Universal Equation Of State Research Articles

Study on performance evaluation framework and design/ selection guidelines of working fluids for subcritical organic Rankine cycle from molecular structure perspective

Organic Rankine cycle (ORC) is a promising power cycle to convert low-grade thermal energy. The quick and easy evaluation of the potential working fluids lacking thermophysical property data is important for the working fluid selection of ORC. This paper proposes a systematic framework of working fluid evaluation from the molecular structure perspective, which couples the quantitative structure property relationship (QSPR) and universal equations of state. The thermodynamic performance of ORC is first correlated with four key thermophysical properties based on universal equations of state. Then, these thermophysical properties are obtained from the corresponding QSPR models based on the molecular structure of working fluids. The influence factors of ORC performance at a micro level are investigated using the QSPR models. Moreover, the effects of molecular characteristics on thermal efficiency are analyzed. The criteria for working fluid design/selection are recommended aiming at the improvement of thermal efficiency. The proposed framework shows sufficient accuracy with the relative errors of −0.41 - 15.85% and mean absolute error of 8.29% compared with the results based on REFPROP. It is found that the cyclization of carbon chain is an ideal method for the working fluid design based on alkanes and alkenes. This work can provide new insights for the evaluation, selection, and design of working fluids on the molecular structure level.

Formulation for the prediction of melting temperature of metallic solids using suitable equation of states

We presents expressions for the pressure dependence of the melting temperature of metals using Murnaghan, Usual-Taits, and Kholiya equations of state. The predicted model explains the corelation among the pressure, melting temperature, bulk modulus, its first pressure derivative and volume compression at zero pressure. The formalism is then applied to determine the Tm(P) of transition and noble metals such as Cu, Al, Zn, Au, Ag, Mn, Cd, and Mg, over a wide range of pressure up to 35 GPa. It is observed that the Murnaghan equation of state gives accurate result for the metals having higher bulk modulus thus having higher melting temperature. Kholiya equation of state shows closest result with the experimental data for those metals whose bulk modulus is decreasing continuously whereas the trend of variation is similar in Usual-Taits equation of state. The Usual-Taits equation of state, also referred to as the universal equation of state, exhibits the similar trend of variation. This study also sheds light in understanding the quantitative effect of pressure on melting temperature. Obtained results show good agreement with previous experiments and calculations thus justifying the validity of our model.

Non-equilibrium strain induces hysteresis and anisotropy in the quasi-static and dynamic elastic behavior of sandstones: Theory and experiments

Materials with grain contacts or partially closed cracks exhibit anomalous elastic behavior: hysteresis in quasi-static experiments and slow dynamics in fast dynamic ones. Albeit the behavior in the two cases (which correspond to very different strain ranges) appears different, it should stem from the same physics and, thus, could be modeled by a universal equation of state. We propose a modification of the standard acoustoelastic theory, introducing the concept of conditioning induced non-equilibrium strain, which allows us to predict the evolution of elastic wave velocity in both quasi-static and dynamic ranges, including the velocity anisotropy induced by external uniaxial loading.

Numerical study of the effect of individual racks in lenses on the operation of nonlinear lenticular membrane-pneumatic systems by the step method

Objective. The purpose of this study is to substantiate the methodology for static calculation of light coatings for large-span structures with lenticular membrane-pneumatic lenses, including racks at individual points of the span, using the step-iterative method of parameter increments.Method. The study involves the phased application of the finite element method (FEM), the universal equation of state of gas and the improved Euler-Cauchy numerical procedure, taking into account the geometric nonlinearity of systems and the physical nonlinearity of the elastic work of air in lenses and taking into account the aftereffect of excess air pressure.Result. A comparison is made in terms of rigidity and load-bearing capacity of membrane-pneumatic lenses, reinforced with individual posts, with the corresponding flexible membrane-pneumatic lenses of the classical type.Conclusion. In the presence of racks, the effect of a significant increase in the rigidity and bearing capacity of lenticular membrane-pneumatic systems is observed for large spans. The distance between the posts along the building can be adjusted during the design and thereby regulate the effect of strengthening the system. The maximum deflections of the lenticular-shaped membrane-pneumatic system reinforced with struts are much less than the maximum deflections of the lenticular membrane-pneumatic system of the classical type under the action of the calculated snow load of the first and second limit states.

