. Furthermore, through the combined law of thermodynamics including the internal entropy production, it is shown that the kinetic coefficient matrix of independent internal processes is diagonal with respect to the conjugate potentials in the combined law, and the cross phenomena that the phenomenological Onsager flux and reciprocal relationships are due to the dependence of the conjugate potential of a molar quantity on nonconjugate molar quantities and other potentials, which can be predicted by the zentropy theory and CALPHAD modeling.

42 ENGINEERING↗

Thermodynamically consistent versions of approximations used in modelling moist air

Abstract Some existing approaches to modelling the thermodynamics of moist air make approximations that break thermodynamic consistency , such that the resulting thermodynamics does not obey the first and second laws or has other inconsistencies. Recently, an approach to avoid such inconsistency has been suggested: the use of thermodynamic potentials in terms of their natural variables , from which all thermodynamic quantities and relationships (equations of state) are derived. In this article, we develop this approach for unapproximated moist‐air thermodynamics and two widely used approximations: the constant‐ approximation and the dry heat capacities approximation. The (consistent) constant‐ approximation is particularly attractive because it leads to, with the appropriate choice of thermodynamic variable, adiabatic dynamics that depend only on total mass and are independent of the breakdown between water forms. Additionally, a wide variety of material from different sources in the literature on thermodynamics in atmospheric modelling is brought together. It is hoped that this article provides a comprehensive reference for the use of thermodynamic potentials in atmospheric modelling, especially for the three systems considered here.

54 ENVIRONMENTAL SCIENCES↗

Carbon Limitation Leads to Thermodynamic Regulation of Aerobic Metabolism

Organic matter (OM) metabolism in freshwater ecosystems is a critical source of uncertainty in global biogeochemical cycles, yet the processes regulating aerobic respiration in aquatic environments remain poorly understood. Aerobic respiration is typically predicted through kinetic controls such as organic carbon and oxygen concentrations, while assuming thermodynamic regulation has no influence. The role of OM thermodynamics has been mainly explored under anaerobic conditions; however, recent observations have suggested that thermodynamic properties of OM may influence aerobic respiration rates. Here, we explicitly test OM thermodynamics as a key regulator of aerobic respiration. We pair controlled microcosm experiments with ultrahigh-resolution OM characterization to show that aerobic respiration increases with OM thermodynamic favorability under carbon limitation. We also demonstrate a shift in the regulation of aerobic respiration from OM thermodynamics to nitrogen content when carbon is in excess, highlighting a central role for OM thermodynamics particularly in carbon-limited ecosystems. This illuminates a structural gap in aquatic biogeochemical models by demonstrating that both kinetic and thermodynamic constraints can modulate aerobic respiration. Our work therefore proposes a new conceptual model in which thermodynamic and nutrient limitations dually control aerobic respiration.

54 ENVIRONMENTAL SCIENCES↗

Evaluation of thermodynamic closure models for partially reacted two-phase mixture of condensed phase explosives

One of the key fundamental issues that is crucial in the continuum modeling of reactive flow phenomena is the thermodynamically consistent description of reaction mixture properties. To define the mixture properties, thermodynamic closure rules that relate the properties of the individual reaction components to the mixture properties are required. In the context of reactive two-phase modeling approaches, various strategies to define the thermodynamic closures have been adopted such as pressure temperature (PT) equilibrium between the individual reaction components, pressure (specific) volume (PV) equilibrium, etc. The choice of closure rules determines the relative distribution of specific volume and energy across the reaction components that comprise the mixture. Therefore, depending on the choice of the closure, the mixture thermodynamic behavior can vary. The present work examines the effect of different closure approaches on the thermodynamic properties of the reaction mixture. The analysis is performed for a condensed phase HMX (octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine) based plastic bonded explosive (PBX) 9501 explosive using four different thermodynamic closures, viz., PT equilibrium, PV equilibrium, volume temperature (VT) equilibrium, and pressure (P) equilibrium with reactants on an isentrope. Furthermore, the relative variations in the thermodynamic properties of the mixture are analyzed and compared under both compression and expansion loading regimes. It is shown that out of the four closure models, only PT equilibrium and P equilibrium closures lead to a thermodynamically accurate description of the mixture under both compression and expansion.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Thermodynamic, Kinetic and Electrochemical Studies on Mixed Proton, Oxygen Ion and Electron (Hole) Conductors

