Bulk Thermodynamic Properties Research Articles

Pressure and speed of sound in two-flavor color-superconducting quark matter at next-to-leading order

Deconfined quark matter at asymptotically high densities is weakly coupled, due to the asymptotic freedom of quantum chromodynamics. In this weak-coupling regime, bulk thermodynamic properties of quark matter, assuming a trivial ground state, are currently known to partial next-to-next-to-next-to-leading order. However, the ground state at high densities is expected to be a color superconductor, in which the excitation spectrum of (at least some) quarks exhibit a gap with a nonperturbative dependence on the strong coupling. In this work, we calculate the thermodynamic properties of color-superconducting quark matter at high densities and zero temperature at next-to-leading order (NLO) in the coupling in the presence of a finite gap. We work in the limit of two massless quark flavors, which corresponds to deconfined symmetric nuclear matter, and further assume that the gap is small compared to the quark chemical potential. In these limits, we find that the NLO corrections to the pressure and speed of sound are comparable in size to the leading-order effects of the gap, and further increase both quantities above their values for nonsuperconducting quark matter. We also provide a parametrization of the NLO speed of sound to guide phenomenology in the high-density region, and we furthermore comment on whether our findings should be expected to extend to the case of three-flavor quark matter of relevance to neutron stars. Published by the American Physical Society 2024

Computational investigation of the effects of polymer grafting on the effective interaction between silica nanoparticles in water.

Understanding and control of the effective interaction between nanoscale building blocks (colloids or nanoparticles) dispersed in a solvent is an important prerequisite for the development of bottom-up design strategies for soft functional materials. Here, we have employed all-atom molecular dynamics simulations to investigate the impact of polymer grafting on the solvent-mediated effective interaction between the silica nanoparticles (Si-NPs) in water, and in turn, on its bulk structural and thermodynamic properties. We found that the nature of the short grafting polymers [characterized by their interaction with water (hydrophobicity or hydrophilicity) and molecular weight] has a profound effect on the range and strength of the effective interaction between the Si-NPs. The hydrophobic polymer [such as polyethylene (PE)]-grafting of Si-NP gives rise to a more attractive interaction between the Si-NPs compared to the hydrophilic polymer [such as polyethylene glycol (PEG)] and non-grafted cases. This study further provides fundamental insights into the molecular origin of the observed behavior of the effective pair interactions between the grafted Si-NPs. For PE-grafted Si-NPs, the confined water (water inside the cavity formed by a pair of Si-NPs) undergoes a partial dewetting transition on approaching below a critical inter-particle separation leading to a stronger attractive interaction. Furthermore, we report that the effective attraction between the PE-grafted Si-NPs can be reliably controlled by changing the grafting PE density. We have also investigated the bulk structural and thermodynamic behavior of the coarse-grained Si-NP system where the particles interact via effective interaction in the absence of water. We believe that the insights gained from this work are important prerequisites for formulating rational bottom-up design strategies for functional materials where nano- (or, colloidal) particles are the building blocks.

A thermodynamic approach to analyzing relative permittivity and solvent mole fraction models, and application to SN1 reactions.

The standard methods for analyzing solvent effects on chemical reactions largely include linear free energy relations that relate kinetic and spectroscopic terms to solvent interactive parameters. The number of these parameters has grown over the years in order to make linear free energy techniques more accurate and cover a wider range of reaction systems. However, even with the myriad of parameters, the details of specific reaction systems make the application of these techniques sometimes unreliable. On the other hand, a thermodynamic approach provides a more precise analysis, and has proven particularly useful for reactions in multi-component solvent systems. In this article we present the mathematical formalism for relating the activation free energy to the bulk thermodynamic properties for a binary (cosolvent) system. We then use this thermodynamic approach, coupled with selected solvent models, to analyze the hydrolysis rates of tert-butyl chloride in the acetonitrile/water solvent system under iso-mole fraction, isodielectric, and isothermal conditions. These analyses allow us to differentiate and quantify bulk electrostatic effects and the effects of close-range solute-solvent interactions.

Local density dependent potentials for an underlying van der Waals equation of state: A simulation and density functional theory analysis.

