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Determination of potential energy function and transport properties of sulphur hexafluoride
Abstract
The potential energy function of sulphur hexafluoride has been determined via the inversion of reduced viscosity collision integrals at zero pressure and fitted to obtain an analytical potential form. A comparison of the potential with the previously determined potential has been included. The interaction potential energy from the inversion procedure reproduces, within experimental error, viscosity, self-diffusion coefficient, thermal conductivity and isotopic thermal diffusion factor of sulphur hexafluoride over a wide temperature range. These properties have also been fitted to very accurate equations.
... is the distance at which the intermolecular potential is zero. The parameter ˝ (2,2) * cs has its usual meanings and are taken from a corresponding states correlation [14]. 0 is the corresponding value of an accurate potential [36]. ...
... This has been used in conjunction with the inner coordinates of the well obtained in the viscosity inversion to give the potential energy in the whole separation range (Fig. 1). The calculated inversion potential of sulfur hexafluoride has been compared with the potential of Goharshadi et al. [14] obtained directly from the inversion of low-density viscosity collision integrals . The calculated potential has been also compared with the potential of Dellis and Samios [17] determined by means of the ability of the potential to reproduce experimental data in a wide range of thermodynamic conditions. ...
... The average percent deviation of our results from the experiment is 10%. It is also shown that our calculated second virial coefficient from our potential are in better agreement with the experiment than those values from the potentials of Goharshadi et al. [14] and Dellis and Samios [17] which confirms the validity of our potential. ...
A new pair-potential energy function of sulfur hexafluoride has been determined via the inversion of reduced viscosity collision integrals at zero pressure and fitted to obtain a Hartree–Fock dispersion (HFD)-like potential form. The pair-potential reproduces the second virial coefficient and transport properties of sulfur hexafluoride in a good accordance with experimental data over wide ranges of temperatures. Molecular dynamics (MD) simulation has been also performed to obtain pressure, self-diffusion coefficient, and radial distribution function of fluid sulfur hexafluoride at different temperatures and densities using the calculated HFD-like pair-potential. We have also obtained pressures of SF6–Ar and SF6–Kr fluid mixtures at constant temperature at different densities using new two-body HFD-like models. To take higher-body forces into account, three-body potentials of Wang and Sadus (2006) 0110 and 0115 and Hauschild and Prausnitz (1993) [24] have been used with the two-body HFD-like potentials of SF6, SF6–Ar, and SF6–Kr systems to improve the prediction of the calculated properties without requiring an expensive three-body calculation. The MD simulation of sulfur hexafluoride has been also used to determine a new equation of state.
Thermal conductivity coefficients for gaseous states of N2 and CO have been calculated by the inversion technique in conjunction with Wang Chang-Uhlenbeck-de Boer (WCUB) approach of the kinetic theory of gases for considering the various contributions of the molecular degrees of freedom to the thermal conductivity. The values of calculated thermal conductivity coefficients are commensurate with best experimental values.
We present results on self-consistent calculations of second pVT–virial coefficients B(T), viscosity data &eegr;(T), and diffusion coefficients &rgr;D(T) for eleven heavy globular gases: boron trifluoride (BF3), carbon tetrafluoride (CF4), silicon tetrafluoride (SiF4), carbon tetrachloride (CCl4), silicon tetrachloride (SiCl4), sulfur hexafluoride (SF6), molybdenum hexafluoride (MoF6), tungsten hexafluoride (WF6), uranium hexafluoride (UF6), tetramethyl methane (C(CH3)4, TMM), and tetramethyl silane (Si(CH3)4, TMS). The calculations are performed mainly in the temperature range between 200 and 900 K by means of isotropic n−6 potentials with temperature-dependent separation rm(T) and potential well depth &Vegr;(T). The potential parameters at T=0 K (&Vegr;, rm,n) and the enlargement of the first level radii δ are obtained solving an ill-posed problem of minimizing the squared deviations between experimental and calculated values normalized to their relative experimental error. The temperature dependence of the potential is obtained as a result of the influence of vibrational excitation on binary interactions. This concept of the isotropic temperature-dependent potential (ITDP) is presented in detail where gaseous SF6 will serve as an example. The ITDP is subsequently applied to all other gases. This approach and the main part of the results presented here have already been published during 1996–2000. However, in some cases the data are upgraded due to the recently improved software (CF4,SF6) and newly found experimental data (CF4,SiF4,CCl4,SF6).
The diatomic potential energy function for helium has been determined via the inversion of reduced viscosity collision integrals at corresponding states and zero pressure. The resulting potential has been fitted to obtain an analytical form. A comparison of newly determined potential with the previously determined potentials is also included. The transport properties of helium such as viscosity, self-diffusion, and thermal conductivity coefficients at different temperatures and pressures have been calculated and compared with experimental data and they are found to be in good agreement with each other. The second virial coefficient of helium has been also calculated using the potential at different temperatures.
The initial density correction to gaseous viscosity using accurate realistic potentials of the noble gases is evaluated using the Rainwater–Friend theory. It is shown that this theory works satisfactorily for densities up to about . Due to the superimposability of the noble gas potential functions, a universal function of the reduced second viscosity virial coefficient is obtained over the entire reduced temperature range. At densities beyond the range of the theory, a variant of the excess viscosity is developed, by which the viscosity of the different gases can be easily calculated above the critical temperature for pressures up to 900 MPa. The accuracy of this method is within the experimental uncertainties.
