Dielectric Virial Coefficients Research Articles

Second dielectric virial coefficient of helium gas: quantum-statistical calculations from an ab initio interaction-induced polarizability

Second dielectric virial coefficient of helium gas: quantum-statistical calculations from an ab initio interaction-induced polarizability

Second dielectric virial coefficient of helium gas: quantum-statistical calculations from an ab initio interaction-induced polarizability

A quantum-statistical expression for the second virial coefficient of the dielectric Clausius-Mossotti function is derived. Calculations of the second dielectric virial coefficient of helium gas at various temperatures are reported. The role of quantum mechanical effects and the convergence properties of the semiclassical expansion are discussed. The calculated second dielectric virial coefficients at various temperatures are compared with experimental data.

Determination of the density in the gas phase with a computer-controlled measuring system of the dielectric constant

A computer-controlled measuring system (CCMS) of the dielectric constant (ε) in the gas phase as a function of pressure (P) and temperature (T) is described. The automated experimental setup is capable of performing the necessary measurements for the determination of the first three dielectric virial coefficients. Combining the value of ε with these dielectric virial coefficients, it is possible to calculate the density and, hence, the compressibility factor of the gas. The CCMS is as accurate as the best methods for the determination of ρ and has the ability to produce numerous experimental data in a short period of time.

Dielectric Constant, Dielectric Virial Coefficients, and Dipole Moments of 1,1,1,2-Tetrafluoroethane

ADVERTISEMENT RETURN TO ISSUEPREVArticleNEXTDielectric Constant, Dielectric Virial Coefficients, and Dipole Moments of 1,1,1,2-TetrafluoroethaneTeresa Barao, Carlos A. Nieto de Castro, Umesh V. Mardolcar, Richard Okambawa, and Jean M. St-ArnaudCite this: J. Chem. Eng. Data 1995, 40, 6, 1242–1248Publication Date (Print):November 1, 1995Publication History Published online1 May 2002Published inissue 1 November 1995https://doi.org/10.1021/je00022a021RIGHTS & PERMISSIONSArticle Views216Altmetric-Citations19LEARN ABOUT THESE METRICSArticle Views are the COUNTER-compliant sum of full text article downloads since November 2008 (both PDF and HTML) across all institutions and individuals. These metrics are regularly updated to reflect usage leading up to the last few days.Citations are the number of other articles citing this article, calculated by Crossref and updated daily. Find more information about Crossref citation counts.The Altmetric Attention Score is a quantitative measure of the attention that a research article has received online. Clicking on the donut icon will load a page at altmetric.com with additional details about the score and the social media presence for the given article. Find more information on the Altmetric Attention Score and how the score is calculated. Share Add toView InAdd Full Text with ReferenceAdd Description ExportRISCitationCitation and abstractCitation and referencesMore Options Share onFacebookTwitterWechatLinked InReddit PDF (699 KB) Get e-Alerts Get e-Alerts

Determination of the compressibility factorZ(p, T) of three methane-ethane mixtures using the dielectric constant method

The compressibility behavior of three mixtures of the CH4 C2 H6, system has been investigated experimentally by means of the dielectric constant method. Precise ( ± 1 ppm) measurements of the dielectric constant (e) as a function of the pressure (P) along one isotherm (T) are combined with the first three dielectric virial coefficients (A,B, andC) in order to obtain accurate values of the molar density (p). The compressibility factorZ=P/( p RT) was obtained from the measured values ofp,P, andT. The coefficientA, is determined from the measurements of e as a function ofP, while the higher-order coefficients (B, andC,) are obtained by an expansion technique. We report the measured values ofZ at 295.15 K up to 12 MPa for three mixtures of CH4-C2-H6 containing, respectively. 9.54, 35.3, and 75.4% (molar) of ethane. Their exact composition was determined by weighing during the mixing process. The first three dielectric virial coefficients and the mixed second dielectric virial coefficient for the CH4,-C2, H6 system agree with the calculated or the literature values within the limits of uncertainties. For the mixture containing 90.46% CH4+C2H6, deviations in compressibility are of the order of 0.4% from GERG.

Temperature Dependence of the Second Dielectric Virial Coefficients of Rare Gases

Second dielectric virial coefficients Bε (T) of the rare gases Ne, Ar, Kr, and Xe are calculated in a broad range of temperature using accurate HFD-type interatomic interaction potentials and available information on the trace of the pair polarizability Δα. It is shown that the experimentally determined temperature-variation of Bε(T) cannot be reproduced by existing theories. However, it is observed that the reduced dimensionless form of Bε(T) follows a remarkably regular pattern, strongly resembling the sign-inverted temperature variation of the second density virial coefficient Bϱ(T) with the same Boyle-temperature.