High Pressure Effects on the Structural Properties of GaN Compound Using Equations of State

The present study is a theoretical calculation for the effects of high pressure on thermodynamic properties on GaN up to 40Gpa at room temperature. Volume compression ratio (V0/Vp), lattice constant (a) and elastic bulk modulus(B) have been established. Furthermore, lattice frequencies and disruptions function by analyzing phonon frequency spectrum (PFS) at (0 K). The entire calculations rely on using of two equation of state (EOS) "Birch-Murnaghan and modified Lennard-Jones" equation of state and with the integration of Grüneisen approximation theory. From the considered equations of state, formulation of bulk modulus was derived, that predicts a rising trend of bulk modulus. The large bulk modulus value of GaN has made a small fraction of change in volume (less than 15%) of the material even under an extreme pressure up to 45Gpa. It was also found that the results of phonon frequency spectrum obtained from Birch-Murnaghan equation of state in a better agreement with the experimental data than that of modified Lennard-Jones equation of state. Given that the Birch-Murnaghan equation of state developed according to Eulerian strain theory accounted as a universal equation of state. Moreover, good agreement between theoretically present calculations and experiment data of phonon frequency spectrum, reveals the validity of the equations of state used in the present study.

Structure and thermodynamics of empty clathrate hydrates below the freezing point of water.

Recently prepared as a new H2O phase, ice XVI was obtained by degassing a Ne-sII clathrate hydrate under vacuum, however very little is known of that crystalline solid under temperatures (T ≤ 220 K) and pressures (p ≤ 5000 bar) relevant for the Earth's environment and geochemistry. In this work, atomically detailed calculations using long time-scale molecular simulations, seldom paralelled before, are employed to probe empty sII clathrate hydrates. It is found that the volumetric response to an applied pressure-temperature gradient is accurately described by the Parsafar and Mason equation of state with an accuracy of at least 99.7%. Structural deformation induced upon the crystals is interpreted by monitoring the unit cell length and isobaric thermal expansivity, whilst benchmarked against previous neutron diffraction measurements of ice XVI and hexagonal ice under room pressure conditions; a critical comparison is established with other sII guest occupied lattices (CH4, CO2 and CnH2n+2 with n = 2, 3, 4), often found in permafrost regions and in the margins of continental shelves. Such an analysis reveals that empty sII frameworks are slightly more stable to thermal deformation than their sI analogues and that hexagonal ice is the structurally most stable of the condensed H2O phases addressed here. Of paramount importance for the oil and natural gas industries, heat capacities obtained from enthalpy profiles are identical for the sI and sII empty clathrates up to 2000 bar and diverge by only ∼7.3% at 5000 bar. The canonical tetrahedral symmetry of water-bonded networks is analysed in terms of an angular and a distance order parameters, which are observed to decrease (increase) as pressure (temperature) increases (decreases). The results now being reported constitute a landmark for future studies dealing with high-pressure and very low-temperature conditions, characteristic of the Earth's permafrost environment and other planetary interiors, whilst contributing to expand our knowledge regarding the recently discovered ice XVI phase.

Dark Solitons in the Unitary Bose Gas

We study the dilute and ultracold unitary Bose gas, characterized by a universal equation of state due to the diverging s-wave scattering length, under a transverse harmonic confinement. From the hydrodynamic equations of superfluids we derive an effective one-dimensional nonpolynomial Schrödinger equation (1D NPSE) for the axial wavefunction which, however, also takes into account the transverse wavefunction. By solving the 1D NPSE we obtain meaningful analytical formulas for the dark (gray and black) solitons of the bosonic system.