There is an ever increasing use of local density dependent potentials in the mesoscale modeling of complex fluids. Questions remain, though, about the dependence of the thermodynamic and structural properties of such systems on the cutoff distance used to calculate these local densities. These questions are particularly acute when it comes to the stability and structure of the vapor/liquid interface. In this article, we consider local density dependent potentials derived from an underlying van der Waals equation of state. We use simulation and density functional theory to examine how the bulk thermodynamic and interfacial properties vary with the cutoff distance, rc, used to calculate the local densities. We show quantitatively how the simulation results for bulk thermodynamic properties and vapor-liquid equilibrium approach the van der Waals limit as rc increases and demonstrate a scaling law for the radial distribution function in the large rc limit. We show that the vapor-liquid interface is stable with a well-defined surface tension and that the interfacial density profile is oscillatory, except for temperatures close to critical. Finally, we show that in the large rc limit, the interfacial tension is proportional to rc and, therefore, unlike the bulk thermodynamic properties, does not approach a constant value as rc increases. We believe that these results give new insights into the properties of local density dependent potentials, in particular their unusual interfacial behavior, which is relevant for modeling complex fluids in soft matter.

Theory of adsorption of ethoxylates at the water | oil and water | air interfaces. 1. Monolayers of single-component and Poisson distributed alkylphenol ethoxylates

Currently, the bulk thermodynamic properties of an arbitrary liquid mixture of oligomers are accessible with reasonable accuracy through popular 3D statistical models (SAFT, Flory-Huggins) under a wide range of conditions. These models are implemented in widely available software suites used for process design. The hypothesis investigated here is that the same is, in principle, achievable with monolayers of mixed surfactants on liquid surfaces. A molecular thermodynamic theory of the adsorption of alkylphenoxypolyethoxyethanols, CnH2n+1C6H4(OC2H4)mOH, on fluid interfaces is presented. It covers homologues of m = 0–10; water|alkane and water|gas interfaces; single surfactants and surfactant mixtures. The adsorption behaviour has been predicted as a function of the structure of the ethoxylated surfactants and the model has been validated against tensiometric data for forty systems. All values of the adsorption parameters have been either predicted, independently determined, or at least compared to a theoretical estimate. The single surfactant parameters have been used to predict the properties of ‘normal’ Poisson distributed mixtures of ethoxylates, in good agreement with literature data. Partitioning between water and oil, micellization, solubility and surface phase transitions are also discussed.

Thermodynamics, formation dynamics, and structural correlations in the bulk amorphous phase of the phase-field crystal model.

We investigate bulk thermodynamic and microscopic structural properties of amorphous solids in the framework of the phase-field crystal (PFC) model. These are metastable states with a non-uniform density distribution, having no long-range order. From extensive numerical simulations, we determine the distribution of free energy density values in varying size amorphous systems and also the point-to-set correlation length, which is the radius of the largest volume of amorphous one can take while still having the particle arrangements within the volume determined by the particle ordering at the surface of the chosen volume. We find that in the thermodynamic limit, the free energy density of the amorphous tends toward a value that has a slight dependence on the initial state from which it was formed-i.e., it has a formation history dependence. The amorphous phase is observed to form on both sides of the liquid linear-stability limit, showing that the liquid to amorphous transition is first order, with an associated finite free energy barrier when the liquid is metastable. In our simulations, this is demonstrated when the noise in the initial density distribution is used to induce nucleation events from the metastable liquid. Depending on the strength of the initial noise, we observe a variety of nucleation pathways, in agreement with previous results for the PFC model, which show that amorphous precursor mediated multi-step crystal nucleation can occur in colloidal systems.

Augmented scaled particle theory for a hard disk fluid

The success of scaled particle theory (SPT) can be certainly ascribed to the appealing physical idea embedded in it, i.e., accounting for the work needed to insert a particle into a liquid by a bulk contribution and a surface contribution. So, it can describe bulk and surface thermodynamic properties in the same framework. The surface tension term in SPT involves one flat-surface contribution and two additional contributions due to surface curvatures. High-order curvature terms (also called non-Hadwiger terms) were evidenced. Recently, we have developed an augmented scaled particle theory (ASPT) by adding one high-order curvature term for a hard sphere fluid. Here, we extend ASPT to a two-dimensional hard disk fluid. As for the 3D case, our 2D ASPT allows for improving both bulk and surface thermodynamic properties of a hard disk fluid with respect to the original SPT.