Static relative permittivity of sulfur hexafluoride up to 30 MPa

AbstractThe static relative permittivity ϵr of sulfur hexafluoride, SF6, has been measured along ten isotherms from 273.15 to 353.15 K at pressures up to 30 MPa. The experimental ϵr‐values obtained were accurate to within ±0.02 per cent, except for some values in the vicinity of the critical point. The critical relative permittivity ϵr,c was estimated to be 1.281 ±0.001 by application of the rectilinear diameter law. The ϵr‐values were combined with densities obtained from the equation of state in the literature to calculate the molar polarization Pm given by the Clausius‐Mossotti equation. The results of ϵr and Pm as a function of fluid density are discussed; the volume polarizability α' of SF6 was evaluated to be 6.67×10−30m3 and 6.59×10−30m3 using the values of the first dielectric virial coefficient Aϵ determined by two methods. Further, the values of α' for carbon dioxide and nitrous oxide were recalculated to be 2.94×10−30 m3 and 3.20×10−30m3, respectively, from Aϵ‐values obtained by the newly employed method.

Spectral interpretation of the refractivity and dielectric virial coefficients of atomic gases

Second electrooptical virial coefficients are expressed in terms of collision-induced intensity redistribution in absorption spectra of gases. Simple relations are obtained giving explicit frequency dependence of the contributions to the incremental dynamic polarizability due to pressure shift and asymmetric broadening of a simple spectral line. The dispersion of the second virial coefficient is shown to be either normal, or reversed (anomalous), depending on the pattern of the absorption cross section redistribution.

Second dielectric and refractivity virial coefficients of the polarizable dipolar hard-sphere fluid

The second dielectric and refractivity virial coefficients, B ε and B R, are calculated numerically, and essentially exactly, for a fluid of anisotropically polarizable dipolar hard spheres. The influence of polarizability is found to be significant, and substantially greater than predicted by previous perturbational approximations. Our results agree well with the available experimental data for CHF3. We also evaluate an extension of Wertheim's renormalization theory of polarizable fluids due to Schröer; for CHF3 at room temperature this recovers about 75% of B ε.

Precise determination of the compressibility factor by using dielectric constant measurements

Abstract We show that precise determination of the dielectric virial coefficients combined with the absolute value of the dielectric constant leads to very accurate values of the density. The higher order dielectric virial coefficients of the Clausius-Mossotti expansion are obtained by using an expansion technique. The compressibility factor of methane determined by using the first three dielectric virial coefficients is compared with the Goodwin equation of state. At 298.15 K and up to about 8 MPa, the compressibility factor calculated with the first two dielectric virial coefficients attains a difference of the order of 0.07% with the Goodwin equation of state. Between 8 MPa and 12 MPa, the first three dielectric virial coefficients are necessary to maintain the same order difference. The compressibility factor of methane determined by the dielectric method for two isotherms (298.15 K and 323.15 K) and pressures up to 15 MPa, compare with the best PVT and refractive index values.

Determination of the density from simultaneous measurements of the refractive index and the dielectric constant of gaseous CH4, SF6, and CO2

Simultaneous measurements of the refractive index ( n ) and the dielectric constant (ϵ) have been carried out for some non polar gases [CH 4 , CO 2 and SF 6 ] to study the comparative advantage of each method for the determination of the density with the use of our own experimental values of the first refractivity and the first dielectric virial coefficients as well as known values of the higher refractivity and dielectric virial coefficients. Measurements were carried out at 289.15, 298.15 and 323.15 K up to 23 MPa for CH 4 , at 323.15, 333.15 and 348.15 K up to 17 MPa for SF 6 and at 308.15, 313.15 and 323.15 K up to 23 MPa for CO 2 . Comparison with the IUPAC EOS values of the density shows good agreement (less than 1.0%) with the density values obtained both from the dielectric constant as well as the refractive index for CH 4 . For SF 6 , the density values obtained from the refractive index and the dielectric constant were compared with the equation of state proposed by de Reuck et al.(1991). For CO 2 , the agreement with IUPAC EOS is good (of the order of 1.0%) both for the dielectric constant as well as the refractive index up to the critical density. Above the critical density one observes a large deviation (of the order of 10%) between the density values obtained from the dielectric constant with those determined from the refractive index. The latter agrees with the EOS within 1.0%. Measurements for CO 2 and SF 6 , were in the supercritical region whereas those for CH 4 were far from the critical point.

The third dielectric and pressure virial coefficients of dipolar hard sphere fluids

We present numerical computations of the third dielectric virial coefficient C*e and the third pressure virial coefficient C* p of a fluid of hard sphere dipoles, over the range 0 < μ*2 < 4. The requisite 9-dimensional quadratures are performed using an adaptive Monte Carlo algorithm. We also compute terms in the high temperature expansions of the virial coefficients up to order μ*20 (C*e) and μ*24 (C* p ). Our work complements and extends earlier investigations by Joslin and by Rushbrooke and Shrubsall. Our results agree well with available experimental data, especially considering the relative crudeness of the molecular model. We also compute the critical point of the fluid.