The report contains a summary of work done during the period of performance September 1, 2015 through August 31, 2021. The principal objective of the work was to conduct thermodynamic, kinetic and electrochemical studies on mixed proton, oxygen ion and electron (hole) conductors. The project also involved studies on cation conductors such as Li + and Na + ion conductors of particular relevance to batteries. The work involved theory and experiments. Since any use of ionic conductors necessarily entails two electrodes, electrode reactions are central to the overall transport processes from one electrode, through the electrolyte, to the other electrode. The role of interfaces and electrochemical reactions is thus of central importance. Transport processes in fuel cells, electrolyzers, lithium batteries and sodium batteries were examined using linear non-equilibrium thermodynamics, which is based on the assumption of small departures from thermodynamic equilibrium. The main approach involved expressing transport processes using the Onsager equations which naturally include coupling of thermodynamic flows and thermodynamic forces. The basic tenet of linear nonequilibrium thermodynamics is the existence of local thermodynamic equilibrium which means that all thermodynamic functions are locally defined. Thus, chemical potentials of various species are defined locally as a function of position and also of time. The existence of local thermodynamic equilibrium has fundamental implications concerning transport of electronic species through a predominantly ionic conductor.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Fundamental Issues Identified for Thermodynamic Description of Molten Salt Systems

Thermodynamic modeling of the molten salt systems is critical in the design of advanced nuclear power plants, materials recycling, and many other important clean energy applications. As one of the most capable computational thermodynamic approaches, the CALPHAD (Calculation of Phase Diagrams) method has been widely used for multicomponent thermodynamic database development and further support more physics-based modeling. Although considerable CALPHAD modeling efforts for molten salt systems have been made, we found that no evaluation has been performed regarding the unary thermodynamic models for the molten salt systems despite the fact that more than one pure substance database is available for the CALPHAD modeling. Therefore, the thermodynamic descriptions of the pure salts should be critically evaluated to ensure a high-fidelity molten salt thermodynamic database. In this work, we comprehensively analyzed some selected molten salts using different available thermodynamic descriptions from two databases as an example. One is the SSUB database released by the SGTE (Scientific Group Thermodata Europe), and the other is the FactPS database from the FactSage. Finally, the significant discrepancies observed in the thermodynamic description between the existing CALPHAD pure substance databases and experiments call for an urgent effort to improve.

42 ENGINEERING↗

Deciphering Reaction Mechanisms of Molecular Proton Reduction Catalysts with Cyclic Voltammetry: Kinetic vs Thermodynamic Control