Construction of a Universal Gel Model with Volume Phase Transition

The physical principle underlying the familiar condensation transition from vapor to liquid is the competition between the energetic tendency to condense owing to attractive forces among molecules of the fluid and the entropic tendency to disperse toward the maximum volume available as limited only by the walls of the container. Van der Waals incorporated this principle into his equation of state and was thus able to explain the discontinuous nature of condensation as the result of instability of intermediate states. The volume phase transition of gels, also discontinuous in its sharpest manifestation, can be understood similarly, as a competition between net free energy attraction of polymer segments and purely entropic dissolution into a maximum allowed volume. Viewed in this way, the gel phase transition would require nothing more to describe it than van der Waals’ original equation of state (with osmotic pressure replacing pressure P). But the polymer segments in a gel are networked by cross-links, and a consequent restoring force prevents complete dissolution. Like a solid material, and unlike a van der Waals fluid, a fully swollen gel possesses an intrinsic volume of its own. Although all thermodynamic descriptions of gel behavior contain an elastic component, frequently in the form of Flory-style rubber theory, the resulting isotherms usually have the same general appearance as van der Waals isotherms for fluids, so it is not clear whether the solid-like aspect of gels, that is, their intrinsic volume and shape, adds any fundamental physics to the volume phase transition of gels beyond what van der Waals already knew. To address this question, we have constructed a universal chemical potential for gels that captures the volume transition while containing no quantities specific to any particular gel. In this sense, it is analogous to the van der Waals theory of fluids in its universal form, but although it incorporates the van der Waals universal equation of state, it also contains a network elasticity component, not based on Flory theory but instead on a nonlinear Langevin model, that restricts the radius of a fully swollen spherical gel to a solid-like finite universal value of unity, transitioning to a value less than unity when the gel collapses. A new family of isotherms arises, not present in a preponderately van der Waals analysis, namely, profiles of gel density as a function of location in the gel. There is an abrupt onset of large amplitude density fluctuations in the gel at a critical temperature. Then, at a second critical temperature, the entire swollen gel collapses to a high-density phase.

Pressure-induced polymorphism in hypervalent CsI3

We report the results of ambient temperature high-pressure synchrotron-based x-ray diffraction, Raman, and electrical resistance study of $\mathrm{Cs}{\mathrm{I}}_{3}$ up to 29, 25, and 8 GPa, respectively, and confirm three-phase transitions under quasihydrostatic conditions. The ambient orthorhombic (space group (SG): Pnma) phase of $\mathrm{Cs}{\mathrm{I}}_{3}$ is stable up to a pressure of $\ensuremath{\sim}1.3\phantom{\rule{0.16em}{0ex}}\mathrm{GPa}$, above which a phase transition to a trigonal ($\mathrm{SG}:P\text{\ensuremath{-}}3c1$) phase is observed. The stability region of the trigonal phase has been found to be up to 22.6 GPa, above which the trigonal phase transforms to a cubic ($\mathrm{SG}:Pm\text{\ensuremath{-}}3n$) phase which remains stable until the maximum pressure of 29 GPa achieved in this study. A third-order Birch-Murnaghan equation of state fit to the pressure volume ($P\text{\ensuremath{-}}V$) data yields a bulk modulus of 17.7(9) GPa for the trigonal phase. Raman spectroscopic measurements however indicate three-phase transitions at $\ensuremath{\sim}1.3,\phantom{\rule{0.16em}{0ex}}4.0$, and 22.6 GPa, respectively. The electrical resistance measured in the low-pressure region up to 8 GPa indicates an electronic transition at around 4 GPa confirming the Raman result observed at 4.0 GPa. The $P\text{\ensuremath{-}}V$ data when transformed to the universal equation of state (UEOS) show a deviation from linearity around 4.0 GPa confirming the electronic transition. The present study has thus revealed a three-phase structural sequence in alkali trihalides, viz., orthorhombic (SG: Pnma) to trigonal ($\mathrm{SG}:P\text{\ensuremath{-}}3c1$) to a cubic ($\mathrm{SG}:Pm\text{\ensuremath{-}}3n$) phase.

How tightly is the nuclear symmetry energy constrained by a unitary Fermi gas?

We examine critically how tightly the density dependence of nuclear symmetry energy \esym is constrained by the universal equation of state (EOS) of the unitary Fermi gas $E_{\rm{UG}}(\rho)$ considering currently known uncertainties of higher order parameters describing the density dependence of the Equation of State of isospin-asymmetric nuclear matter. We found that $E_{\rm{UG}}(\rho)$ does provide a useful lower boundary for the \esym. However, it does not tightly constrain the correlation between the magnitude $E_{\rm{sym}}(\rho_0)$ and slope $L$ unless the curvature $K_{\rm{sym}}$ of the symmetry energy at saturation density $\rho_0$ is more precisely known. The large uncertainty in the skewness parameters affects the $E_{\rm{sym}}(\rho_0)$ versus $L$ correlation by the same almost as significantly as the uncertainty in $K_{\rm{sym}}$.

