Reduced Temperature Range Research Articles

Vapour-liquid equilibria of stockmayer fluids

By M. E. VAN LEEUWEN, B. SMIT and E. M. HENDRIKS Koninklijke/Shell-Laboratorium, Amsterdam, P.O. Box 3003, 1003 AA Amsterdam, The Netherlands (Received 16 April 1992; accepted 1 July 1992) Gibbs ensemble simulation data for Stockmayer fluids with #.2 = 3.0 and #.2 = 4.0 in the reduced temperature range of 0-77 (resp. 0.80)-098 and pre- sented and compared with predictions based on the perturbation theories of Stell, G., Rasaiah, J. C., and Narang, H., 1972, Molec. Phys., 23, 393; 1974, 27, 1393. The description of the reference fluid is improved by applying the mod- ified Benedict-Webb-Rubin equation of state instead of the Verlet-Weis imple- mentation of the Weeks-Chandler-Andersen perturbation scheme. Second virial coefficients predicted by perturbation theory to order #4 agree for Stock- mayer fluids with #,2 < 4 very well with exact values. Perturbation theory is capable of describing the low-density region of Stockmayer fluids with rather strong dipole moments. For these high values of the dipole moment, the Pad6 approximation of perturbation theory deviates significantly from the simulated coexistence curves in density and pressure. Compared with perturbation theory to order #4, however, it is a far better approximation of the Stockmayer fluid coexistence curve. The behaviour of the Pad6 approximation in the critical region is not satisfactory. 1. Introduction Electrostatic interactions affect thermodynamic behaviour. For relatively simple polar model fluids several theories have been developed [1-3]. A convenient model for a polar fluid is a 'soft-core' dipolar molecule, represented by the Stockmayer potential (Lennard-Jones potential with an embedded point dipole). The two most important molecular theories for model polar fluids are integral equation theories and (Pople-Stell) perturbation theories. If the Ornstein-Zernike equation is supplemented with an approximate closure relation, an integral equation is obtained for the direct correlation function and the radial distribution function [2]. For polar fluids this involves expansions of angular- dependent functions. Starting from the well known hypernetted-chain equation Patey and others [4-6] considered linear expressions (LHNC) and quadratic expressions (QHNC), and obtained a numerically tractable scheme. Fries and Patey [7] devel- oped a general method for fluids with anisotropic interactions, the reference hypernetted-chain (RHNC) theory. Lee et al. [8] applied this approximation to Stockmayer fluids, and found that the dielectric constant predicted with the full RHNC theory agrees better with computer simulation results than those predicted with the LHNC and QHNC theories. Another approach to describe the behaviour of simple polar model fluids is the use of perturbation theories, as pioneered by Pople and further developed by Stell et al. [9-13]. In these theories, the free Helmholtz energy is expressed as the sum of a

The susceptibility critical exponent for a nonaqueous ionic binary mixture near a consolute point

We report turbidity measurements of a nonaqueous ionic solution of triethyl n-hexylammonium triethyl n-hexylboride in diphenyl ether. A classical susceptibility critical exponent γ=1.01±0.01 is obtained over the reduced temperature range 10−4≤ t≤10−1. The best fits of the sample transmission had a standard deviation of 0.39% over this range. Ising and spherical model critical exponents are firmly excluded. The correlation length amplitude ξ0 from fitting is 1.0±0.2 nm which is much larger than values found in neutral fluids and some aqueous binary mixtures.

The effect of fluctuations on the electrical transport behaviour in YBa2Cu3O7-x

The excess conductivity behaviour of highly oriented YBa2Cu3O7-x thin films prepared by both coevaporation and laser ablation has been studied in detail in the reduced-temperature range 9*10-4<t<1. The excess conductivity in all the films studied was found to diverge sharply near Tc, in agreement with the conventional mean-field theory. However, the detailed temperature dependence could not be fitted to either the power-law or the logarithmic functional forms as predicted by the theory. The excess conductivity of all the films was found to be exponentially dependent on the temperature over nearly three decades for 9*10-4<t<10-1, in contradiction to the mean-field theory.

Dynamic critical behavior of the random-exchange Ising system Fe0.9Zn0.1F2 determined via Mössbauer spectroscopy.