The kinetics and thermodynamics of elementary reaction steps involved in the catalytic reduction of protons to hydrogen define the reaction landscape for catalysis. The mechanisms can differ in the order of the elementary proton transfer, electron transfer, and bond-forming steps and can be further differentiated by the sites at which protons and electrons localize. Access to fully elucidated mechanistic, kinetic, and thermochemical details of molecular catalysts is crucial to facilitate the development of new catalysts that operate with optimal efficiency, selectivity, and durability. The mechanism by which a catalyst operates, as well as the kinetics and thermodynamics associated with the individual steps, can often be accessed through electroanalytical studies. Here, this Account details the application of cyclic voltammetry to interrogate reaction mechanisms and quantify the kinetics and thermodynamics of elementary reaction steps for a series of molecular catalysts that mediate electrochemical proton reduction. I distinguish the limiting scenarios wherein a catalyst operates under kinetic control vs thermodynamic control, with a focus on detecting how cyclic voltammetry features shift with proton source strength and concentration, as well as scan rate. For systems that operate under kinetic control, catalytic currents are observed at, or slightly positive toward, the formal potential for the redox process that triggers catalysis. Under thermodynamic control, catalytic responses shift as a function of the proton source pKa and effective pH of the solution. After drawing this distinction, we introduce the appropriate voltammetry experiments and accompanying analytical expressions for extracting key metrics from the data. To illustrate analytical strategies to quantify elementary reaction steps of catalysts operating under kinetic control, I describe our studies of proton reduction catalysts Co(dmgBF 2 ) 2 (CH 3 CN) 2 (dmgBF 2 = difluoroboryl-dimethylglyoxime) and [Ni(P 2 Ph N 2 Ph ) 2 ] 2+ (P 2 Ph N 2 Ph = 1,5-phenyl-3,7-phenyl-1,5-diaza-3,7-diphosphacyclooctane). Here, peak shift analysis, foot-of-the-wave analysis, and plateau current analysis are applied to data sets wherein voltammetric response are recorded as a function of catalyst concentration, proton source concentration, proton source strength, and scan rate to quantify rate constants for elementary proton transfer and bond-forming steps in a catalytic cycle. Further, the case study of [Ni(P 2 Ph N 2 Ph ) 2 ] 2+ illustrates how complementary spectroscopic methods can bolster the mechanistic assignment. Collectively, these two studies showcase how detailed mechanistic studies inform on rate-limiting elementary steps in catalysis and other key processes underpinning catalysis. Second, I present analytical strategies to interrogate catalysts operating under thermodynamic control, centered on the case study of [Ni II (P 2 Ph N 2 Bn ) 2 ] 2+ (P 2 Ph N 2 Bn = 1,5-dibenzyl-3,7-diphenyl-1,5-diaza-3,7-diphosphacyclooctane). Here, the application of nonaqueous Pourbaix theory to extract thermodynamic information is introduced, and the construction of a coupled Pourbaix diagram is detailed. This study identifies ligand-based protonation as the key process that places catalysis under thermodynamic control and influences the reaction mechanism. Together, the work detailed in this Account showcases the utility of electroanalytical methods to disentangle complex reaction mechanisms and extract key thermochemical and kinetic parameters for elementary steps of catalysis. Through detailed presentation of the key analytical expressions that underpin these analyses, this Account seeks to facilitate the adoption of cyclic voltammetry by the community to fully extract kinetic, thermochemical, and mechanistic information on electrochemical small-molecule activation.

catalysts↗

Thermodynamic modeling of the Ti-Nb-Sn system and its preliminary applications in aging precipitation and solidification simulations

Abstract Gasping the thermodynamic and phase diagram of the materials being studied is essential for further guiding the development process, like composition design, heat treatment optimization and so on. Nb and Sn are common alloying elements in Ti-based biomedical alloys. In this work, the Ti-Nb-Sn system has been thermodynamically assessed based on experimental phase equilibria. A self-consistent thermodynamic description for the Ti-Nb-Sn system including two ternary compounds Ti 3 Nb 3 Sn 2 and Ti 3 NbSn has been obtained. Based on the comparison between the calculated and experimental phase equilibria, the reliability of the presently obtained thermodynamic description has been verified. The influence of Nb and Sn contents on the precipitation temperature and amount of hcp α -Ti phase in bcc β -(Ti, Nb) has been investigated based on thermodynamic calculations. Results show that the increase of Nb or Sn content in Ti-based alloys would significantly reduce the precipitation amount and transformation temperature of hcp α -Ti phase in bcc β -(Ti, Nb) and the influence of Nb content is more effective than that of Sn. The solidified phases in several as-cast alloys have been thermodynamically predicted based on Scheil solidification simulations. The presently developed thermodynamic description of the Ti-Nb-Sn system can serve as a sub-ternary one in the thermodynamic database for multicomponent Ti-based biomedical alloys.

