Empirical Equation Of State Research Articles

'SAXS-osmometer' method provides measurement of DNA pressure in viral capsids and delivers an empirical equation of state.

We present a novel method that provides a measurement of DNA pressure in viral capsids using small angle X-ray scattering (SAXS). This method, unlike our previous assay, does not require triggering genome release with a viral receptor. Thus, it can be used to determine the existence of a pressurized genome state in a wide range of virus systems, even if the receptor is not known, leading to a better understanding of the processes of viral genome uncoating and encapsidation in the course of infection. Furthermore, by measuring DNA pressure for a collection of bacteriophages with varying DNA packing densities, we derived an empirical equation of state (EOS) that accurately predicts the relation between the capsid pressure and the packaged DNA density and includes the contribution of both DNA-DNA interaction energy and DNA bending stress to the total DNA pressure. We believe that our SAXS-osmometer method and the EOS, combined, provide the necessary tools to investigate physico-chemical properties of confined DNA condensates and mechanisms of infection, and may also provide essential data for the design of viral vectors in gene therapy applications and development of antivirals that target the pressurized genome state.

A Fundamental Equation of State for the Calculation of Thermodynamic Properties ofn-Octane

An empirical equation of state in terms of the Helmholtz energy is presented for n-octane. It is valid from the triple-point temperature 216.37 K to 650 K with a maximum pressure of 1000 MPa and allows for the calculation of all thermodynamic properties in the vapor and liquid phase, in the supercritical region, and in equilibrium states. In the homogeneous liquid phase, the uncertainty in density is 0.03% at atmospheric pressure. For pressures up to 200 MPa and temperatures between 270 and 440 K, density is described with an uncertainty of 0.1%. Outside this region, the uncertainty in the liquid phase increases to 0.5%. Densities in the vapor phase are estimated to be accurate within 0.5%. The uncertainty in vapor pressure depends on the temperature range and varies from 0.02% to 0.4%. Speed of sound in the liquid phase at temperatures below 500 K is described with an uncertainty of 0.1% or less. The isobaric heat capacity in the liquid phase can be calculated with an uncertainty of 0.1% and in the gas phase with 0.2%. A reasonable physical behavior of the equation of state was ensured by the analysis of numerous thermodynamic properties.

Effect of high strain rate and confinement on the compressive properties of autoclaved aerated concrete

Autoclaved aerated concrete (AAC), also known as autoclaved cellular concrete, is a highly porous and light-weight material with a huge amount of closed air bubbles. It has been widely used in over 40 countries around the world to make masonry units such as infill walls or other nonstructural elements such as wall panels. Some structures during their service life might be exposed to blast and impact loads. Such extreme dynamic loads owing to their specific characteristics such as high amplitude and short duration induce very different structural responses and damage as compared to static and low-rate dynamic load. Understanding the properties of AAC material under dynamic and complex stress states is essential for accurate prediction of the response of structural components made of AAC subjected to highly dynamic loads. This study investigates the compressive behavior of AAC material under uniaxial quasi-static and impact and quasi-static triaxial loading tests. AAC material with nominal density of 500 kg/m3 was used to prepare specimens in all tests. For uniaxial compressive tests, the strain rate ranged from 3.3 × 10−5s−1 to 100 s−1 by using electric universal testing machine and INSTRON VHS 160/100–20 high-strain-rate testing system. A high-speed camera was used to capture the failure processes of AAC specimens during the tests. Based on testing data and high-speed camera images, the failure mechanism was investigated. Dynamic stress-strain curves under different strain rates were derived, and rate effects on the compressive strength were discussed. The corresponding empirical DIF (dynamic increase factor) relations were proposed. For quasi-static pseudo triaxial compressive tests, the deviatoric stress-strain curves of AAC specimens under different levels of confining pressure were obtained and compared. The damage induced by hydrostatic pressure and the corresponding failure modes were investigated. The compressive meridian and the empirical EOS (equation of state) relations were proposed based on the test data.

Caloric and isothermal equations of state of solids: empirical modeling with multiply broken power-law densities

Empirical equations of state (EoSs) are developed for solids, applicable over extended temperature and pressure ranges. The EoSs are modeled as multiply broken power laws, in closed form without the use of ascending series expansions; their general analytic structure is explained and specific examples are studied. The caloric EoS is put to test with two carbon allotropes, diamond and graphite, as well as vitreous silica. To this end, least-squares fits of broken power-law densities are performed to heat capacity data covering several logarithmic decades in temperature, the high- and low-temperature regimes and especially the intermediate temperature range where the Debye theory is of limited accuracy. The analytic fits of the heat capacities are then temperature integrated to obtain the entropy and caloric EoS, i.e. the internal energy. Multiply broken power laws are also employed to model the isothermal EoSs of metals (Al, Cu, Mo, Ta, Au, W, Pt) at ambient temperature, over a pressure range up to several hundred GPa. In the case of copper, the empirical pressure range is extended into the TPa interval with data points from DFT calculations. For each metal, the parameters defining the isothermal EoS (i.e. the density–pressure relation) are inferred by nonlinear regression. The analytic pressure dependence of the compression modulus of each metal is obtained as well, over the full data range.