We have made M\"ossbauer-effect-spectroscopy (MES) measurements of the dynamical broadening of the M\"ossbauer lines above ${\mathit{T}}_{\mathit{N}}$ for a high-quality single crystal of ${\mathrm{Fe}}_{0.9}$${\mathrm{Zn}}_{0.1}$${\mathrm{F}}_{2}$ with an inhomogeneity-induced N\'eel-temperature (${\mathit{T}}_{\mathit{N}}$) broadening of less than 25 mK. In the reduced-temperature range 3\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}4}$t (==T/${\mathit{T}}_{\mathit{N}}$-1)${10}^{\mathrm{\ensuremath{-}}2}$, we find that the excess linewidth diverges as ${\mathit{t}}^{\mathrm{\ensuremath{-}}\mathit{w}}$ with w=0.79(7). On the assumption of a single divergent relaxation time, this measurement of w implies a dynamical exponent z=2.18(10) via dynamic-scaling theory. Our value for z involves an asymptotic approach to ${\mathit{T}}_{\mathit{N}}$, which is an order of magnitude closer than previous MES and neutron-spin-echo measurements and agrees with the renormalization-group prediction z\ensuremath{\approxeq}2.11 for the d=3 random-exchange Ising model. The result does not agree with the predictions of conventional van Hove theory, z=1.97, or the results of previous, fundamentally less asymptotic, measurements.

Thermophysical properties of gaseous refrigerants from speed-of-sound measurements. III. Results for 1,1-dichloro-2,2,2-trifluoroethane (CHCl2-CF3) and 1,2-dichloro-1,2,2-trifluoroethane (CHClF-CClF2)

The speed of sound in gaseous 1,1-dichloro-2,2,2-trifluoroethane (CHCl2CF3, commonly known as R123) has been measured at temperatures T between 260 and 335 K at pressures p from 1.6 to 77 kPa. Perfect-gas heat capacities and second and third acoustic virial coefficients have been calculated from the results. The second and third acoustic virial coefficients are used to estimate the density virial coefficients B(T ) and C(T ) and an effective square-well potential. The acoustic estimates of B(T ) and C(T ) are consistent with B(T ) and C(T ) deduced from high-quality (p,Vm, T ) results. The combined values of B(T ) and C(T ) cover a reduced temperature range of 0.57 to 0.99. We have also measured the speed of sound in 1,2-dichloro-1,2,2-trifluoroethane (CHClF-CClF2, commonly known as R123a). This isomer of R123 is a significant impurity in R123 as manufactured and used. We provided estimates of the vibrational relaxation time for R123.

Asymmetry of the coexistence curve in binary systems. Size effect

The asymmetry of the coexistence curve in binary systems is either due to a difference of size between the components or to mixed fields as seen in the liquid–vapor case. The size effect may be corrected if the proper order parameter is used. Taking advantage of the many formal possibilities of choosing the order parameter in these systems, we show that the size effect may be exactly corrected for asymmetric mean field models. Making the same type of calculation on real systems with critical indices, we found that the same type of correction is possible. In these cases, there were no mixed field effects detected (t1−α divergence of the diameter), at least in a reduced temperature range t&amp;lt;0.02. The details of the calculation are reported only for acetonitrile–cyclohexane system which is one of the best sets of data found in literature. A new computing method to determine the parameters of the coexistence curve is also presented. The shape of the coexistence curve, including extended scaling correction, as well as the curvature of the diameter and the critical constants Tc and xc may be obtained from a single fit; we show the interest of analyzing, in detail, the coupling between all the parameters.

Ferromagnetism of Ni(SCN)2(C2H5OH)2

The magnetic properties of Ni(SCN)2(C2H5OH)2 have been studied, the first Ni(II) system in the general family of compounds M(SCN)2(ROH)2 (where M=divalent Mn, Fe, Co, or Ni and R=CH3, C2H5, i- or n-C3H7) to be examined at low temperatures. In contrast to previously studied Mn(II) and Co(II) members of this family, which exhibit predominant antiferromagnetism, the present compound is ferromagnetic. The susceptibility of a polycrystalline sample is of Curie–Weiss form only above 75 K, with ḡ = 2.175 ± 0.01 and S=1 and with θ=24.1±1.0 K. The initial susceptibility is well accounted for by an asymptotic critical law, χ0 = Γ[T/Tc − 1]−γ, in the reduced temperature range 0.147–0.013, with Tc = 13.081 ± 0.01 K, γ=1.354±0.02, and Γ=0.0925±0.003 emu/mol. The γ value is between 3D-XY and 3D-Heisenberg model predictions. The susceptibility in the paramagnetic regime well above Tc is analyzed including the effects of axial and rhombic crystal field distortions, represented by D[Ŝ2z − S(S + 1)/3] and E[Ŝ2x − Ŝ2y] terms in the spin Hamiltonian, and incorporating exchange interactions in a mean-field approximation. An excellent fit is obtained with g=2.175, D/k=−64.3±5 K, E/k=23.1±4 K, and zJ/k=19.4±1 K. The magnitude of D is the largest we know of in a Ni(II) compound. The three spin states of the 3A crystal field ground term are strongly split, probably contributing to the relatively low value of Tc compared to zJ/k. Some two-dimensional character in the exchange, as has been found for other members of this family of compounds, may also contribute.

