Semiempirical Equation Of State Research Articles

A global equation-of-state model from mathematical interpolation between low- and high-density limits

The ideal gas equation of state (EOS) model is a well-known low-density limiting model. Recently, an ideal dense matter EOS model for the high-density limit symmetric to the ideal gas model has been developed. Here, by mathematically interpolating between the ideal gas and ideal dense matter limiting models, we establish a global model containing two EOS in the form of P-V-T and P-S-T for arbitrary ranges of densities. Different from empirical or semi-empirical EOS, the coefficients in the global EOS have a clear physical meaning and can be determined from a priori knowledge. The proposed global model is thermodynamically consistent and continuous. It reduces to the ideal gas model when approaching the low-density limit and to the ideal dense matter model when approaching the high-density limit. Verifications for 4He show that the global model reproduces the large-range behavior of matter well, along with providing important insight into the nature of the large-range behavior. Compared to the third-order virial EOS and the Benedict–Webb–Rubin EOS, the global P-V-T EOS has higher descriptive accuracy with fewer coefficients over a wide range of data for N2. The global model is shown to work well in extreme applied sciences. It predicts a linear, inverse relationship between entropy and volume when the temperature-to-pressure ratio is constant, which can explain the entropy-production behavior in shock-Hugoniots.

P-V-T Equation of state of gold to high pressure and temperature, derived from statistical moment method

P-V-T equation of state (P-V-T EOS) of gold to high pressure and temperature are studied by the statistical moment method. We obtain P-V-T equation of state for gold of simple analytic form, without adjustment parameters. The numerical results of the pressure P at compression x on the isotherms T of gold by this equation of state in good agreement with the data calculated by the semi-empirical equations of state, which have adjustable parameters, up to 600kbar and 2000K. The thermodynamic quantities of gold are also obtained from this equation of state. The numerical results of the thermal expansion coefficient, heat capacity of gold are in excellent agreement with the experimental data. Due to the simplicity and efficiency of gold equation of state obtained, this equation of state can be used as pressure scales to 600kbar and 2000K.

Gibbsian Surface Thermodynamics.

Gibbsian composite-system thermodynamics is the framework governing the equilibrium of composite systems, including systems that at equilibrium have more than one value of pressure because of the action of surface tension, semipermeable membranes, or fields, and thus cannot be treated as simple systems. J. W. Gibbs's paper that lays out composite-system thermodynamics, "On the Equilibrium of Heterogeneous Substances", communicated in two parts in 1876 and 1878, is widely regarded as one of the most important pieces of scientific literature of its century. Many scientists adopted and stressed the importance of Gibbsian thermodynamics. In 1960, H. B. Callen wrote a textbook that made Gibbsian composite-system thermodynamics more accessible to thermodynamicists. However, Callen's book left out Gibbs's work on curved fluid interfaces and did not treat the complicated nonideal systems of interest to today's thermodynamicists. In this Feature Article, I have attempted to convey in a comprehensive manner the framework of Gibbsian composite-system thermodynamics including in detail the treatment of systems with interface effects and with nonideal, multicomponent phases. This work lays out the relationships between important equilibrium equations including the following: the Gibbs-Duhem equation, the Gibbs adsorption equation, the Young-Laplace equation, the Young equation, the Cassie-Baxter equation, the Wenzel equation, the Kelvin equation, the Gibbs-Thompson equation, and the Ostwald-Freundlich equation, including nonideal and multicomponent forms. Equations of state that are often useful for Gibbsian composite-system thermodynamics are reviewed including adsorption isotherms and our own work on two semiempirical equations of state: the Elliott et al. form of the osmotic virial equation and the Shardt-Elliott-Connors-Wright equation for the temperature and composition dependence of surface tension. I summarize the work of our group developing Gibbisan composite-system thermodynamics including new equations for such things as the curvature-induced depression of the eutectic temperature or the removal of azeotropes by nanoscale fluid interface curvature. Gibbsian composite-system thermodynamics has broad applications in biotechnology, nanostructured materials, surface textures and coatings, microfluidics, nanoscience, atmospheric and environmental physics, among others.

A Molecular-Based Equation of State for Vapour-liquid Equilibrium of Pure Substances

A semi-empirical equation of state has been studied for modelling vapour-liquid data of pure substances. The specific molecular based equation of state is employed here as basis because of its mathematical simplicity. The semi-empirical extension has been accomplished to real fluids by correlating the density dependence of the attraction term to vapour liquid data of a reference fluid. The resulting attraction term is mathematically relatively simple and fulfills the topological requirements given by the physical background. With this model vapour-liquid equilibrium data for pure substances have been correlated. The investigated systems include n-alkanes, 1-alkanols, acetone and carbon dioxide. The results are compared with those obtained by PR (Peng-Robinson), SRK (Soave-Redlich-Kwon) and RM (Riazi-Mansoori) equations of state.