Peng, Yingbiao↗

Thermodynamic and Diffusion Model Estimates on Metamorphic Temperatures and Timescales for Basaltic Eucrite GRA 98098

Introduction: HED meteorites are thought to rep-resent igneous rocks from Vesta’s basaltic crust and preserve evidence of early crustal metamorphism. Determining the temperatures and timescales of thermal metamorphism is important for reconstructing crustal evolution in the early solar system. Here, we study basaltic eucrite Graves Nunataks (GRA) 98098, which has been identified as a highly metamorphosed eucrite [1]. We present new estimates on metamorphic temperatures determined via thermodynamic modeling as well as the initial results from diffusion models constraining timescales of thermal metamorphism. Sample Description: GRA 98098 is an unbrecciated eucrite with a granoblastic plagioclase and pyroxene mineralogy. Millimeter to cm-long lathes of tridymite cross-cut and poikilitically enclose plagioclase and pyroxene [1,this work]. Pyroxene grains have exsolved into Ca-rich (~Wo38En29Fs33) and Ca-poor (~Wo4.5En36Fs59.5) lamellae. Both unzoned and zoned plagioclase grains are observed. Unzoned plagioclase grains are found solely with tridymite laths. These grains have ~An92 compositions. The cores of the zoned plagioclase grains have the same composition and thin, relatively sodic rims (~An67), (Fig. 1). The bulk sample is unusually enriched in highly in-compatible elements and has one of the most fractionated REE patterns reported [1]. Maximum metamorphic temperatures of 985±78°C have been estimated using two-pyroxene thermometry [2]. Methods: Thermodynamic modeling. Thermodynamic models were constructed using the software Perple_X, which employs a Gibbs free energy minimization in order to determine the most stable phase assemblage for a given bulk rock composition [3]. Bulk composition was calculated using mineral com-positions acquired via EMPA (this study) and the observed abundancies present in the thin section. Two bulk compositions were estimated; 1) includes all phases present in the thin section, (assumes that all phases are present during metamorphism), 2) excludes tridymite from the bulk calculation (assumes that tridymite was not present during metamorphism). In order to determine whether metamorphic equilibria was achieved and estimate temperatures of metamorphism, we compared measured pyroxene compositions with thermodynamically predicted compositions [4, Fig. 2]. Diffusion Modeling. Several time-temperature de-pendent diffusion profiles were calculated in order to determine the best match for XAn chemical profiles observed at the edges of the zoned plagioclase (Fig. 3). We assumed that the start condition was a stepwise gradient at the plagioclase/pyroxene interface. We also assumed an average diffusion coefficient (D) and a constant temperature using the equation in [5]. D was determined for two temperatures (T = 1060ºC; near eucrite solidus [6] and T = 985ºC; metamorphism reported in [4]) and then XAn was calculated as a function of distance from plagioclase core to rim using an error function solution to Fick’s second law. Results: Thermodynamic model results are summarized in Fig. 2. For a bulk composition that includes all phases in the thin section, pyroxene endmember compositions plot in the following temperature ranges: Fs ~660-860ºC, En~1000ºC & 1150ºC, and Wo~760-900ºC (Fig. 2a). For a bulk composition that excludes tridymite from the peak metamorphic assemblage (i.e., the bulk composition minus the contribution from tridymite), a temperature range could not be determined for the Fs component of pyroxene. For Wo, T~760-900ºC and En, T~1000ºC & 1150ºC (Fig. 2b). Fig. 3 summarizes the diffusion model results. For T = 1060°C & 985°C, the most appropriate time interval was estimated based on which diffusion curve most matched (solid lines, Fig. 3) the EMPA data. For T = 1060°C, the best looking match was t = 500 ka. For T = 985°C, the best match was t = 7 Ma. Discussion and future work: Temperature estimates from thermodynamic models are not conclusive because the temperature ranges determined for pyroxene endmember stability do not overlap (colored fields in Fig. 2), thus implying that there is disequilibrium between pyroxene crystals and the bulk composition considered [4]. Thus, additional exploration is needed to define a metamorphically equilibrated do-main that accurately records peak temperature. The utility of defining metamorphically equilibrated do-mains to improve the accuracy and level of detail elucidated regarding the petrogenetic history of metamorphose samples has been demonstrated previously [4,7]. We suggest that in the case of Fig. 2a, the thin section composition is not representative of the length scales over which metamorphic equilibrium was achieve and in the case of Fig. 2b, the assumption that tridymite was not present during metamorphism was incorrect. However, results from thermodynamic models can provide insight into the relative timing of mineral and compositional textures. For example from texture alone, it is unclear whether tridymite was igneous in origin and represents the last bits of melt in a crystallizing magma chamber, or if it formed during (and possibly initiated) open system thermal metamorphism. The latter could be consistent with a partial melt hypothesis [8,9] while the former implies that simple fractional crystallization can yield the textures present in GRA 98098. The lack of coincidence be-tween pyroxene endmember compositions in Fig. 2b suggest that the bulk composition minus tridymite was not the assemblage in equilibrium with the pyroxene, suggesting that tridymite was present during metamorphism and formed during igneous crystallization. We conclude that the development of the Na-rich plagioclase rims likely occurred during or immediately after peak thermal metamorphism, because eucrites of similar metamorphic grade and texture have unzoned plagioclase (~An92) [2,4,8], and Na zoning is only observed in the plagioclase not included in the tridymite. This suggests that the zoning formed after tridymite formation, and therefore after igneous crystallization. Thus, the timescales calculated via diffusion modeling possibly represent the time interval over which thermal metamorphism occurred. Cooling rates approximated for the Vestan crust predict that the crust cooled below 300°C around 35-40 Ma after formation[10]. This is consistent with our modeling results that predict formation of the Na rich plagioclase rims occurring at higher temperatures over a period of 0.5 to 7 Ma years. Future work. Additional thermodynamic modeling work will focus on selecting an equilibrated bulk rock domain in which to elucidate metamorphic conditions. Diffusion models currently provide a minimum time-scale, since diffusion slows down as the system cools. Future work with will focus on integrating cooling into the diffusion models and constraining the depth at which thermal metamorphism occurs because it could be used to determine whether the range of time-scales calculated for thermal metamorphism are consistent with the geologic environment.