The Phases of Cyclohexane Predicted by MD Simulation

Phase changes in cyclohexane have been studied by MD simulation on the AMT DAP computer, using a zero-pressure technique to simulate clusters of 512 molecules. This work builds upon a previous study [1] in which we performed MD calculations on a smaller sample and found a phase intermediate between the experimentally determined low temperature crystalline structure (C2/c) and the high temperature plastic one (Fm3m). This new phase had not been observed experimentally in the bulk at ambient pressure [2]. We determined the intermediate structure to be rhombohedral with a space group of [Formula: see text]. A subsequent neutron diffraction study of cyclohexane at high pressures (&lt; 5) kbar has permitted the identification of two orthorhombic phases [3] which occur for deuterated cyclohexane. In addition, for very small sample sizes another, as yet unidentified, phase has been observed at ambient pressure [4]: clear evidence that there are differences between the crystal structure in the bulk and in small clusters. We therefore decided to extend our earlier work in order to investigate the behaviour of the phase as a function of sample size. Using a larger sample we find behaviour much closer to that seen in the bulk material. The rhombohedral structure is still observed but over a very much reduced temperature range and the transition temperatures are closer to those seen experimentally. Although -we cannot identify the structure observed by Bosio and Dumas [4] with that simulated it is clear that there is an obvious parallel with the behaviour of the model. A further study of this system is underway.

Neutron diffraction study of the structure of the antifluorite crystal (NH4)2TeCl6

A neutron diffraction study of the crystal structure of (NH4)2TeCl6 is presented. The data support a previous contention that this crystal undergoes a ferrorotative structural phase transition at 85 K, from a cubic structure with space group Oh5 to a trigonal structure with space group C3i2. The primary-order parameter is the rotation angle, Φ, of the TeCl6 octahedra about a [111] axis of the cubic phase. The data indicate that the temperature dependence of Φ is non-mean-field like over an extended reduced temperature range.

Laminar Forced-Convection Condensation of Saturated Vapors in the Subcritical Region.

A numerical analysis is presented for laminar forced-convection condensation of saturated vapors of water and carbon dioxide on a flat surface in the reduced temperature range TS/TC=0.990∼0.999. The heat transfer coefficient in the region TS/TC<0.998 can be correlated by using Fujii and Uehara's equation for constant physical properties when the representative physical properties are evaluated at the film temperature. The reduction of condensation mass flux or the heat flux at the vapor-liquid interface due to the convection term in the film is expressed as a function of the phase change number with the average isobaric specific heat.

Formulation of the Generalized Correlations for the Thermodynamic Properties at the Saturated State for Component Substances contained in the Natural Gases.

As a first step to predict the thermophysical properties of natural gases, generalized correlations for the saturated properties such as the vapor pressure, the saturated liquid density, the saturated vapor density, and the heat of vaporization have been formulated on the basis of the three-parameter principle of corresponding states with acentric factor for 9 component substances contained in the natural gases, i. e., CH4, C2H6, C3H8, n-C4H10, i-C4H10, N2, CO2, H2S, and O2, and 3 simple fluids of Ar, Kr, and Xe. The present generalized correlation for the vapor pressure reproduces the experimental data within a deviation of ±1.0% in the reduced temperature range Tr>0.4. The present generalized correlation for the saturated liquid density reproduces the experimental data within a deviation of ±1.0% in the temperature range from the triple point to the critical point. The present generalized correlation for the saturated vapor density reproduces the experimental data within a deviation of ±2.0% in the reduced temperature range Tr>0.5. The reliability of the present generalized correlations for the vapor pressure and saturated liquid density was confirmed by the comparison with the experimental data for R22 and R114. The experimental data for the heat of vaporization are reproduced within a deviation of ±2.0% in the reduced temperature range Tr>0.5 by Clapeyron equation with the present generalized correlations for the vapor pressure, the saturated liquid density, and the saturated vapor density.

Search for weak random anisotropy effects in the critical region of Pd80Co20

Following a suggestion by I. A. Campbell, we have conducted Mossbauer source experiments on disordered alloys of57CoPd80Co20 in search for evidence of random anisotropy (RA) effects on critical behavior. The result, β=0.38(3) in the reduced temperature range 10−2<1−T/Tc<0.2, though not strictly asymptotic, is consistent with the d=3 Heisenberg model, with no evidence for RA. In this paper we argue that among transition metal ferromagnetic alloys there are no better candidates for RA effects than our chosen system.