Bulk Thermodynamics Determines Surface Hydrogen Concentration in Membranes

AbstractThe functioning of hydrogen selective metal membranes relies on the fine‐tuned interaction of their surfaces with the inner bulk. The link between hydrogen permeation and surface concentration is unveiled using a novel combination of thin film preparation and surface science analysis to probe and intentionally modify the surface properties of palladium vanadium composite membranes. The in situ preparation allows for observation of ultra‐clean hydrogenation and the quantification of the permeation as a function of temperature and pressure. The sub‐surface hydrogen concentration is determined by operando reflecting electron energy loss spectroscopy (REELS) and surface elemental characterization by X‐ray photoelectron spectroscopy and Auger electron spectroscopy under oxygen‐free conditions as a function of pressure and temperature, from which the surface hydrogen pressure‐composition isotherms are derived. The energy dependence of REELS reveals that the VHx layer exhibits a hydrogen concentration gradient. Modeling of the permeation behavior and surface hydrogen concentration yields activation energies in good agreement with similar hydrogen absorbing thin film systems for the overall process, the dissociation at the Pd surface, the diffusion in the membrane, and the dissociation at the V surface. The bulk thermodynamic properties of the metal hydride govern the desorption process.

Quantum theory, thermal gradients and the curved Euclidean space

The Euclidean space, obtained by the analytical continuation of time, to an imaginary time, is used to model thermal systems. In this work, it is taken a step further to systems with spatial thermal variation, by developing an equivalence between the spatial variation of temperature in a thermal bath and the curvature of the Euclidean space. The variation in temperature is recast as a variation in the metric, leading to a curved Euclidean space. The equivalence is substantiated by analyzing the Polyakov loop, the partition function and the periodicity of the correlation function. The bulk thermodynamic properties like the energy, entropy and the Helmholtz free energy are calculated from the partition function, for small metric perturbations, for a neutral scalar field. The Dirac equation for an external Dirac spinor, traversing a thermal bath with spatial thermal gradients, is solved in the curved Euclidean space. The fundamental behavior exhibited by the Dirac spinor eigenstate, may provide a possible mechanism to validate the theory, at a more basal level, than examining only bulk thermodynamic properties. Furthermore, in order to verify the equivalence at the level of classical mechanics, the geodesic equation is analyzed in a classical backdrop. The mathematical apparatus is borrowed from the physics of quantum theory in a gravity-induced space–time curvature. As spatial thermal variations are obtainable at quantum chromodynamic or quantum electrodynamic energies, it may be feasible for the proposed formulation to be validated experimentally.

Ab initio development of generalized Lennard-Jones (Mie) force fields for predictions of thermodynamic properties in advanced molecular-based SAFT equations of state.

A methodology for obtaining molecular parameters of a modified statistical associating fluid theory for variable-range interactions of Mie form (SAFT-VR Mie) equation of state (EoS) from ab initio calculations is proposed for non-associative species that can be modeled as single spherical segments. The methodology provides a strategy to map interatomic or intermolecular potentials obtained from ab initio quantum-chemistry calculations to the corresponding Mie potentials that can be used within the SAFT-VR Mie EoS. The inclusion of corrections for quantum and many-body effects allows for an excellent, fully predictive description of the vapor-liquid envelope and other bulk thermodynamic properties of noble gases; this description is of similar or superior quality to that obtained using SAFT-VR Mie with parameters regressed in the traditional way using experimental thermodynamic-property data. The methodology is extended to an anisotropic species, methane, where similar levels of accuracy are obtained. The efficacy of using less-accurate quantum-chemistry methods in this methodology is explored, showing that these methods do not provide satisfactory results, although we note that the description is nevertheless substantially better than those obtained using the conductor-like screening model for describing real solvents (COSMO-RS), the only other fully predictive ab initio method currently available. Overall, the reliance on thermophysical data is completely dispensed with, providing the first extensible, wholly predictive SAFT-type EoSs.