J S Gorce↗

Thermodynamics shapes the in vivo enzyme burden of glycolytic pathways

Thermodynamically constrained reactions and pathways are hypothesized to impose greater protein demands on cells, requiring higher enzyme amounts to sustain a given flux compared to those with stronger thermodynamics. To test this, we quantified the absolute concentrations of glycolytic enzymes in three bacterial species— Zymomonas mobilis, Escherichia coli , and Clostridium thermocellum —which employ distinct glycolytic pathways with varying thermodynamic driving forces. By integrating enzyme concentration data with corresponding in vivo metabolic fluxes and ΔG measurements, we found that the highly favorable Entner-Doudoroff pathway in Z. mobilis requires only one-fourth the amount of enzymatic protein to sustain the same flux as the thermodynamically constrained pyrophosphate-dependent glycolytic pathway in C. thermocellum , with the Embden-Meyerhof-Parnas pathway in E. coli exhibiting intermediate thermodynamic favorability and enzyme demand. Across all three pathways, early reactions with stronger thermodynamic driving forces generally required lower enzyme investment than later, less favorable steps. Additionally, reflecting differences in glycolytic strategies, the highly reversible ethanol fermentation pathway in C. thermocellum requires 10-fold more protein to maintain the same flux as the irreversible, forward-driven ethanol fermentation pathway in Z. mobilis . Thus, protein investment across glycolytic pathways reflects differences in their thermodynamic favorability.