Equations of State and the Phase Diagram of Dielectric and Metallic Helium-4

A new form of the semiempirical equation of state for the liquid phase of helium-4 is proposed that is based on the assumption that the structure of this phase consists of a mixture of dielectric and metallic components. It is postulated that solid dielectric helium with density higher than 5.3 g/cm3 becomes a metal. The values of the parameters of the equations of state for both solid phases and the liquid phase of helium are calculated. The unknown values of the initial data for helium are taken by analogy with the parameters for deuterium. The phase diagram, shock adiabat, isentropes, isotherms, and electrical conductivity in these processes are calculated with the use of the equations of state of solid and liquid phases of helium-4. The results of calculation are compared with experimental data in the range of pressures of up to 35 GPa for an isotherm, up to 150 GPa for a shock adiabat, up to 42 GPa for the melting curve, and up to 2000 GPa for isentropes, and showed quite satisfactory agreement. Numerical extrapolation of the melting curve is performed to a range of ultrahigh pressures of up to 8000 GPa.

The Hugoniot adiabat of crystalline copper based on molecular dynamics simulation and semiempirical equation of state

The molecular dynamics (MD) method was used for prediction of properties of copper under shock-wave compression and clarification of the melting region of crystal copper. The embedded atom potential was used for the interatomic interaction. Parameters of Hugonoit adiabats of solid and liquid phases of copper calculated by the semiempirical Grüneisen equation of state are consistent with the results of MD simulations and experimental data. MD simulation allows to visualize the structure of cooper on the atomistic level. The analysis of the radial distribution function and the standard deviation by MD modeling allows to predict the melting area behind the shock wave front. These MD simulation data are required to verify the wide-range equation of state of metals. The melting parameters of copper based on MD simulations and semiempirical equations of state are consistent with experimental and theoretical data, including the region of the melting point of copper.

Investigating effects of molecular structure on the behavior of saturated liquid hydrocarbons using a novel semi-empirical equation of state

In this study, a novel equation of state has been developed to investigate the behavior of saturated liquid hydrocarbons. The developed equation was used to study the effects of molecular structure on this behavior. A set of logical rules was obtained to estimate the power of the presented equation of state. Finally, this equation and the obtained logics were validated using experimental data.

The formation and evolution of the core-corona structure in the electrical explosion of aluminum wire in vacuum: experimental and numerical investigations

Experimental and numerical investigations on the formation and evolution of the core-corona structure in the electrical explosion of aluminum wire in vacuum are presented. In the experiments of aluminum wire explosion, shadowgraphy, interferometry and schlieren optical diagnostics are constructed with a laser probe to study the morphological evolution and distribution of the core and corona. A set of computational models with cold start conditions, consisting of a thermodynamic calculation and magnetohydrodynamic model combined with a semi-empirical equation of state and transport coefficients, are established to reproduce the behavior of the electrical explosion of aluminum wire. The radial profiles of the density, temperature, current density and magnetic field, addressing the physical scenario of the formation and evolution of the core-corona structure are analyzed. The numerical results are also compared with relevant experimental data.

Equation of state of quartz glass and cerium in their abnormal compressibility range

In this work, the semiempirical equation of state of quartz glass and polycrystalline γ-cerium are plotted and verified at the compressive pressures to 3 GPa. The proposed equations are shown to uniformly describe the thermophysical and physicomechanical properties of quartz glass and polycrystalline γ-cerium at their abnormal compressibility in compression. The room isotherms of these materials are discussed, as well.

Electrical conductivity and polymorphic transition of titanium in the megabar shock pressure range

The effect of high dynamic pressures on the electrical resistance of titanium has been studied. The electrical resistance of titanium samples has been measured under conditions of step shock compression followed by unloading. The history of shock-wave loading of titanium has been calculated using the semiempirical equations of state. It has been shown that, in the phase of compression at a pressure of 83(5) GPa, the resistance of titanium samples stepwise decreases by 30%. In the unloading phase in the same region of dynamic loads, the reverse variation in the electrical resistance of titanium takes place. The observed effect is interpreted as a consequence of the ω ↔ γ polymorphic transition in shock-compressed titanium.