Measurement of the superfluid density in silica aerogels

We have conducted torsional oscillator measurements of the superfluid density in 4 He-filled aerogel where the aerogel density is 0.20g/cc. The superfluid densiyy ϱ s is observed to obey a power-law ϱ s = ϱ so t ξ over a reduced temperature range 10 −4.3 <t<10 −1.8 with rms deviations of less than 2 percent. The exponent ξ is 0.812±0.004. This value is remarkably close to the exponent, 0.813±0.009, reported earlier for an aerogel sample of density 0.13g/cc.

Critical behavior in alloys with random magnetic anisotropy

We have studied the critical behavior in amorphous Tb65Co35. Scaling analyses were done over a number of reduced temperature (t=‖T−Tc‖/Tc) ranges to ascertain that the critical regime had been reached. The magnetization follows linear (ferromagnetic) scaling at high fields (1–55 kOe) and nonlinear (spin-glass) scaling at low fields (&amp;lt;1 kOe). The critical exponents for ferromagnetic scaling and for spin-glass scaling are not a function of reduced temperature range.

AN EMPIRICAL VIRIAL-LIKE CUBIC EQUATION OF STATE FOR PHASE EQUILIBRIUM CALCULATIONS

An empirical cubic equation of state(EOS) was obtained by truncating the virial expansion in reciprocal of molar volume after the third term. The constants of the EOS was generalized in terms of critical temperature, critical pressure and Pitzer's acentric factor. In pure component applications the EOS exhibited a performance comparable to Peng-Robinson (1976) EOS in the reduced temperature range of 0.5 to 1. The present EOS tends to predict better saturation liquid volumes at reduced temperatures below 0.8, and better estimations for second virial coefficient at high reduced temperatures. The EOS was successfully employed for vapor liquid equilibrium calculations for some mixtures of normal or slightly polar fluids with traditional one binary parameter mixing rule at moderately high pressures. At low reduced temperatures, where conventional one adjustable parameter applications of the cubic equations compare unfavorably with dual methods based on excess Gibbs energy functions for the liquid phase, a new ...

Influence of thermodynamic variables and molecular parameters in the solubility of gases in liquids

Abstract

Critical behavior of p(2 x 2) oxygen on Ru(001): An example of four-state Potts critical exponents.

Atomic oxygen on the hexagonally close-packed Ru(001) surface forms a p(2\ifmmode\times\else\texttimes\fi{}2) structure on threefold-coordinated hcp sites. The critical behavior of the structural order-disorder phase transition was studied with low-energy electron diffraction at a relative coverage \ensuremath{\Theta}=0.25. Quantitative profile analysis of superstructure beams together with measurements of integrated and peak intensities as a function of temperature in the reduced temperature range 0.004ltl0.1 were used to determine the exponents \ensuremath{\alpha}, \ensuremath{\beta}, \ensuremath{\gamma}, and \ensuremath{\nu}. They agree within 3% to 10% with the values of the two-dimensional four-state Potts universality class. Conditions and limitations of this determination are discussed.

Critical behavior of hydrogen.

We have studied the critical behavior of equilibrium ${\mathrm{H}}_{2}$ using optical techniques. From measurements of the liquid-vapor coexistence curve covering the reduced temperature range 3.2\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}5}$7.0\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}2}$ we find the critical exponent \ensuremath{\beta}=0.326\ifmmode\pm\else\textpm\fi{}0.003 and the corrections-to-scaling exponent \ensuremath{\Delta}=0.46\ifmmode\pm\else\textpm\fi{}0.02. From compressibility measurements we find the critical exponent \ensuremath{\gamma}=1.19\ifmmode\pm\else\textpm\fi{}0.05 and the universal amplitude ratio ${\ensuremath{\Gamma}}_{0}^{+}$/${\ensuremath{\Gamma}}_{0}^{\mathrm{\ensuremath{-}}}$=5.2\ifmmode\pm\else\textpm\fi{}0.4. These results are in accord with theoretical predictions. Measurements of the coexistence curve diameter show deviations from the classical law of rectilinear diameter in the opposite direction from those observed in other fluids, possibly indicating the presence of attractive many-body interactions in fluid hydrogen.

An augmented hard core equation of state generalized in terms of Tc, Pc, and ω

Abstract

Performance of electronic ballast and controls with 34 and 40 Watt F40 fluorescent lamps

The electric and photometric characteristics of 40-W, cool white (CW) and 34 W, so-called lite white (LW) F40 T-12 fluorescent lamps were compared by operating them with electronic ballasts, static controls, and dynamic controls of different designs. The energy-saving krypton-filled 34 W lamp-ballast system is, at best, slightly more efficacious than the standard 40 W argon-filled lamp-ballast system by virtue of the use of lite white phosphor. The 34 W system is shown to have limitations that include higher starting voltages, reduced temperature range of operation, smaller dimming range, and poorer color rendering than the standard cool white 40 W lamp system.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>