Second virial coefficient data and viscosity were used to evaluate effective isotropic intermolecular potential functions proposed in the literature for sulfur hexafluoride. It was found that none of the potentials could predict the properties simultaneously. We have constructed a Morse–Morse–Spline–van der Waals (MMSV) potential which satisfactorily correlates second virial coefficient and viscosity data at the same time.
The pair-potential energy functions for He–N2, Ne–N2, and Ar–N2 have been determined from a direct inversion of the experimentally reduced viscosity collision integrals obtained from the corresponding-states correlation. The resulting potentials are in excellent agreement with the potentials independently obtained from molecular beam scattering measurements. The potentials have been used to predict the diffusion and viscosity coefficients for each system, and they are found to be in reasonable agreement with experimental values.
The potential energy function of methane has been determined via the inversion of reduced viscosity collision integrals at zero pressure. A comparison of the potential with the previously determined potentials is included. The viscosity, thermal conductivity, and self-diffusion coefficient of methane at different temperatures and pressures have been calculated and compared with experiment. The interaction potential of methane from the inversion method has been fitted to obtain an analytical potential form.
This paper contains the background for a complete synthesis of all the properties-equilibrium as well as transport-of the five noble gases and of the 26 mixtures that can be formed with them. The synthesis is valid for the zero-density limit only, but covers the temperature range from absolute zero to the onset of ionization. The synthesis is based on a thorough revision of the two-parameter extended law of corresponding states of Kestin, Ro and Wakeham. The paper recalls the basis for the original corresponding-states principle, identifies the places at which experiment and the theory of statistical mechanics suggest deviations, and proceeds to remove them to a point where almost perfect agreement between calculation and a very large body of diverse experimental data is achieved, in the sense that deviations of experimental data from calculation are of the same order as the uncertainty in the best contemporary measurements. The basis of the revised corresponding-states principle is a set of five parameters which characterize each pair-interaction together with a fully consistent and asymptotically correct set of universal collision integrals and functionals that appear in the rigorous theory. These are reinforced with selected quantum-mechanical calculations applied in regions where they are significant.
The initial density dependences of both viscosity and thermal conductivity are calculated according to a microscopically based theory which includes effects due to collisional transfer (from only free two-body phase space), three-monomer collisions, and monomer—dimer collisions. A Lennard-Jones potential is used to model the interactions. Comparison of the calculated results with experiment (in reduced form) shows very good agreement for both viscosity and thermal conductivity over a wide temperature range.
The pair-potential energy functions SF6-noble gases have been determined from a direct inversion of the experimentally reduced-viscosity collision integrals obtained from the corresponding states correlation. The resulting potentials are in an excellent agreement with the previously determined potentials. The collision integrals and thier ratios of these potentials which are necessary to calculate the theoretical values of transport coefficients are computed. The collision integrals have been used to predict the diffusion coefficients of the binary mixtures of hexafluoride with noble gases. The results indicate the agreement between theory and experiment is within the experimental uncertainties.
Two new methods of partitioning the second virial coefficient B into free, bound, and metastable parts, which differ from the well known partitioning of Stogryn and Hirschfelder, are presented. It is shown that the proper partitioning to use depends on the specific physical problem of interest. In particular, in the kinetic theory of moderately dense gases due to Curtiss, Snider, and co‐workers, certain collision integrals reduce unambiguously to linear sums of B and its temperature derivatives for repulsive potentials, but it has not been clear to what such integrals reduce for realistic potentials. It is shown that such integrals reduce to the previously derived expressions with B replaced by one of our two new definitions of its free part. This contrasts with previous applications to real gases in which Curtiss and co‐workers have used the full B and Kuznetsov has used the free part of B as defined by Stogryn and Hirschfelder. Also, original numerical calculations for the collision integrals are presented and the numerical consistency of the theory is verified.
The potential energy function of carbon tetrafluoride has been determined via the inversion of reduced viscosity collision integrals at corresponding states and zero pressure and fitted to obtain an analytical potential form. A comparison of the potential with the recently determined potential by means of ab initio molecular orbital calculations at the MP2/6-31+G(3d) level of theory has been included. The interaction potential energy from the inversion procedure reproduces, within experimental error, the viscosity, self-diffusion coefficient, and second virial coefficient of carbon tetrafluoride over a wide temperature range. We have also derived very accurate equations for the viscosity, self-diffusion coefficient, and second virial coefficient of carbon tetrafluoride in a more extended temperature range than those of previous ones.
The direct inversion scheme of Smith and co-workers has been modified so as to remove the requirement that the well depth ϵ be known independently before the interaction potential can be determined from gas viscosity data. It is shown that the entire potential, including ϵ, can be determined within about 5% even when the viscosity measurements are uncertain by 1%.
Results of a new investigation of the viscosity of sulphur hexafluoride are reported. The measurements have been performed in an oscillating-disk viscometer, with small gaps, completely made of quartz, from room temperature up to 690 K and for densities between 1.0 and 8.5 kgm−3, i.e., between 0.007 and 0.058 mol 1−1.The values of the second viscosity virial coefficient Bη obtained from the initial density dependence of viscosity increase with increasing temperature from zero at room temperature up to about 75 cm3 mol−1 at 690 K. They are compared with results of the complete modified Enskog theory as well as of the Rainwater-Friend theory for the Lennard-Jones 12-6 potential.Furthermore, our experimental results at 0.1 MPa are compared with data from existing literature and additionally used in order to deduce an improved individual data correlation similar to one by Wakeham and co-workers.