Resistivity and equation of state of warmed gallium melt in megabar pressure

The electrical conductivity of gallium melt was measured under multiple-shock compression up to ≈ 100 GPa. The semi-empirical equations of state (EOS) are constructed in the shock pressure range 30-300 GPa. The EOS were used for reconstruction of the thermodynamic history of the sample in the experiments and for the subsequent definition of the volume-temperature dependence of gallium melt resistivity. It was shown that the volume-temperature dependence of gallium melt is proportional to temperature and inversely to the square of characteristic temperature in the shock pressure range 30-80 GPa and temperatures of 1000-2000 K. Thus warmed high pressure gallium phase melt possesses metal conductivity.

Measurement and Correlation of Solid Drugs Solubility in Supercritical Systems

A dynamic experimental set-up was utilized to measure ibuprofen solubility in supercritical CO2 at the pressure range of 8-13 MPa and the temperatures of 308, 313 and 318 K. Mole fraction values varied from 0.015×10−3 to 3.261×10−3 and correlated by using seven different semi empirical equations of state (Bartle, Modified Bartle, Mendez-Teja, Modified Mendez-Teja, Kumar-Johnson, Sung-shim and Gordillo) as well as seven cubic equations of state (van der Waals, Redlich-Kwong, Soave-Redlich-Kwong, Peng-Robinson, Stryjek-Vera, Patel-Teja-Valderana and Pazuki). Single and twin-parametric van der Walls mixing rules (vdW1, vdW2) were applied in order to estimate the supercritical solution properties. The physicochemical properties were also obtained using Joback, Lydersen and Ambrose methods. Absolute average relatives deviation (AARD) were calculated and compared for all the correlating systems. Results showed that among the cubic equations of state (EOSs) the Pazuki equation (AARD19.85% using vdW1 and AARD8.79% using vdW2) and SRK equation (AARD19.20% using vdW1 and AARD10.03% using vdW2) predicted the ibuprofen solubility in supercritical CO2 with the least error in comparison to the others. Among the semi-empirical EOSs the most desirable deviation (AARD<10%) was obtained by using Modified Bartle and Modified Mendez-Teja equations in all the studied temperatures.

Unified low-parametrical equation of state for engineering calculations of thermodynamic properties of substances

The new simple semi empirical equation of state for description of P --T data of normal substances was specified. New equation of state has 10 individual adjustable coefficients and it describes thermal properties of gas, liquid and fluid in the main with the accuracy within the error of experimental data, except of critical region. The caloric properties and the speed of sound of argon, nitrogen and carbon dioxide were calculated with the help of known thermodynamic equations and in general divergences between calculated and tabular caloric data do not exceed the experimental error. New equation can be used for engineering calculations at the deficit of experimental data, especially on the caloric properties of substances.

Equation of state of polytetrafluoroethylene for calculating shock compression parameters at megabar pressures

Semi-empirical equations of state (thermal and caloric) are obtained to calculate not only the kinematic parameters (shock wave velocity, particle velocity, and reverberation of waves) but also the thermodynamic parameters (temperature, pressure, and compression) of monolithic and porous polytetrafluoroethylene at high shock pressures. The equations of state are used to model wave interaction in shock-wave experiments using the developed hydrocode. The equations are verified by comparison simulation results with published results of experiments and the data of our shock compression tests of solid and porous samples of PTFE in the range of 10–170 GPa.

Equation of state model for metals with ionization effectively taken into account. Equation of state of tantalum, tungsten, aluminum, and beryllium

A model of a wide-range semi-empirical equation of state for metals is presented. The specific heat and Gruneisen coefficients of ions and electrons are functions of temperature and density. At low temperatures, the heat capacity varies according to Debye theory. The removal of the degeneration of the electron gas with increasing temperature is taken into account. The effect of ionization on the thermodynamic functions is effectively taken into account. The equation of state allows the calculation of states in a two-phase liquid-vapor region. This model was used to develop the equations of state for Ta, W, Al, and Be. For its range of applicability, the equation of state contains a relatively small number of free parameters, most of which have a physical meaning. Comparison of calculations of various isolines using equations of state with experimental data and calculations based on other models show that the equations of state for Ta, W, Al, and Be, describe most experimental data for these substances. At ultrahigh pressures and temperatures, calculations using the equations of state are in good agreement with calculations using the Thomas-Fermi model with corrections.

