Ab initiopair potential energy curve for the argon atom pair and thermophysical properties for the dilute argon gas. II. Thermophysical properties for low-density argon

Impact of Combination Rules, Level of Theory, and Potential Function on the Modeling of Gas- and Condensed-Phase Properties of Noble Gases

The systems of noble gases are particularly instructive for molecular modeling due to the elemental nature of their interactions. They do not normally form bonds nor possess a (permanent) dipole moment, and the only forces determining their bonding/clustering stems from van der Waals forces─dispersion and Pauli repulsion, which can be modeled by empirical potential functions. Combination rules, that is, formulas to derive parameters for pair potentials of heterodimers from parameters of corresponding homodimers, have been studied at length for the Lennard-Jones 12-6 potentials but not in great detail for other, more accurate, potentials. In this work, we examine the usefulness of nine empirical potentials in their ability to reproduce quantum mechanical (QM) benchmark dissociation curves of noble gas dimers (He, Ne, Ar, Kr, and Xe homo- and heterodimers), and we systematically study the efficacy of different permutations of combination relations for each parameter of the potentials. Our QM benchmark comprises dissociation curves computed by several different coupled cluster implementations as well as symmetry-adapted perturbation theory. The two-parameter Lennard-Jones potentials were decisively outperformed by more elaborate potentials that sport a 25-30 times lower root-mean-square error (RMSE) when fitted to QM dissociation curves. Very good fits to the QM dissociation curves can be achieved with relatively inexpensive four- or even three-parameter potentials, for instance, the damped 14-7 potential (Halgren, J. Am. Chem. Soc. 1992, 114, 7827-7843), a four-parameter Buckingham potential (Werhahn et al., Chem. Phys. Lett. 2015, 619, 133-138), or the three-parameter Morse potential (Morse, Phys. Rev. 1929, 34, 57-64). Potentials for heterodimers that are generated from combination rules have an RMSE that is up to 20 times higher than potentials that are directly fitted to the QM dissociation curves. This means that the RMSE, in particular, for light atoms, is comparable in magnitude to the well-depth of the potential. Based on a systematic permutation of combination rules, we present one or more combination rules for each potential tested that yield a relatively low RMSE. Two new combination rules are introduced that perform well, one for the van der Waals radius σij as ( 1 2 ( σ i 3 + σ j 3 ) ) 1 / 3 and one for the well-depth ϵij as ( 1 2 ( ϵ i - 2 + ϵ j - 2 ) ) - 1 / 2 . The QM data and the fitted potentials were evaluated in the gas phase against experimental second virial coefficients for homo- and heterodimers, the latter of which allowed evaluation of the combination rules. The fitted models were used to perform condensed phase molecular dynamics simulations to verify the melting points, liquid densities at the melting point, and the enthalpies of vaporization produced by the models for pure substances. Subtle differences in the benchmark potentials, in particular, the well-depth, due to the level of theory used were found here to have a profound effect on the macroscopic properties of noble gases: second virial coefficients or the bulk properties in simulations. By explicitly including three-body dispersion in molecular simulations employing the best pair potential, we were able to obtain accurate melting points as well as satisfactory densities and enthalpies of vaporization.

Representative deflection angle for the single-deflection method of direct simulation Monte Carlo

The total cross section of binary collision is, in general, unbounded due to the long-range interations of molecules. It is conventional to truncate the small angle deflections of collisions. The present work suggests an alternative way of avoiding the difficulty of unboundedness. We employ the mean value theorem of definite integral over the deflection angle for the cross section. A series of numerical experiments were carried out to look for the representative collision cross section through which the single-angle simulation is amenable to the solution of the Boltzmann equation. Results show that the cross section should be 〈Σ〉=Σ_{D}^{2}/(2Σ_{D}-Σ_{μ}), and the representative deflection for the single-angle simulation be cos〈χ〉=Σ_{μ}/Σ_{D}-1, where Σ_{D} is the diffusion cross section and Σ_{μ} is the viscosity cross section. The single-angle computations for the inverse power law and the Lennard-Jones force law perfectly reproduce the conventional scattering algorithms for one-dimensional (1D) simulations of transport coefficients and 1D shock thickness. The computation costs for Lennard-Jones molecules are comparable to the costs for inverse power-law models.