An improved method for the simultaneous determination of dielectric and p, rho , T, virial coefficients

An experimental method for the determination of dielectric and p, rho , T, virial coefficients of gases is presented. It is derived from the cyclic expansion method originally proposed by Orcutt and Cole (1967) but improved with respect to the convergence of the working equation. A new equation for the experimental determination of p, rho , T, virial coefficients is also given, which simultaneously provides these quantities with the dielectric virial coefficients. The method is demonstrated on measurements on 1,1-difluoroethylene at 373 K, 398 K and 423 K. First, second and third dielectric, and second and third p, rho , T, virial coefficients, dipole moment and polarizability are reported.

Direct Measurements of the Dielectric Virial Coefficients of 4He between 3 K and 18 K

The second and third dielectric virial coefficients of 4He have been measured by the symmetrical gas-expansion technique of Buckingham, Cole and Sutter for six isotherms between 3,00 K and 17,68 K. The effects of helium adsorption are important, and are considered in detail. No temperature dependence of the second coefficient is seen at a level of δb=±0,008 cm3 mol-1, and average values of the second and third coefficients are b = 0,006 (10) cm3 mol-1 and c = -5 (4) cm6 mol-2, respectively. The uncertainty for b is relatively large because it has a systematic dependence on c: reanalysis of all the existing data shows that a more probable value of the third coefficient is c = -2 (1) cm6 mol-2, which when combined with our data gives b (3 K - 18 K) = -0,001 (4) cm-3 mol-1. The very small value suggests that theoretical calculations of the excess polarizability of the helium diatom need to be reconsidered. The small value and the small uncertainty of b indicate that future work to improve experimental values of the second density virial coefficient of 4He for this temperature range may without ambiguity make use of the methods of dielectric constant gas thermometry.

Experimental determination of the dielectric virial coefficients of atomic gases as a function of temperature

The second dielectric virial coefficient of atomic gases has been measured precisely as a function of temperature in the range 77 to 407 K. The experimental values are compared with the ab initio calculations and the collision-induced polarized scattered spectra (CIS). Except for helium, the Bε values derived from ab initio calculations and CIS parameters do not agree with the experimental values.

Determination of the quadrupole moment of nitrogen from the dielectric second virial coefficient

Dielectric virial coefficients of nitrogen have been measured at 323.15 K. By combining the dielectric second virial coefficient with the refractivity second virial coefficient we determined the quadrupole moment of nitrogen to be (1.47±0.07)×10−26 esu cm2. In calculating the molecular quadrupole moment from the dielectric second virial coefficient, effects due to various interaction energy terms were taken into consideration. These energy terms are due to quadrupole–quadrupole interaction, quadrupole-induced dipole interaction, reaction fields of induced moments and anisotropic effects.

Second virial coefficients in closed form for a Kihara (2m-m)-potential

In the literature second virial coefficients are calculated by series expansions or by direct numerical integration. For thermodynamic quantities such as thermodynamic functions, analytical expressions are wanted. This paper gives closed formulas for the second virial coefficient for a convex-body Kihara potential of the type U(ρ)= U0[(ρ0/ρ)2m-2(ρ0/ρ)m], where m can be a rational number n>3. Furthermore, a number of related problems such as dielectric virial coefficients and Buckingham-Pople integrals are reduced to the same Laplace-transformation-type technique.

The second dielectric virial coefficient of asymmetrical polar hard dumb-bell fluids

We have calculated the second dielectric virial coefficient B ϵ of some asymmetrical polar hard dumb-bell fluids. In the case of molecules with a short bond length, the effect of the asymmetry of molecular shapes is to increase B ϵ. In contrast, for molecules with a long bond length, the effect is to decrease B ϵ gradually.

Collision-induced light scattering of hydrogen gas at low density.

The room-temperature, binary, collision-induced, translational, and rotational spectra of molecular hydrogen are reported. The translational pair spectrum is separated into completely depolarized and polarized components; both are analyzed with quantum line-shape calculations based on the isotropic potential approximation and the dipole-induced-dipole (DID) model for the pair polarizability. A small overlap correction to the DID anisotropy yields a computed line shape that agrees with the observed depolarized, collision-induced spectrum. A substantial overlap correction to the DID trace is needed to produce a line shape consistent with the measurement of the collision-induced trace spectrum. Additionally, this modified DID trace reproduces the experimental data on the second dielectric virial coefficient.

The second dielectric virial coefficient of non-ideal polar hard-sphere fluids and polar hard dumb-bell fluids

The second dielectric virial coefficient, B ϵ, of fluids is calculated for the two liquids: non-ideal polar hard-spheres (two point charges +q and -q are embedded in the hard-sphere); polar hard dumb-bells. B ϵ depends sensitively on the shape of molecule. B ϵ for the non-ideal polar hard-sphere fluids is a positive value, and increases with separation of two charges. On the other hand, B ϵ for polar hard dumb-bell fluids decreases, becoming negative with the increasing length of the molecules. This behaviour agrees with the experimental results.