Signature of helium rain and dilute cores in Jupiter's interior from empirical equations of state

Measurements of Jupiter's gravity field by Juno have been acquired with unprecedented precision, but uncertainties in the planet’s hydrogen–helium equation of state (EOS) and the hydrogen–helium phase separation have meant that differences remain in the interior model predictions. We deduce an empirical EOS from Juno gravity field observations in terms of the hydrostatic equation and then investigate the structure and composition of Jupiter by comparison of the empirical EOS with Jupiter's adiabats obtained from the physical EOS. The deduced helium mass fraction suggests depletion of helium in the outermost atmosphere and helium concentration in the inner molecular hydrogen region, which is a signature of helium rain in Jupiter's interior. The deduced envelope metallicity (the heavy-element mass fraction) is as high in the innermost envelope as 11–13 times the solar value. Such a high metallicity provides sharp support to the dilute core model with the heavy elements dissolved in hydrogen and expanded outward. No matter how the core mass is varied, the empirical EOS derived from the two-layer interior model generally suggests higher densities in the innermost envelope than does the best-fit Jupiter's adiabat; this result is, again, a signature of dilute cores in Jupiter's interior. Moreover, no matter the core mass, the empirical EOS is found to exhibit an inflexion point in the deep interior, around 10 Mbar, which can be explained as the combined effect of helium concentration in the upper part and dilute cores in the lower part.

Relative density and isobaric expansivity of cold and supercooled heavy water from 254 to 298 K and up to 100 MPa.

A dual-capillary apparatus was developed for highly accurate measurements of density of liquids, including the supercooled liquid region. The device was used to determine the density of supercooled heavy water in the temperature range from 254 K to 298 K at pressures ranging from atmospheric to 100 MPa, relative to density at reference isotherm 298.15 K. The measurements of relative density were reproducible within 10 ppm, and their expanded (k = 2) uncertainty was within 50 ppm. To obtain absolute values of density, thermodynamic integration was performed using recent accurate speed of sound measurements in the stable liquid region. An empirical equation of state (EoS) was developed, giving specific volume as a rational function of pressure and temperature. The new experimental data are represented by EoS within their experimental uncertainty. Gibbs energy was obtained by EoS integration allowing computation of all thermodynamic properties of heavy water using Gibbs energy derivatives. Although based on data in relatively narrow temperature and pressure ranges, the developed EoS shows an excellent agreement with literature data for densities, isothermal compressibilities, and isobaric expansivities of deeply supercooled heavy water. The curvature of the thermodynamic surface steeply increases toward low temperatures and low pressures, thus supporting the existence of the hypothesized liquid-liquid coexistence boundary in a close vicinity of existing experimental data.

Equation of State of Detonation Products Based on Exponential‐6 Potential Model and Analytical Representation of the Excess Helmholtz Free Energy

AbstractOne of the most important tasks associated with theoretical prediction of performance of explosives by thermochemical calculation is accurate description of the equation of state (EOS) of detonation products. Widely used empirical equations of state, such is Becker‐Kistiakowsky‐Wilson (BKW EOS), have limited accuracy when it comes to energetic materials with unusual elemental composition. Replacing empirical EOS with more sophisticated and theoretically based EOS, the accuracy of thermochemical calculations can be increase. We present an equation of state of detonation products based on the Buckingham α‐exponential‐6 equation (Exp‐6) and an analytical representation of the excess thermodynamic functions for classical fluid mixture. The excess Helmholtz free energy, as a function of reduced density, temperature, and stiffness parameter, is calculated applying KLRR perturbation statistical mechanical theory, and so obtained data are approximated by multinomial coefficients. The interpolation domain is defined so to describe accurately the range of pressures, densities, and temperatures relevant for detonation studies. The equation is incorporated in EXPLO5 thermochemical code. Good agreement with Monte‐Carlo calculations is obtained, as well as between calculated and experimental detonation parameters for a series of explosives.