Collision-induced three-body polarizability of helium

We present the first-principles determination of the three-body polarizability and the third dielectric virial coefficient of helium. Coupled-cluster and full configuration interaction methods were used to perform electronic structure calculations. The mean absolute relative uncertainty of the trace of the polarizability tensor, resulting from the incompleteness of the orbital basis set, was found to be 4.7%. Additional uncertainty due to the approximate treatment of triple and the neglect of higher excitations was estimated at 5.7%. An analytic function was developed to describe the short-range behavior of the polarizability and its asymptotics in all fragmentation channels. We calculated the third dielectric virial coefficient and its uncertainty using the classical and semiclassical Feynman-Hibbs approaches. The results of our calculations were compared with experimental data and with recent Path-Integral Monte Carlo (PIMC) calculations [Garberoglio et al., J. Chem. Phys. 155, 234103 (2021)] employing the so-called superposition approximation of the three-body polarizability. For temperatures above 200 K, we observed a significant discrepancy between the classical results obtained using superposition approximation and the ab initio computed polarizability. For temperatures from 10 K up to 200 K, the differences between PIMC and semiclassical calculations are several times smaller than the uncertainties of our results. Except at low temperatures, our results agree very well with the available experimental data but have much smaller uncertainties. The data reported in this work eliminate the main accuracy bottleneck in the optical pressure standard [Gaiser et al., Ann. Phys. 534, 2200336 (2022)] and facilitate further progress in the field of quantum metrology.

The ab initio potential energy curves of atom pairs and transport properties of high-temperature vapors of Cu and Si and their mixtures with He, Ar, and Xe gases

The potential energy curves (PECs) for the homonuclear He-He, Ar-Ar, Cu-Cu, and Si-Si dimers, as well as heteronuclear Cu-He, Cu-Ar, Cu-Xe, Si-He, Si-Ar, and Si-Xe dimers, are obtained in quantum Monte Carlo (QMC) calculations. It is shown that the QMC method provides the PECs with an accuracy comparable with that of the state-of-the-art coupled cluster singles and doubles with perturbative triples corrections [CCSD(T)] calculations. The QMC data are approximated by the Morse long range (MLR) and (12-6) Lennard-Jones (LJ) potentials. The MLR and LJ potentials are used to calculate the deflection angles in binary collisions of corresponding atom pairs and transport coefficients of Cu and Si vapors and their mixtures with He, Ar, and Xe gases in the range of temperature from 100 K to 10 000 K. It is shown that the use of the LJ potentials introduces significant errors in the transport coefficients of high-temperature vapors and gas mixtures. The mixtures with heavy noble gases demonstrate anomalous behavior when the viscosity and thermal conductivity can be larger than that of the corresponding pure substances. In the mixtures with helium, the thermal diffusion factor is found to be unusually large. The calculated viscosity and diffusivity are used to determine parameters of the variable hard sphere and variable soft sphere molecular models as well as parameters of the power-law approximations for the transport coefficients. The results obtained in the present work include all information required for kinetic or continuum simulations of dilute Cu and Si vapors and their mixtures with He, Ar, and Xe gases.

Thermodynamic properties of krypton from Monte Carlo simulations using ab initio potentials

Ten different thermodynamic properties of the noble gas krypton were calculated by Monte Carlo simulations in the isothermal-isobaric ensemble using a highly accurate ab initio pair potential, Feynman-Hibbs corrections for quantum effects, and an extended Axilrod-Teller-Muto potential to account for nonadditive three-body interactions. Fourteen state points at a liquid and a supercritical isotherm were simulated. To obtain results representative for macroscopic systems, simulations with several particle numbers were carried out and extrapolated to the thermodynamic limit. Our results agree well with experimental data from the literature, an accurate equation of state for krypton, and a recent virial equation of state (VEOS) for krypton in the region where the VEOS has converged. These results demonstrate that very good agreement between simulation and experiment can only be achieved if nonadditive three-body interactions and quantum effects are taken into account.