Clostridium thermocellum↗

Recycling of Lead Pastes from Spent Lead–Acid Batteries: Thermodynamic Constraints for Desulphurization

Lead–acid batteries are important to modern society because of their wide usage and low cost. The primary source for production of new lead–acid batteries is from recycling spent lead–acid batteries. In spent lead–acid batteries, lead is primarily present as lead pastes. In lead pastes, the dominant component is lead sulfate (PbSO 4 , mineral name anglesite) and lead oxide sulfate (PbO•PbSO 4 , mineral name lanarkite), which accounts for more than 60% of lead pastes. In the recycling process for lead–acid batteries, the desulphurization of lead sulfate is the key part to the overall process. In this work, the thermodynamic constraints for desulphurization via the hydrometallurgical route for recycling lead pastes are presented. The thermodynamic constraints are established according to the thermodynamic model that is applicable and important to recycling of lead pastes via hydrometallurgical routes in high ionic strength solutions that are expected to be in industrial processes. The thermodynamic database is based on the Pitzer equations for calculations of activity coefficients of aqueous species. The desulphurization of lead sulfates represented by PbSO 4 can be achieved through the following routes. (1) conversion to lead oxalate in oxalate-bearing solutions; (2) conversion to lead monoxide in alkaline solutions; and (3) conversion to lead carbonate in carbonate solutions. Among the above three routes, the conversion to lead oxalate is environmentally friendly and has a strong thermodynamic driving force. Oxalate-bearing solutions such as oxalic acid and potassium oxalate solutions will provide high activities of oxalate that are many orders of magnitude higher than those required for conversion of anglesite or lanarkite to lead oxalate, in accordance with the thermodynamic model established for the oxalate system. An additional advantage of the oxalate conversion route is that no additional reductant is needed to reduce lead dioxide to lead oxide or lead sulfate, as there is a strong thermodynamic force to convert lead dioxide directly to lead oxalate. As lanarkite is an important sulfate-bearing phase in lead pastes, this study evaluates the solubility constant for lanarkite regarding the following reaction, based on the solubility data, PbO•PbSO 4 + 2H + ⇌ 2Pb 2+ + SO 4 2– + H 2 O(l).

25 ENERGY STORAGE↗

Extending the thermodynamic form factor bootstrap program: multiple particle-hole excitations, crossing symmetry, and reparameterization invariance

In this study, we further the thermodynamic bootstrap program which involves a set of recently developed ideas used to determine thermodynamic form factors of local operators in integrable quantum field theories. These form factors are essential building blocks for dynamic correlation functions at finite temperatures or non-equilibrium stationary states. In this work we extend this program in three ways. Firstly, we demonstrate that the conjectured annihilation pole axiom is valid in the low energy particle-hole excitations. Secondly, we introduce a crossing relation, which establishes a connection between form factors with different excitation content. Typically, the crossing relation is a consequence of Lorentz invariance, but due to the finite energy density of the considered states, Lorentz invariance is broken. Nonetheless a crossing relation involving excitations with both particles and holes can established using the finite volume representation of the thermodynamic form factors. Finally, we demonstrate that the thermodynamic form factors satisfy a reparameterization invariance, an invariance which encompasses crossing. Reparameterization invariance exploits the fact that the details of the representation of the thermodynamic state are unimportant. In the course of developing these results, we demonstrate the internal consistency of the thermodynamic form factor bootstrap program in a number of ways. Finally, we provide explicit computations of form factors of conserved charges and densities with crossed excitations and show our results can be used to infer information about thermodynamic form factors in the Lieb-Liniger model.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Thermodynamic description of molten salt systems: KCl-LiCl-NaCl and KCl-LiCl-NdCl 3