Bridging Structure, Dynamics, and Thermodynamics: An Example Study on Aqueous Potassium Halides.

Aqueous salt systems are ubiquitous in all areas of life. The ions in these solutions impose important structural and dynamic perturbations to water. In this study, we employ a combined neutron scattering, nuclear magnetic resonance, and computational modeling approach to deconstruct ion-specific perturbations to water structure and dynamics and shed light on the molecular origins of bulk thermodynamic properties of the solutions. Our approach uses the atomistic scale resolution offered to us by neutron scattering and computational modeling to investigate how the properties of particular short-ranged microenvironments within aqueous systems can be related to bulk properties of the system. We find that by considering only the water molecules in the first hydration shell of the ions that the enthalpy of hydration can be determined. We also quantify the range over which ions perturb water structure by calculating the average enthalpic interaction between a central halide anion and the surrounding water molecules as a function of distance and find that the favorable anion-water enthalpic interactions only extend to ∼4 Å. We further validate this by showing that ions induce structure in their solvating water molecules by examining the distribution of dipole angles in the first hydration shell of the ions but that this perturbation does not extend into the bulk water. We then use these structural findings to justify mathematical models that allow us to examine perturbations to rotational and diffusive dynamics in the first hydration shell around the potassium halide ions from NMR measurements. This shows that as one moves down the halide series from fluorine to iodine, and ionic charge density is therefore reduced, that the enthalpy of hydration becomes less negative. The first hydration shell also becomes less well structured, and rotational and diffusive motions of the hydrating water molecules are increased. This reduction in structure and increase in dynamics are likely the origin of the previously observed increased entropy of hydration as one moves down the halide series. These results also suggest that simple monovalent potassium halide ions induce mostly local perturbations to water structure and dynamics.

First-principles Calculations of Bulk and Interfacial Thermodynamic Properties of the T1 phase in Al-Cu-Li alloys

We recently proposed a new, low-energy atomic structure of the Al2CuLi (T1) phase using first-principles calculations based on density functional theory [Acta Mater. 145 (2018) 337-346]. Here, we refine the Li positions in the proposed T1 structure and find that the T1 phase has a tie-line with Al at finite-temperature by vibrational entropic stabilization on the Gibbs triangle of the ternary Al-Cu-Li system. We also derive a low-energy T1/Al coherent interfacial structure and find that Ag and Mg solutes are predicted to segregate to the coherent interface, which is in agreement with recent experimental observations by atom probe tomography.

When do short-range atomistic machine-learning models fall short?

We explore the role of long-range interactions in atomistic machine-learning models by analyzing the effects on fitting accuracy, isolated cluster properties, and bulk thermodynamic properties. Such models have become increasingly popular in molecular simulations given their ability to learn highly complex and multi-dimensional interactions within a local environment; however, many of them fundamentally lack a description of explicit long-range interactions. In order to provide a well-defined benchmark system with precisely known pairwise interactions, we chose as the reference model a flexible version of the Extended Simple Point Charge (SPC/E) water model. Our analysis shows that while local representations are sufficient for predictions of the condensed liquid phase, the short-range nature of machine-learning models falls short in representing cluster and vapor phase properties. These findings provide an improved understanding of the role of long-range interactions in machine learning models and the regimes where they are necessary.

Mean-field theory of inhomogeneous fluids.

The Barker-Henderson perturbation theory is a bedrock of liquid-state physics, providing quantitative predictions for the bulk thermodynamic properties of realistic model systems. However, this successful method has not been exploited for the study of inhomogeneous systems. We develop and implement a first-principles "Barker-Henderson density functional," thus providing a robust and quantitatively accurate theory for classical fluids in external fields. Numerical results are presented for the hard-core Yukawa model in three dimensions. Our predictions for the density around a fixed test particle and between planar walls are in very good agreement with simulation data. The density profiles for the free liquid vapor interface show the expected oscillatory decay into the bulk liquid as the temperature is reduced toward the triple point, but with an amplitude much smaller than that predicted by the standard mean-field density functional.

