Accurate thermodynamic and dielectric equations of state for high-temperature simulated water

The thermodynamic and dielectric properties of the simple point charge extended (SPC/E) water model are examined over wide temperature and density range by means of molecular dynamic simulations. Accurate analytical thermodynamic and dielectric equations of state for the SPC/E pair-potential are presented. Parameterizations cover a broad range of high temperature states including the critical region. The critical point parameters of SPC/E water were determined to be ρ_c = 0.276 g/cm³, T_c = 640.25 K and p_c = 164.37 bar. The value of the static dielectric constant of SPC/E water at its critical point was calculated to be 5.35, which compares remarkably well with the corresponding experimental value of 5.36. Analytical thermodynamic and dielectric equations for the saturated liquid and vapor densities are also given.     

The van der Waals equation: analytical and approximate solutions

The thermodynamic properties, enthalpy of vaporization, entropy, Helmholtz function, Gibbs function, but especially the heat capacity at constant volume of a van der Waals gas (and liquid) at the phase transition are examined in two different limit approximations. The first limit approximation is at the near-critical temperatures, i.e., for T/T _c → 1, where T _c is the critical temperature, the other limit approximation is at the near-zero temperatures, T→ 0. In these limits, the analytical equations for liquid and gas concentrations at saturated conditions were obtained. Although the heat capacities at constant volume of a van der Waals gas and liquid do not depend on the volume, they have different values and their change during the phase transition was calculated. It should be noticed that for real substances the equations obtained at the near-zero temperature are only valid for T > T _{triple point} and T ≪ T _c , which means that found equations can be used only for substances with T _{triple point} ≪ T _c .     

Analysis of thermo-magnetic fluctuations above the glass-transition temperature in Bi1.6Pb0.5Sr2−xEuxCa1.1Cu2.1O8+δ (0.000 ≤ x ≤ 0.180) system

The resistivity of Bi_1.6Pb_0.5Sr_2−xEu_xCa_1.1Cu_2.1O_8+δ (0.000 ≤ x ≤ 0.180) superconductor has been measured as a function of temperature and magnetic field. The resistivity shows a glassy behavior even at higher temperatures and magnetic fields for the Eu-doped samples as compared with the Eu free sample. The values of glass-transition temperature [T_g], magnetic field dependent activation energy [U₀(B)] and the temperature and magnetic field dependent activation energy [U₀(B,T)] are found to be maximum for optimal doping levels (x = 0.135) which shows that the flux lines are effectively pinned in this sample. Also for temperatures below the superconducting transition temperature (T_C), a scaling of measured resistivity curves in magnetic field (B = 0.4 and 0.8 T) is obtained and this scaling is quite useful for better understanding of the behavior of the flux vortices in high temperature superconductors.     

Oxygen-18 surface exchange and diffusion in Li2O-deficient single crystalline lithium niobate

¹⁸O/¹⁶O isotope exchange in combination with SIMS depth profiling was used to investigate oxygen transport in Li₂O-deficient single crystalline LiNbO₃ in the temperature range 983 ≤ T/K ≤ 1188 at 200 mbar oxygen. Within the limit of experimental error and for the investigated range of temperatures no significant differences between transport parallel and transport perpendicular to the c-axis were found. The following temperature dependencies were determined: for oxygen tracer diffusion D = 6.4 × 10⁻³exp[−333 kJ/mol/(RT)] m²/s; and for oxygen surface exchange k = 7.8 × 10²exp[−288 kJ mol⁻¹/(RT)] m/s. The activation enthalpy obtained for tracer diffusion can be interpreted as the enthalpy of migration of extrinsic oxygen vacancies induced by impurities with lower valency on niobium sites.     

Measurement and correlation of the ( p, ρ, T) relation of sulphur hexafluoride (SF 6). II. Saturated-liquid and saturated-vapour densities and vapour pressures along the entire coexistence curve

Comprehensive and accurate measurements of the saturated-liquid and saturated-vapour densities together with the vapour pressure of pure sulphur hexafluoride were carried out from the temperature T =  224 K (triple-point temperature T_t =  223.555 K) to 0.033 K below the critical temperature ( T_c =  318.723 K). Typical values of the total uncertainties of the measurements are: ⩽ ± 0.01 percent for the vapour pressures,⩽ ± 0.015 percent for the saturated-liquid densities, and⩽ ± 0.016 percent for the saturated-vapour densities. The values for the critical density and the critical pressure ( ρ_c =  742.26 kg · m ^− 3, p_c =  3.7550 MPa) and the isothermal compressibilities in the critical region close to the phase boundary have also been determined from these measurements. Comparisons with experimental results of previous workers are presented. Using the new values of this work, new correlation equations for the vapour pressure, the saturated-liquid density, and the saturated-vapour density have been established.     