The mixture of KCl and LiCl has been used as electrolyte in the electrorefining process to recover uranium from used nuclear fuels due to the low melting point. However, lanthanides and sodium in the reactor waste continuously dissolve into it and thus alter its thermodynamic properties. To understand the thermodynamic behavior evolution of the electrolyte with the accumulation of impurities, thermodynamic modeling for KCl-LiCl-NaCl and KCl-LiCl-NdCl 3 and four constituent binary systems in the entire composition space was performed using the CALPHAD (CALculation of PHAse Diagrams) approach. The ionic liquid was described by the two-sublattice model, where neutral species were introduced to consider short-range ordering (SRO) within the melt, whereas the solid solution was modeled based on the Compound Energy Formalism. Literature data on phase equilibria and thermochemical properties were critically evaluated and used during the optimization of thermodynamic parameters for KCl-LiCl-NaCl and KCl-LiCl-NdCl 3 and their subsystems. The calculated phase diagrams and mixing enthalpies are in good agreement with the experimental data. The thermodynamic modeling for the KCl-LiCl-NdCl 3 system was carried out for the first time. To fill the gap in experimental measurement, enthalpy of mixing for the KCl-LiCl-NdCl 3 melt was estimated using the surrounded-ion model. These data then served as critical inputs for thermodynamic optimization. Furthermore, the present study can provide insights into thermodynamic property evolution of the electrolyte and solubility limit of various impurities during the electrorefining process.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

In Vivo Thermodynamic Analysis of Glycolysis in Clostridium thermocellum and Thermoanaerobacterium saccharolyticum Using 13 C and 2 H Tracers

Clostridium thermocellum and Thermoanaerobacterium saccharolyticum are thermophilic anaerobic bacteria with complementary metabolic capabilities that utilize distinct glycolytic pathways for the conversion of cellulosic sugars to biofuels. We integrated quantitative metabolomics with 2 H and 13 C metabolic flux analysis to investigate the in vivo reversibility and thermodynamics of the central metabolic networks of these two microbes. We found that the glycolytic pathway in C. thermocellum operates remarkably close to thermodynamic equilibrium, with an overall drop in Gibbs free energy 5-fold lower than that of T. saccharolyticum or anaerobically grown Escherichia coli . The limited thermodynamic driving force of glycolysis in C. thermocellum could be attributed in large part to the small free energy of the phosphofructokinase reaction producing fructose bisphosphate. The ethanol fermentation pathway was also substantially more reversible in C. thermocellummthan in T. saccharolyticum. These observations help explain the comparatively low ethanol titers of C. thermocellum and suggest engineering interventions that can be used to increase its ethanol productivity and glycolytic rate. In addition to thermodynamic analysis, we used our isotope tracer data to reconstruct the T. saccharolyticum central metabolic network, revealing exclusive use of the Embden-Meyerhof-Parnas (EMP) pathway for glycolysis, a bifurcated tricarboxylic acid (TCA) cycle, and a sedoheptulose bisphosphate bypass active within the pentose phosphate pathway. Thermodynamics constitutes a key determinant of flux and enzyme efficiency in metabolic networks. Here, we provide new insights into the divergent thermodynamics of the glycolytic pathways of C. thermocellum and T. saccharolyticum, two industrially relevant thermophilic bacteria whose metabolism still is not well understood. We report that while the glycolytic pathway in T. saccharolyticum is as thermodynamically favorable as that found in model organisms, such as E. coli or Saccharomyces cerevisiae , the glycolytic pathway of C. thermocellum operates near equilibrium. The use of a near-equilibrium glycolytic pathway, with potentially increased ATP yield, by this cellulolytic microbe may represent an evolutionary adaptation to growth on cellulose, but it has the drawback of being highly susceptible to product feedback inhibition. The results of this study will facilitate future engineering of high-performance strains capable of transforming cellulosic biomass to biofuels at high yields and titers.

59 BASIC BIOLOGICAL SCIENCES↗