Singular perturbed components of flows – linear precursors of shock waves

A comparative analysis of the infinitesimal symmetries of various well-known systems of governing equations used for mathematical descriptions of flows and waves in fluids has shown that only the basic system of equations, including the empirical equation of state and the partial differential equations of mass, momentum, energy and matter transport, is characterized by a ten-parameter Galilean transformation group. An analysis of the complete solutions of the linearized system of fundamental equations for weakly dissipating media reveals a wide class of previously unknown singularly perturbed solutions supplementing well investigated regular solutions describing propagating waves. Fine flow components, whose geometry is typical for internal boundary layers that supplement the wave fields exist both at the boundaries and inside the volume of the liquid, are classified as linear precursors of shock waves. The calculated pattern of periodic internal waves beams covered with high-gradient envelopes agrees with data from independently performed experiments on measurements and visualization of the fine structure of linear and nonlinear waves in continuously stratified media.

Constraints on the nuclear equation of state from nuclear masses and radii in a Thomas-Fermi meta-modeling approach

The question of correlations among empirical equation of state (EoS) parameters constrained by nuclear observables is addressed in a fully empirical meta-modeling approach. A recently proposed meta-modeling for the nuclear EoS in nuclear matter, is augmented with a single finite size term to produce a minimal unified EoS functional able to describe the smooth part of the nuclear ground state properties. This meta-model can reproduce the predictions of a large variety of models, and interpolate continuously between them. The parameter space is sampled and filtered through the constraint of nuclear mass reproduction. We show that this simple analytical meta-modeling has a predictive power on masses, radii, and skins comparable to full HF or ETF calculations with realistic energy functionals. The covariance analysis on the posterior distribution shows that no physical correlation is present between the different EoS parameters. Concerning nuclear observables, a strong correlation between the slope of the symmetry energy and the neutron skin is observed, in agreement with previous studies.

Chemical potentials of water, methanol, carbon dioxide and hydrogen sulphide at low temperatures using continuous fractional component Gibbs ensemble Monte Carlo

Chemical potentials of coexisting gas and liquid phases for water, methanol, hydrogen sulphide and carbon dioxide for the temperature range K to K are computed using two different methodologies: (1) Widom’s test particle insertion (WTPI) method in the conventional Gibbs Ensemble (GE), and (2) the Continuous Fractional Component Gibbs Ensemble Monte Carlo (CFCGE MC) method. It is shown that the WTPI method fails to accurately compute the chemical potentials of water and methanol in the liquid phase at low temperatures, while accurate chemical potentials in the liquid phase are computed using CFCGE MC method. For the CFCGE MC method, the statistical uncertainty for computed chemical potentials of water and methanol in the liquid phase are considerably smaller compared to the WTPI method. For the water models considered in this study (SPC, TIP3P-EW, TIP4P-EW, TIP5P-EW), computed excess chemical potentials based on three-site models are in better agreement with the chemical potentials computed from an empirical equation of state from the NIST database. For water, orientational biasing is applied during test particle insertion to check whether certain orientations of test particle are energetically unfavourable. A two-dimensional Overlapping Distribution Method (ODM) in the NVT ensemble is derived for this purpose. It is shown that failure of the WTPI method for systems with a strong hydrogen bonding network does not depend on orientation of the test molecule in that system. For all systems in this study, the WTPI method breaks down when the void fraction of the system drops below approximately 0.50.

Effects of pH on wetting behavior of ‘star-like’ block copolymer surfactant solutions

Wetting behavior of aqueous solutions of four polyoxyalkylated diethylenetriamine (DETA) polymeric surfactants (named A–D) are studied and pH effect is assessed. Surfactants A, B and C have a ‘star-like’ structure differing only by the number of polymeric branches: 4, 6 and 9 in the mentioned order while the forth one, D, is of a dendritic type with 4–6 primary and 2–3 secondary branches. Experimental data about liquid/air surface tension, contact angle θ and equilibrium wetting film thickness of the surfactant solutions in pH range of 1–12 are obtained. The liquid/solid and the air/solid surface tension are calculated using the empirical equation of state and Berthelot’s combining rule. Results from the studies indicate that pH affects polymer solution properties at liquid/solid and liquid/air interfaces, and influences parameters such as surface tension, solid surface hydrophobicity, equilibrium film thickness, etc.