An effective series expansion to the equation of state of unitary Fermi gases

Using universal properties and a basic statistical mechanical approach, we propose a general equation of state for unitary Fermi gases. The universal equation of state is written as a series solution to a self consistent integral equation where the general solution is a linear combination of Fermi functions. First, by truncating our series solution to four terms with already known exact theoretical inputs at limiting cases, namely the first three virial coefficients and using the Bertsch parameter as a free parameter, we find a good agreement with experimental measurements in the entire temperature region in the normal state. This analytical equation of state agrees with experimental data up to the fugacity z = 18, which is a vast improvement over the other analytical equations of state available where the agreements is only up to . Second, by truncating our series solution to four terms again using first four virial coefficients, we find the Bertsch parameter , which is in good agreement with the direct experimental measurement of . This second form of equation of state shows a good agreement with self-consistent T-matrix calculations in the normal phase.

Criticality and surface tension in rotating horizon thermodynamics

We study a modified horizon thermodynamics and the associated criticality for rotating black hole spacetimes. Namely, we show that under a virtual displacement of the black hole horizon accompanied by an independent variation of the rotation parameter, the radial Einstein equation takes a form of a ‘cohomogeneity two’ horizon first law, , where E and J are the horizon energy (an analogue of the Misner–Sharp mass) and the horizon angular momentum, Ω is the horizon angular velocity, A is the horizon area, and σ is the surface tension induced by the matter fields. For fixed angular momentum, the above equation simplifies and the more familiar (cohomogeneity one) horizon first law is obtained, where P is the pressure of matter fields and V is the horizon volume. A universal equation of state is obtained in each case and the corresponding critical behavior is studied.

A phenomenological approach to the equation of state of a unitary Fermi gas

We propose a phenomenological approach for the equation of state of a unitary Fermi gas. The universal equation of state is parametrized in terms of Fermi–Dirac integrals. This reproduces the experimental data over the accessible range of fugacity and normalized temperature, but cannot describe the superfluid phase transition found in the MIT experiment [Ku et al, Science 335, 563 (2012)]. The most sensitive data for compressibility and specific heat at phase transition can, however, be fitted by introducing into the grand partition function a pair of complex conjugate zeros lying in the complex fugacity plane slightly off the real axis.

Universal equation of state and pseudogap in the two-dimensional Fermi gas.

We determine the thermodynamic properties and the spectral function for a homogeneous two-dimensional Fermi gas in the normal state using the Luttinger-Ward, or self-consistent T-matrix, approach. The density equation of state deviates strongly from that of the ideal Fermi gas even for moderate interactions, and our calculations suggest that temperature has a pronounced effect on the pressure in the crossover from weak to strong coupling, consistent with recent experiments. We also compute the superfluid transition temperature for a finite system in the crossover region. There is a pronounced pseudogap regime above the transition temperature: the spectral function shows a Bogoliubov-like dispersion with backbending, and the density of states is significantly suppressed near the chemical potential. The contact density at low temperatures increases with interaction and compares well with both experiment and zero-temperature MonteCarlo results.

Near-Equilibrium Solubility of Nanocrystalline Alloys

ABSTRACTGrain boundaries are the dominating type of defect in nanocrystalline materials. Understanding their properties is crucial to the comprehension of nanocrystalline materials behavior. A facile thermodynamic model for alloy grain boundaries is developed. The macroscopic analysis is based on established descriptions of metallic solutions and the universal equation of state at negative pressure, using mainly parameters obtainable from measurements on macroscopic samples. The free energy of atoms in grain boundaries is derived as a function of excess volume, composition, and temperature. Interfacial enrichment is computed using equilibrium conditions between bulk phase and grain boundaries. The excess volume of symmetric ‘100’ tilt grain boundaries in Cu as a common system is obtained by atomistic computer simulation. In a general case the predictions of the proposed model are compared to experimental grain boundary segregation data, yielding a good match. The near-equilibrium solubility of Ag in nanocrystalline Cu and of Cu in nanocrystalline Fe is calculated.