Constant-Volume Heat Capacity of H2O + Na2CO3 Solutions Near the Critical Point of Pure Water

The results of new isochoric heat capacity measurements of H₂O + Na₂CO₃ solutions as a function of temperature along several isochores in the near-critical region of pure water are reported. The measurements cover temperatures from 331 to 661 K at Na₂CO₃ mole fraction 0.008869. The experiments were performed at seven densities between 245 and 875 kg-m^–3. The measurements were made in a high-temperature, high-pressure, adiabatic, and nearly constant-volume calorimeter. Uncertainties of the isochoric heat capacity measurements are estimated to be 1–2% in the liquid phase, 2–3% in the vapor phase, and 4–5% near the critical point. Measurements were made in the two-phase (vapor–liquid, liquid–solid, vapor–solid) and three-phase (vapor–liquid–solid) regions. Two peaks in isochoric heat capacity have been found near the critical point of pure water. One of the peaks at T _S1 occurs on the three-phase (L–V–S) curve and another peak at T _S2 corresponds to a two-phase (L–S or V–S) curve. The experimental values of phase transition temperatures T _S() on each isochore was determined. Uncertainty in the phase transition temperature measured was no greater than ±0.03 to 0.05 K.     

The magnetic phase diagram of HoGe1−xSix studied by neutron diffraction and magnetic measurements

Several samples (0.2 ≤ x ≤ 1.0) of HoGe_1−xSi_x (CrB type) were studied over an extensive temperature range by neutron diffraction. The relative stability of the two existing magnetic structures with wave vectors and [q_x 0 q_z] depends on both the temperature and composition. The corresponding stability regions are shown in a magnetic phase diagram. The Néel temperature T_N and the transition temperature T_ic between the lock-in structure and the incommensurate structure increase with silicon content. At T_ic the wave vector jumps from the value to the incommensurate value [q_x 0 q_z]. With increasing temperature the q_x and q_z components show a linear decrease and increase, respectively. The transition at T_ic is most probably of first order. The magnetic moments of Ho are confined to a direction close to the c-axis (5–7°) over the whole temperature range and order with a pure sinus modulation between T_ic and T_N.     

The liquid–gas interface of oxygen–nitrogen solutions: 1. Surface tension

The capillary method of surface tension measurement has been used to measure the surface tension of oxygen–nitrogen solutions in the temperature range from 80 to 132 K. At temperatures below the nitrogen critical temperature (T_c = 126.2 K) the capillary constant and the surface tension of solutions are smaller than their additive values and vary linearly with the temperature. Experimental data are compared with the results of calculating the surface tension by the theories of Pinnes and Rowlinson.     

Liquid-phase hydrogenation of methyl oleate on a Ni/α-Al2O3 catalyst: A study based on kinetic models describing extreme and intermediate adsorption regimes

The kinetics of the hydrogenation of methyl oleate on a Ni/α-Al₂O₃ catalyst was studied in the absence of mass-transport limitation, at 398 ≤ T ≤ 443 K and 3.7 ≤ P_H2 ≤ 6.5 bar. The kinetic modeling was performed on the basis of elementary step mechanisms involving different regimes of competition between hydrogen and methyl oleate. Admitting a distinction between occupied-sites and covered-sites by the large molecule of methyl oleate, a rigorous proposal was made to link the seemingly separate kinetic models corresponding to the extreme modes of competitive and non-competitive adsorption, without having to draw the common distinction between two types of surface sites. General rate equations were formulated without expressing opinion a priori on whether the adsorption regime is competitive or non-competitive. Then, typical LHHW rate equations for both extreme adsorption regimes were straightforwardly derived as special cases. Statistical results demonstrated the inadequacy of the models approaching non-competitive adsorption to describe the experimental data but results did not allow a definite discrimination between rival models with competitive and semi-competitive adsorption. A mechanistic model featuring dissociative adsorption of hydrogen, molecule of methyl oleate interacting with a single atom of Ni, and second insertion of hydrogen as RDS, proved to be the best candidate to describe the experimental data satisfactorily with physically reasonable parameters. As a distinctive feature, the model considering semi-competitive adsorption gave additional indication that the adsorbed molecule of methyl oleate could cover up to seven surface sites. From this finding, the semi-competitive model seems to be more realistic than the competitive one.     