Tolman–Oppenheimer–Volkoff equations in nonlocal f(R) gravity

Nonlocal f(R) gravity was proposed as a powerful alternative to general relativity (GR). This theory has potentially adverse implications for infrared (IR) regime as well as ultraviolet (UV) early epochs. However, there are a lot of powerful features, making it really user-friendly. A scalar–tensor frame comprising two auxiliary scalar fields is used to reduce complex action. However, this is not the case for the modification complex which plays a distinct role in modified theories for gravity. In this work, we study the dynamics of a static, spherically symmetric object. The interior region of space–time had rapidly filled the perfect fluid. However, it is possible to derive a physically based model which relates interior metric to nonlocal f(R). The Tolman–Oppenheimer–Volkoff (TOV) equations would be a set of first-order differential equations from which we can deduce all mathematical (physical) truths and derive all dynamical objects. This set of dynamical equations govern pressure p, density ρ, mass m and auxiliary fields {ψ, ξ}. The full conditional solutions are evaluated and inverted numerically to obtain exact forms of the compact stars Her X-1, SAX J 1808.4-3658 and 4U 1820-30 for nonlocal Starobinsky model of f(◻-1 R) = ◻-1 R+α(◻-1 R)2. The program solves the differential equations numerically using adaptive Gaussian quadrature. An ascription of correctness is supposed to be an empirical equation of state [Formula: see text] for star which is informative in so far as it excludes an alternative nonlocal approach to compact star formation. This model is most suited for astrophysical observation.

Density and isothermal compressibility of supercritical H2O–NaCl fluid: molecular dynamics study from 673 to 2000 K, 0.2 to 2 GPa, and 0 to 22 wt% NaCl concentrations

AbstractWe report on molecular dynamics (MD) simulations for predicting the density and isothermal compressibility of an H2O–NaCl fluid as a function of temperature (673–2000 K), pressure (0.2–2.0 GPa), and salt concentration (0.0–21.9 wt%). The atomistic behavior was analyzed via the hydration number of ions and number of ion pairs. Hydration numbers of Na+ and Cl− increased with increasing pressure and decreasing temperature. Conversely, the fraction of Na–Cl ion pairs increased with decreasing pressure and increasing temperature. This hydration and association behavior is consistent with the low dielectric constant of H2O under these conditions. The presence of polynuclear clusters of Na–Cl was confirmed at high temperatures, low pressures, and high salt concentrations. We propose a purely empirical equation of state (EoS) for H2O–NaCl fluids under high temperatures and pressures that should be useful for estimating the fluid distribution in Earth's crust and upper mantle in relation to effects on earthquakes and volcanic eruptions.

Continuity of states between the cholesteric → line hexatic transition and the condensation transition in DNA solutions.

A new method of finely temperature-tuning osmotic pressure allows one to identify the cholesteric → line hexatic transition of oriented or unoriented long-fragment DNA bundles in monovalent salt solutions as first order, with a small but finite volume discontinuity. This transition is similar to the osmotic pressure-induced expanded → condensed DNA transition in polyvalent salt solutions at small enough polyvalent salt concentrations. Therefore there exists a continuity of states between the two. This finding, together with the corresponding empirical equation of state, effectively relates the phase diagram of DNA solutions for monovalent salts to that for polyvalent salts and sheds some light on the complicated interactions between DNA molecules at high densities.

Thermodynamic properties of aqueous NaCl solutions to 1073 K and 4.5 GPa, and implications for dehydration reactions in subducting slabs

NaCl is the most common solute in aqueous fluids in many geological settings but the thermodynamic properties of binary NaCl–H2O solutions have remained understudied at pressures above 0.5GPa. We report the first high-pressure (>0.5GPa) density data for NaCl–H2O fluids derived from acoustic velocity measurements in 1m and 3m NaCl solutions in diamond anvil cells to 673K and 4.5GPa using Brillouin scattering spectroscopy. An empirical equation of state (EoS) for NaCl–H2O fluids has been generated fitting the new density data together with literature data for water, and used for extrapolation of thermodynamic data to 1073K and 4.8m NaCl at 0.5–4.5GPa, spanning the conditions for fluids expelled by subducted slabs. The EoS yields densities for binary NaCl–H2O solutions with uncertainty lower than 0.3–0.5% below 673K and lower than 2–4% in the extrapolation region. The EoS may allow extrapolations beyond 1073K although the resulting uncertainties are difficult to assess. Densities for NaCl–H2O fluids computed from the EoS at 0.5GPa generally agree within 1% with published data below 673K, although differences of up to 5% are observed at 1073K. The experimentally-based EoS is more reliable in the calculation of pure water fugacities and phase equilibria involving fluid phases than previous formulations, particularly in the high pressure range. The presence of dissolved NaCl substantially decreases the activity of water, indicating large non-ideality in NaCl aqueous fluids at subduction zone conditions. This behavior has important implications for the localization of dehydration reactions in the slab, as the dehydration boundaries of hydrous phases shift toward shallower depths in the presence of dissolved NaCl in the fluid.