Iron isotope exchange and fractionation between jarosite and aqueous Fe(II)

Jarosite is one of the critical minerals that regulates acidity and contaminants in acid-sulfate environments and its Fe isotope composition may shed light on its formation, transformation and recrystallization over time. Interpretation of its Fe isotope composition requires understanding the equilibrium Fe isotope fractionation factor between jarosite and other Fe-bearing minerals and aqueous species. Here we explore Fe isotope exchange and fractionation between jarosite and Fe(II)aq under acidic conditions using the three-isotope method (54Fe-56Fe-57Fe). A reversal-approach to equilibrium was applied by reacting synthetic jarosite and natural natrojarosite with two 57Fe-enriched Fe(II)aq solutions that had initial 56Fe/54Fe ratios above and below the predicted equilibrium value. No change in dissolved Fe(II) concentrations were observed with time but the 57Fe/56Fe ratio of Fe(II)aq decreased towards the system mass balance, suggesting a high degree of equilibration of the fluid with the solid phase despite no net Fe(II) sorption (within error). There is a negative relationship between pH and Fe isotope exchange, with Fe isotope exchange proceeding as pH decreases. This may be explained by dissolution of hydronium jarosite and reprecipitation of natrojarosite, coupled H3O+ - Na+ exchange, or jarosite decomposition, although no Fe-oxyhydroxide phases were identified from XRD. Calculation of the amount of Fe atoms in jarosite that exchanged with Fe(II)aq indicates that jarosite recrystallization was limited to a few percent. When the initial δ56Fe value of Fe(II)aq was greater than the presumed equilibrium value its isotopic value substantially decreased with time whereas the δ56Fe values of Fe(II)aq increased with time when it had an initial value below the suspected equilibrium composition. In each case, the isotopic composition of Fe(II)aq approached similar values, providing a high degree of confidence of an attainment of equilibrium. Calculation of the Fe(II)aq–jarosite and Fe(II)aq-natrojarosite equilibrium fractionation factors at 22 °C were −2.26‰ (±0.27‰, 2σ) and −2.19‰ (±0.18‰, 2σ), respectively. This indicates that during jarosite recrystallization in the presence of Fe(II), jarosite is expected to become isotopically heavier as lighter isotopes are fractionated into Fe(II). These values differ from the estimated fractionation factors derived from NRIXS spectroscopy and molecular modeling. The differences between experiments and theory may reflect surface exchange, which was likely in our study, versus predicted bulk thermodynamic properties of the mineral.

Critical properties of the Ising model in hyperbolic space.

The Ising model exhibits qualitatively different properties in hyperbolic space in comparison to its flat space counterpart. Due to the negative curvature, a finite fraction of the total number of spins reside at the boundary of a volume in hyperbolic space. As a result, boundary conditions play an important role even when taking the thermodynamic limit. We investigate the bulk thermodynamic properties of the Ising model in two- and three-dimensional hyperbolic spaces using Monte Carlo and high- and low-temperature series expansion techniques. To extract the true bulk properties of the model in the Monte Carlo computations, we consider the Ising model in hyperbolic space with periodic boundary conditions. We compute the critical exponents and critical temperatures for different tilings of the hyperbolic plane and show that the results are of mean-field nature. We compare our results to the "asymptotic" limit of tilings of the hyperbolic plane: the Bethe lattice, explaining the relationship between the critical properties of the Ising model on Bethe and hyperbolic lattices. Finally, we analyze the Ising model on three-dimensional hyperbolic space using Monte Carlo and high-temperature series expansion. In contrast to recent field theory calculations, which predict a non-mean-field fixed point for the ferromagnetic-paramagnetic phase-transition of the Ising model on three-dimensional hyperbolic space, our computations reveal a mean-field behavior.

Augmented Scaled Particle Theory.