Thermodynamic model of alloy grain boundaries

A facile thermodynamic model for grain boundaries in dilute alloys is developed. The macroscopic analysis is based on known descriptions of metallic solutions and the universal equation of state. The thermodynamic variable free energy is derived as a function of composition and excess volume. Employing Guggenheim’s condition for equilibrium between bulk and grain boundaries, the segregation behavior and the interface free energy of two model systems, copper–silver and copper–bismuth, are calculated. The results show good agreement with experimental data.

Low-dimensional weakly interacting Bose gases: Nonuniversal equations of state

The zero-temperature equation of state is analyzed in low-dimensional bosonic systems. We propose to use the concept of energy-dependent $s$-wave scattering length for obtaining estimations of nonuniversal terms in the energy expansion. We test this approach by making a comparison to exactly solvable one-dimensional problems and find that the generated terms have the correct structure. The applicability to two-dimensional systems is analyzed by comparing with results of Monte Carlo simulations. The prediction for the nonuniversal behavior is qualitatively correct and the densities, at which the deviations from the universal equation of state become visible, are estimated properly. Finally, the possibility of observing the nonuniversal terms in experiments with trapped gases is also discussed.

Universal equation of state for alkali halide solids

A universal equation of state for solids is proposed. The equation exactly accounts for the cohesive energy; no physically incorrect oscillations exists, and its action is correct in both high pressure and expanded regions. The new equation and several typical equations in literature are applied to 15 alkali halide solids, and one alkaline earth oxide. The results show that the new equation can well fit experimental data, and can give correct cohesive energy. The parameters determined from the Vinet and Morse equations are sensitive to the data range, whereas the new equation is not . This implies that the applicability of new equation is better than the Vinet and Morse equations.

Molecular dynamics studies of CaAl 2Si 2O 8 liquid. Part II: Equation of state and a thermodynamic model

A thermodynamic model and equation of state (EOS) is developed from the molecular dynamics simulation experiments of Spera et al. (2009) for CaAl 2Si 2O 8 liquid over the temperature range 3500–6000 K and pressure interval 0–125 GPa. The model is constructed utilizing the isothermal Universal EOS of Vinet et al. (1986) combined with an expression for the temperature-dependence of the internal energy derived from density functional theory ( Rosenfeld and Tarazona, 1998). It is demonstrated that this model is more successful at reproducing the data than the temperature-dependent Universal EOS ( Vinet et al., 1987) or the volume-explicit EOS of Ghiorso (2004a). Distinct parameterizations are required to model low (<20 GPa) and high (>20 GPa) pressure regimes. This result is ascribed to the affect of liquid structure on macroscopic thermodynamic properties, specifically the interdependence of average cation-oxygen coordination number on the bulk modulus. The thermodynamic transition between the high- and low-pressure parameterizations is modeled as second order, although the nature of the transition is open to question and may well be first order or lambda-like in character. Analysis of the thermodynamic model reveals a predicted region of liquid–liquid un-mixing at low-temperatures (<1624 K) and pressures (<1.257 GPa). These pressure–temperature conditions are above the glass transition temperature but within the metastable liquid region. They represent the highest temperatures yet suggested for liquid–liquid un-mixing in a silicate bulk composition. A shock wave Hugoniot curve is calculated for comparison with the experimental data of Rigden et al. (1989) and of Asimow and Ahrens (2008). The comparison suggests that the model developed in this paper underestimates the density of the liquid by roughly 10% at pressures greater than ∼20 GPa.

Entropy stabilization of deformed regions characterized by an excess volume for hydrogen storage applications

A general framework using the universal equation of state is given to quantify the excess entropy present in deformed regions of metals and metal hydrides characterized by an excess volume. The conditions under which the excess entropy leads to a stabilization of the deformed regions with respect to multiple hydriding/dehydriding cycles are determined. The impact of the energy barrier created by the excess entropy on the recrystallization rate of the deformed regions is quantified using a homogeneous nucleation and crystal growth model. At high temperature, due to the energy barrier, metal hydride systems containing a large excess volume can have a recrystallization rate that is several orders of magnitude smaller than the recrystallization rates of regions containing low excess volume. This entropy stabilization can create a regime where the reduced enthalpy of formation of the metal hydride could be maintained over multiple cycles because of the increased stability of the nanostructures responsible for the reduction in the enthalpy of formation.