A generalised perturbation-based equation of state for thermodynamic modelling of fluids over a wide range of density

A new generalized perturbed thermodynamic nonlinear isotherm regularity (GPTNLIR) equation of state (EoS) has been proposed for the fluids over the entire density range from gas to liquid. The GPTNLIR has been derived on the basis of an effective nearest neighbor pair interaction of an extended average effective pair potential (AEPP) in the framework of the thermodynamic perturbation theory (TPT). The selected AEPP is an extended Lennard-Jones (12, 6, 3) type which considers the repulsive, dispersion, dipole-dipole and longer-range interactions between pair molecules, respectively. Based on the EoS, a non-linear relationship exists between (Z– Z_CS)v² and ρ for each isotherm of fluid, where Zis the compression factor, v=1/ρis the molar volume, Z_CS is Carnahan–Starling (CS) expression for the compression factor of the reference fluid with the temperature-dependent effective hard-core diameter (σ_eff). The validity of EoS against the experimental p–v–Tdata were tested for a variety of fluids, including polar, non-polar, hydrogen bonded and quantum fluids. This EoS provides the estimation of σ_eff at T>T_c, T=T_c and T<T_c, in which T_c is critical temperature, for each real fluid using its experimental p–v–T data and the extension of TPT theory as well.     

Measurements and predictions of density and carbon dioxide solubility in binary mixtures of ethanol and n-decane

The solubility of carbon dioxide (CO₂) in binary mixtures of ethanol and n-decane has been measured using an in-house developed pressure-volume-temperature (PVT) apparatus at pressures up to 6 MPa and two different temperatures (303.2 and 323.2 K). Three different binary mixtures of ethanol and n-decane were prepared, and the densities of the prepared mixtures were measured over the studied pressure and temperature ranges. The experimental data of CO₂ solubility in the prepared mixtures and their saturated liquid densities were then reported at each temperature and pressure. The solubility data indicated that the gas solubility reduced as the ethanol mole fraction in the liquid mixture increased. The dissolution of CO₂ in the liquid mixtures resulted in the increase in the saturated liquid densities. The impact of gas dissolution on the saturated liquid densities was more pronounced at the lower temperature and lower ethanol compositions. The experimental solubility and density data were compared with the results of two cubic equations of state (EOSs), Soave–Redlich–Kwong (SRK) and Peng–Robinson (PR). The modeling results demonstrated that both EOSs could predict the solubility data well, while the saturated liquid densities calculated with the PR EOS were much better than those predicted with the SRK EOS.     

Critical Behavior of the Electrical Conductivity of Concentrated Electrolytes: Ethylammonium Nitrate in n-Octanol Binary Mixture

The electrical conductivity of highly concentrated binary ionic mixtures of ethylammonium nitrate in n-octanol at a critical salt mole fraction x = 0.766 and at an off-critical one x = 0.908 was measured over an extended temperature range above the critical consolute point. Far from the critical temperature T _c, the conductivity is accurately described by the Vogel–Fulcher–Tammann (VFT) law. However, in a temperature range T = (T – T _c) 3 K, the conductivity exhibits a monotonous deviation from the VFT behavior. This anomaly is finite at T _c and, for the critical mixture, its amplitude is 0.23% of (T _c). The asymptotic behavior of the conductivity anomaly is described by a power law ^{(1 – )}, with = (T – T _c)/T _c, the reduced temperature, and , the critical exponent of the specific heat anomaly at constant pressure. This critical anomaly is similar to the one observed in other highly concentrated critical electrolytes. The degree of dissociation of the salt for the critical mixture, _diss 0.78 ± 0.04, is estimated from the value of the Walden product computed at T _c, and accounts for the effective free ion concentration in the reduced critical coordinates of the system.     

Comparison of methods for calculating thermodynamic properties of binary mixtures in the sub and super critical state: Lee–Kesler and cubic equations of state for binary mixtures containing either CO2 or H2S

The (ρ,T,p) and (vapor + liquid) equilibria for fluid mixtures containing either CO₂ or H₂S have been determined from 13 equations of state. The estimated values have been compared with published experimental results. CO₂ and H₂S were used to represent non-polar and polar fluids, respectively. The equations of state investigated were as follows: (a) the Lee–Kesler equation; (b) two equations that included new reference fluids for the Lee–Kesler method; (c) three so-called extended equations of state; and (d) seven cubic equations of state. After adjustment of the binary interaction parameters the predicted values differed from the experimental data by about 0.8% for CO₂ mixtures while for H₂S mixtures the uncertainty was about ±2.8%. Somewhat larger errors, although still lower than ±5%, were obtained for co-existing phase densities; the Lee–Kesler method provided results of the highest accuracy. The cubic equations proposed by Schmidt and Wenzel and Valderrama provide the most reliable predictions of both single and co-existing phase densities. Comparison of the predicted (vapor + liquid) equilibrium with experiment shows that each of the seven cubic equations provides results of similar accuracy and all within ±6%.     