The original motivation for scaled particle theory (SPT) is to derive a simple equation of state for a bulk hard sphere (HS) fluid. It is now widely recognized that SPT provides also the surface tension of a HS fluid near a spherical hard wall, including three contributions, i.e., the planar surface tension and two bending rigidities due to the surface curvatures (integrated mean and Gauss curvatures). This conforms to the basic assumption of morphological thermodynamics. The existence of non-Hadwiger terms, i.e., higher-order curvature terms, has been evidenced recently. Augmenting SPT by only one non-Hadwiger term, i.e., third-order curvature term, allows us to obtain two new analytical theories, which not only describe very accurately bulk thermodynamic properties but also improve systematically surface ones with respect to SPT.

Design and Synthesis of Ir/Ru Pyrochlore Catalysts for the Oxygen Evolution Reaction Based on Their Bulk Thermodynamic Properties.

Density functional theory (DFT) has proven to be an invaluable and effective tool for identifying highly active electrocatalysts for the oxygen evolution reaction (OER). Herein, we take a computational approach to first identify a series of rare-earth pyrochlore oxides based on Ir and Ru as potential OER catalysts. The DFT-based phase diagrams, Pourbaix diagrams (E vs pH), projected density of states, and band energy diagrams were used to identify prospective OER catalysts based on rare-earth Ir and Ru pyrochlores. The predicted materials were synthesized using the spray-freeze freeze-drying approach to afford nanoparticulate oxides conforming to the pyrochlore structural type A2B2O7 where A = Nd, Gd, or Yb and B = Ir or Ru. In agreement with the computed Pourbaix diagrams, the materials were found to be moderately stable under OER conditions. All prepared materials show higher stability as compared to the benchmark IrO2 catalyst, and the OER mass activity of Yb2Ir2O7 and the ruthenate pyrochlores (Nd2Ru2O7, Gd2Ru2O7, and Yb2Ru2O7) were also found to exceed those of the benchmark IrO2 catalyst. We find that the OER activity of each pyrochlore series (i.e., iridate or ruthenate) generally improves as the size of the A-site cation decreases, indicating that maintaining control over the structure can be used to influence the electrocatalytic properties.

Linked cluster theory in the spin polaron problem

The Linked Cluster Theory in the spin polaron formulation is investigated in this paper using the finite temperature (Matsubara) Green’s function method. We use a representation where holes and spins are described as spinless fermions and normal bosons, respectively. An analytic expression of the thermodynamic potential of high-temperature superconductors in the superconducting state was obtained using the Linked Cluster theory and an expression for its normal state by setting the energy gap to zero. The expression of the thermodynamic potential enabled us to calculate two bulk thermodynamic properties of high-temperature superconductors, entropy and specific heat, both in the normal and superconducting states.

Compositional control of radionuclide retention in hollandite‐based ceramic waste forms for Cs‐immobilization

AbstractHollandite materials, as a class of crystalline nuclear waste forms, are promising candidates for the immobilization of radioactive elements, such as Cs, Ba, as well as a variety of lanthanide and transition‐metal fission products. In this study, three Ga‐doped titanate hollandite‐type phases, Ba1.33Ga2.67Ti5.33O16, Ba0.667Cs0.667Ga2Ti6O16, and Cs1.33Ga1.33Ti6.67O16, were synthesized using a solid‐state reaction route. All synthesized phases adopted a single phase tetragonal structure, as determined by powder X‐ray diffraction (XRD), and elemental analysis confirmed the measured stoichiometries were close to targeted compositions. Extended X‐ray absorption fine structure spectroscopy (EXAFS) was used to determine the local structural features for the framework of octahedrally coordinated cations. EXAFS data indicated that Cs1.33Ga1.33Ti6.67O16 possessed the most disordered local structure centered around the Ga dopant. The enthalpies of formation of all three hollandite phases measured using high‐temperature oxide melt solution calorimetry were found to be negative, indicating enthalpies of formation of these hollandites from oxides are thermodynamically stable with respect to their constituent oxides. Furthermore, the formation enthalpies were more negative and hence more favorable with increased Cs content. Finally, aqueous leaching tests revealed that high Cs content hollandite phases exhibited greater Cs retention as compared to low Cs content hollandite. While preliminary in nature, this work draws attention to the links between the capacity for radionuclide retention, atomistic level structural features and bulk thermodynamic properties of materials.