High Pressure Equation of State for Nanomaterials

Shanker Equation of State is used to study the volume compression of nanocrystalline materials under different pressure. On comparing with the experimental data it gives good results at low pressure, but for higher compression it deviates from the experimental points. Therefore, the Equation of State is modified empirically to study the pressure-volume relation for nanomaterials, namely, n-Rb3C60, n-CdSe (rocksalt phase), n-TiO2 (anatase and rutile phase), Fe-filled nanotube, and γ-Fe2O3, at high pressure. The results obtained from the empirical Equation of State are found to be in better agreement with the available experimental data.

Mechanical properties and hardness of new carbon-rich superhard C11N4 from first-principles investigations

The structural, mechanical properties and hardness of the new carbon-rich material C11N4 are studied by first-principles total energy calculations based on the density-functional theory. We use the empirical equations of state (EOS) to investigate the lattice properties and bulk modulus. It is found that the calculated lattice constants and bulk modulus are in good agreement with previous calculations. And the full set elastic constants are calculated using the stress-strain method. The Voigt-Reuss-Hill approximation is used to evaluate the mechanical moduli. The elastic constants show that the two phases of C11N4 are mechanically stable. The tetragonal-C11N4 (α-C11N4) exhibits larger mechanical moduli than the orthorhombic-C11N4 (β-C11N4). The mechanical anisotropy is calculated of several different anisotropic indexes and factors, such as universal anisotropic index (AU), the percent anisotropy (AG and AB) and shear anisotropic factors (A1, A2 and A3). Furthermore, the hardness of α-C11N4 and β-C11N4 are evaluated according to the intrinsic hardness calculation theory. α-C11N4 is predicted to be a superhard material with the Vickers hardness of 67.17GPa, which is slightly higher than that of the cubic boron nitride. And the β-C11N4 is also a superhard material with the calculated Vickers hardness of 45.63GPa. C11N4 can be considered as candidate superhard compounds.

An empirical equation of state of liquid diethyl ketone for isochoric processes at 333–513 K

Temperature and density dependences of pressure for an isochoric process are given. The density corresponding to a kink of a linear density dependence on pressure and the temperature at which there is no such a kink for diethyl ketone were determined for the first time. An empirical equation of state for liquid diethyl ketone with only three constant coefficients found experimentally over the temperature range 333–513 K was obtained.

Quantitative Study of 4He Real Gas Effects Using Supersonic Beams

Abstract The experimental realization of accurately defined source conditions, combined with an undisturbed flight path of precisely known length, permits the generation of supersonic molecular beams with an extremely well characterized axial velocity distribution. This achievement can be used for a quantitative assessment of theoretical models of condensation during the jet expansion, based on high accuracy equations of state. For helium-4, which is commonly put on a level with the ideal gas, we contrast two empirical equations of state with respect to enthalpy changes. These can be validated through a comparison with experimentally determined mean terminal flow velocities. At cryogenic temperatures, strong deviations from the ideal gas behavior are observed. Most notably, even the differences between the predictions of the two fundamental equations are large enough to be distinguished by high-resolution time-of-flight measurements.

A comment on the Equation of State and the freezing point equation with respect to subglacial lake modelling

The empirical Equation of State ( EoS) allows the calculation of the density of water in dependence of salinity, temperature, and pressure. Water density is an important quantity to determine the internal structure and flow regime of ocean and lakes. Hence, its exact representation in numerical models is of utmost importance for the specific simulation results. The three parameters namely salinity, temperature, and pressure have a complex interdependency on the EoS. Whether warmer water parcels sink or rise, therefore depends on the surrounding salinity and pressure. The empirical Equation of Freezing Point ( EoFP) allows to calculate the pressure- and salinity-dependent freezing point of water. Both equations are necessary to model the basal mass balance below Antarctic ice shelves or at the ice–water interface of subglacial lakes. This article aims three tasks: first we comment on the most common formulations of the EoS and the EoFP applied in numerical ocean and lake models during the past decades. Then we describe the impact of the recent and self-consistent Gibbs thermodynamic potential formulation of the EoS and the EoFP on subglacial lake modelling. Finally, we show that the circulation regime of subglacial lakes covered by at least 3000 m of ice, in principle, is independent of the particular formulation, in contrast to lakes covered by a shallower ice sheet, like e.g., Subglacial Lake Ellsworth. However, as modelled values like the freezing and melting patterns or the distribution of accreted ice at the ice–lake interface are sensitive to different EoS and EoFP, we present updated values for Subglacial Lake Vostok and Subglacial Lake Concordia.