The &amp;quot;tipping&amp;quot; temperature within Subglacial Lake Ellsworth, West Antarctica and its implications for lake access

Abstract. We present results from new geophysical data allowing modelling of the water flow within Subglacial Lake Ellsworth (SLE), West Antarctica. Our simulations indicate that this lake has a novel temperature distribution due to significantly thinner ice than other surveyed subglacial lakes. The critical pressure boundary (tipping depth), established from the semi-empirical Equation of State, defines whether the lake's flow regime is convective or stratified. It passes through SLE and separates different temperature (and flow) regimes on either side of the lake. Our results have implications for the location of proposed access holes into SLE, the choice of which will depend on scientific or operational priorities. If an understanding of subglacial lake water properties and dynamics is the priority, holes are required in a basal freezing area at the North end of the lake. This would be the preferred priority suggested by this paper, requiring temperature and salinity profiles in the water column. A location near the Southern end, where bottom currents are lowest, is optimum for detecting the record of life in the bed sediments; to minimise operational risk and maximise the time span of a bed sediment core, a location close to the middle of the lake, where the basal interface is melting and the lake bed is at its deepest, remains the best choice. Considering potential lake-water salinity and ice-density variations, we estimate the critical tipping depth, separating different temperature regimes within subglacial lakes, to be in about 2900 to 3045 m depth.

Pseudopotential and full-electron DFT calculations of thermodynamic properties ofelectrons in metals and semiempirical equations of state

In the present work, we compare the thermal contribution of electrons to thermodynamicfunctions of metals in different models at high densities and electron temperatures. One ofthe theoretical approaches, the full-potential linear-muffin-tin-orbital method, treats allelectrons in the framework of density functional theory (DFT). The other approach,VASP, uses projector-augmented-wave pseudopotentials for the core electronsand considers the valent electrons also in the context of DFT. We analyze thelimitations of the pseudopotential approach and compare the DFT results with afinite-temperature Thomas–Fermi model and two semiempirical equations of state.

Lattice Boltzmann method for Lennard-Jones fluids based on the gradient theory of interfaces

In the present study we propose a lattice Boltzmann equation (LBE) model derived from density gradient expansions of the discrete BBGKY evolution equations. The model is based on the mechanical approach of the gradient theory of interfaces. The basic input is the radial distribution function, which is related exclusively to the molecular interaction potential, rather than semiempirical equations of state used in previous LBE models. This function can be provided from independent molecular simulations or from approximate theories. Evidently the accuracy of the interaction potential, and thus the radial distribution function, reflects on the accuracy of the thermodynamic properties and consistency of the derived LBE model. We have applied the proposed model to obtain equilibrium bulk and interfacial properties of a Lennard-Jones fluid at different temperatures, T, close to critical, T(c). The results demonstrate that the LBE model is in excellent agreement with gradient theory as well as with independent literature results based on different molecular simulation approaches. Hence the proposed LBE model can recover accurately bulk and interfacial thermodynamics for a Lennard Jones fluid at T/T(c)>0.9.

Properties of saturated fluorocarbons: Experimental data and modeling using perturbed-chain-SAFT

We present experimental speed of sound data for the saturated fluorocarbons used most frequently in particle detector cooling systems. Data were collected over the moderate range of pressure (≤0.4 MPa) and temperature 250–340 K. A commercial sound/density analyzer operating on the vibrating tube principle was employed for the measurements in liquid state. A dedicated sonar analyser – described in detail – was recently redesigned and developed for the speed of sound measurements in gas phase. Data for speed of sound in saturated fluorocarbons presented in previous papers [V. Vacek, G. Hallewell, S. Ilie, S. Lindsay, Fluid Phase Equilib. 174 (2000) 191–201; V. Vacek, G. Hallewell, S. Lindsay, Fluid Phase Equilib. 185 (2001) 305–314] were reanalyzed and corrected and some new measured data were added. Our experimental data were then used to validate a theoretically based equation of state application rather than the empirical or semi-empirical equations of state mostly used up to now in fluorocarbon applications.

Semiempirical equation of state with few constants for cesium vapor

Statistical analysis is performed of consistency of the known experimental data on the density of cesium vapor. A semiempirical equation of state with few constants is employed, which is based on “pseudogroup” expansions of pressure and density in powers of activity. The second group integral is theoretically calculated using spectroscopic and quantum-mechanical data on atomic interaction. A modification of this equation of state is suggested, which enables one to approximate experimental data both at low and moderate densities and in the near-critical region. Equations of state are derived, which describe both the data of single experiments and the majority of these data taken together. The experimental data indicative of the significant effect of anomalous ionization of cesium vapor on its thermodynamic behavior are shown to be invalid.