Structural, magnetic, and thermal characteristics of the phase transitions in Gd5GaxGe4−x magnetocaloric materials

Temperature-dependent, single crystal and powder X-ray diffraction studies as well as magnetization, and heat capacity measurements were carried out on two phases of the Gd₅Ga_xGe_4−x system: for x=0.7 and 1.0. Gd₅Ga_0.7Ge_3.3 shows three structure types as a function of temperature: (i) from 165 K to room temperature, the orthorhombic Sm₅Ge₄-type structure exists; (ii) below 150 K, it transforms to a orthorhombic Gd₅Si₄-type structure; and (iii) a monoclinic Gd₅Si₂Ge₂-type component is observed for the intermediate temperature range of 150 K≤T≤165 K. This is the first time that all these three structure types have been observed for the same composition. For Gd₅Ga_1.0Ge_3.0, the room temperature phase belongs to the orthorhombic Pu₅Rh₄-type structure with interslab contacts between main group atoms of 2.837(4) Å. Upon heating above 523 K, it transforms to a Gd₅Si₄-type structure with this distance decreasing to 2.521(7) Å before decomposing above 573 K.     

Phase equilibrium modeling of triglycerides in supercritical fluids

To design a reactor and separator for a supercritical biodiesel process, phase equilibria of multi-component mixtures in supercritical fluids should be determined using group contribution with association equation of state (GCA-EOS) as a thermodynamics method. The model is considered for two systems of reactants and products. System 1 is comprised of methanol and triglycerides from two sources (palm and Jatropha oils); and System 2 is unconverted methanol, FAME (product) and glycerol (by-product). Pressure and temperature diagrams were developed at different mole fraction of methanol (x_MeOH). As x_MeOH increased, the critical temperature (T_c) and pressure (p_c) increased. The increasing temperature causes the immiscibility region and the amount of methanol at the plait point to decrease. The maximum plait point pressure was observed at 19.20 MPa for palm and 19.33 MPa for Jatropha oil systems.     

Capture of asymmetric top dipolar molecules by ions: Rate constants for capture of H2O, HDO, and D2O by arbitrary ions

The capture of rotationally state-selected and unselected asymmetric top polar molecules by ions is investigated. Analytical expressions (for all rotational states up to j = 2) of capture rate constants in the perturbed-rotor second-order limit are derived for application to low temperature conditions. Approximate analytical representations over wider temperature ranges are also given for rotationally unselected molecules. The capture of H₂O, D₂O, and HDO by arbitrary ions is chosen for demonstration of the approach. Capture rate constants for the about 60 reactions of H₂O with ions listed in the UMIST 2006 data base for astrochemistry are calculated, compared with experimental data, and represented in the format k_cap(T) ≈ c₁ + c₂(T/300 K)^−1/2. The parameters c₁ and c₂ can be predicted in a very simple way. The approach allows one to identify capture-controlled mechanisms and/or to trace experimental artifacts. The approach applies equally well to the capture of symmetric top and linear dipole molecules by arbitrary ions.     

EuTZn (T=Pd, Pt, Au) with TiNiSi-type structure—Magnetic properties and Eu Mössbauer spectroscopy

The europium compounds EuTZn (T=Pd, Pt, Au) were synthesized from the elements in sealed tantalum tubes in an induction furnace. These intermetallics crystallize with the orthorhombic TiNiSi-type structure, space group Pnma. The structures were investigated by X-ray diffraction on powders and single crystals: a=732.3(2), b=448.5(2), c=787.7(2) pm, R₁/wR₂=0.0400/0.0594, 565 F² values for EuPdZn, a=727.8(3), b=443.7(1), c=781.7(3) pm, R₁/wR₂=0.0605/0.0866, 573 F² values for EuPtZn, and a=747.4(2), b=465.8(2), c=789.1(4) pm, R₁/wR₂=0.0351/0.0590, 658 F² values for EuAuZn, with 20 variables per refinement. Together the T and zinc atoms build up three-dimensional [TZn] networks with short T–Zn distances. The EuTZn compounds show Curie–Weiss behavior in the temperature range from 75 to 300 K with μ_eff=7.97(1), 7.70(1), and 7.94(1) μ_B/Eu atom and θ_P=18.6(1), 34.9(1), and 55.5(1) K for T=Pd, Pt, and Au, respectively, indicating divalent europium. Antiferromagntic ordering was detected at 15.1(3) K for EuPdZn and canted ferromagnetic ordering at 21.2(3) and 51.1(3) K for EuPtZn and EuAuZn. ¹⁵¹Eu Mössbauer spectroscopic measurements confirm the divalent nature of the europium atoms by isomer shift values ranging from −8.22(8) (EuPtZn) to −9.23(2) mm/s (EuAuZn). At 4.2 K full magnetic hyperfine field splitting is observed in all three compounds due to magnetic ordering of the europium magnetic moments.     

Molecular modelling of polymers, 1. Prediction of critical values of oligomethylenes

Most procedures for the estimation of critical values of oligomethylenes assume these critical values to depend only on the chain length n and/or the molecular weight M. In this work, we introduce new equations for estimating the critical values by inclusion of quantum chemical data calculated by a semiempirical SCF-MO

1 SCF-MO: Self-consistent field, molecular orbital.

method (AM1). These models give a much superior prediction for the critical values such as the normal boiling point T_b, critical temperature T_c, critical pressure P_c, critical valume V_c, surface tension y_b and enthalpy of vaporization ΔH_vp of 18 oligomethylenes. The predictions for polyethylene (with infinite chain length) for the values of T_b, T_c, P_c, V_c, ΔH_vp and y_b are 1029.3 K, 1029.3 K, 1.013 bar, 15723.3 m³/mol, 0 KJ/mol and 0 mN/m, respectively.     

Exploration of the superconducting properties of Y3Ba5Cu8O18 with and without Ca doping by magnetic measurements

The superconducting Y₃Ba₅Cu₈O₁₈ (Y-358) and Y₃Ba₅Ca₂Cu₈O₁₈ (YCa-358) compounds have been synthesized by using the sol–gel method. Hence, the influence of doping of Ca into the compound Y-358 has been studied by comparing the resistivities, DC magnetizations both M(H) and M(T),flux pinning properties, AC susceptibilities and critical current densities of the undoped and doped compounds, at low temperatures. The AC susceptibility and resistivity measurements showed that the superconducting transition temperature, T_c, is suppressed (about 6 K) with the addition of Ca into the main compound. The hysteresis loops of YCa-358 show peak like projecting parts at temperatures below 45 K and around zero applied field that may be due to the local modulation of the composition in YCa-358. Such a behavior has been observed for the first time. The critical current densities, J_c, determined from the hysteresis measurements decrease with the addition of Ca into Y-358. At 15 K, the maximum values of J_c, for the compounds Y-358 and YCa-358 are found to be 8 × 10⁴ A/cm² and 4.5 × 10⁴ A/cm², respectively. The flux pinning force, F_p, calculated from the field dependence of the J_c values shows that the irreversibility line shifts to lower magnetic fields with the doping of Ca into Y-358. Furthermore, the measurements of the inphase and out off components of the ACsusceptibilities clearly demonstrate that the superconducting volume fraction of Y-358 decreases with the addition of Ca.     

Measurements of the isochoric heat capacity,the critical point (TC, ρC) and vapor–liquid coexistence curve (TS, ρS) of high-purity toluene near the critical point

Isochoric heat capacities (C_V, V, T), phase boundary properties (T_S, ρ_S) and the critical (T_C, ρ_C) parameters for high-purity (0.9999+ mole fraction) toluene have been measured with a high temperature, high pressure, nearly constant volume adiabatic calorimeter and quasi-static thermogram technique. Measurements were made at three selected liquid and vapor isochores 777.8, 555.25, and 214.64 kg m⁻³ in the temperature range from 379 to 591 K. For five near-critical isochores 268.68, 281.68, 296.62, 301.52, and 318.28 kg m⁻³, the measurements were made in the immediate vicinity of the coexistence curve in order to accurately determine the phase transition temperatures (T_S, ρ_S) (shape of the coexistence curve near the critical point) and the critical parameters (T_C, ρ_C). The total combined uncertainty of heat capacity, density, and temperature measurements were estimated to be less than 2%, 0.06%, and 15 mK, respectively. The uncertainties reported in this paper are expanded uncertainties at the 95% confidence level with a coverage factor of k = 2. The uncertainty of the phase transition and the critical temperature value was 0.02 K. The Krichevskii parameter for some toluene-containing binary mixtures was calculated. The derived values of the Krichevskii parameter were used to estimate the effect of dilute impurities on the critical parameters of toluene. The measured values of saturated density near the critical point were interpreted in terms of the “complete scaling” theory in order to study singularity behavior of the coexistence curve diameter. The measured isochoric heat capacities and saturated densities were compared with the data reported by other authors and values calculated from an equation of state and other correlations.