Thermodynamic properties of argon from Monte Carlo simulations using ab initio potentials

Ten different thermodynamic properties of the noble gas argon in the liquid and supercritical regions were obtained from semiclassical Monte Carlo simulations in the isothermal-isobaric ensemble using ab initio potentials for the two-body and nonadditive three-body interactions. Our results for the density and speed of sound agree with the most accurate experimental data for argon almost within the uncertainty of these data, a level of agreement unprecedented for many-particle simulations. This demonstrates the high predictive but yet unexploited power of ab initio potentials in the field of molecular modeling and simulation for thermodynamic properties of fluids.

Rotational spectroscopy of the argon dimer by time-resolved Coulomb explosion imaging of rotational wave packets

We report time-domain rotational spectroscopy of the argon dimer, Ar₂, by implementing time-resolved Coulomb explosion imaging of rotational wave packets. The rotational wave packets are created in Ar₂ with a linearly polarized, nonresonant, ultrashort laser pulse, and their spatiotemporal evolution is fully characterized by measuring angular distribution of the fragmented Ar⁺ promptly ejected from Ar₂²⁺ generated by the more intense probe pulse. The pump-probe measurements have been carried out up to a delay time of 16 ns. The alignment parameters, derived from the observed images, exhibit periodic oscillation lasting for more than 15 ns. The pure rotational spectrum of Ar₂ is obtained by Fourier transformation of the time traces of the alignment parameters. The frequency resolution in the spectrum is about 90 MHz, the highest ever achieved for Ar₂. The rotational constant and the centrifugal distortion constant are determined with much improved precision than the previous experimental results: B₀ = 1.72713 ± 0.00009 GHz and D₀ = 0.0310 ± 0.0005 MHz. The present B₀ value does not match within the quoted experimental uncertainty with that from the VUV spectroscopy, so far accepted as an experimental reference to assess theories. The present improved constants would stand as new references to calibrate state-of-the-art theoretical investigations and an indispensable experimental source for the construction of an accurate empirical intermolecular potential.

Bulk viscosity of gaseous argon from molecular dynamics simulations

The bulk viscosity of dilute argon gas is calculated using molecular dynamics simulations in the temperature range 150-500 K and is found to be proportional to density squared in the investigated range of densities 0.001-1 kg m^{-3}. A comparison of the results obtained using Lennard-Jones and Tang-Toennies models of pair interaction potential reveals that the value of the bulk viscosity coefficient is sensitive to the choice of the pair interaction model. The inclusion of the Axilrod-Teller-Muto three-body interaction in the model does not noticeably affect the values of the bulk viscosity in dilute states, contrary to the previously investigated case of dense fluids.

Path-integral calculation of the third dielectric virial coefficient of noble gases

We present a rigorous framework for fully quantum calculation of the third dielectric virial coefficient C_ɛ(T) of noble gases, including exchange effects. The quantum effects are taken into account with the path-integral Monte Carlo method. Calculations employing state-of-the-art pair and three-body potentials and pair polarizabilities yield results generally consistent with the few scattered experimental data available for helium, neon, and argon, but rigorous calculations with well-described uncertainties will require the development of surfaces for the three-body nonadditive polarizability and the three-body dipole moment. The framework, developed here for the first time, will enable new approaches to primary temperature and pressure metrology based on first-principles calculations of gas properties.

Transport coefficients of isotopic mixtures of noble gases based on ab initio potentials

The transport coefficients such as viscosity, thermal conductivity, diffusion and thermal diffusion of neon, argon, krypton, and xenon are computed for a wide range of temperatures taking into consideration their real isotopic compositions. A new concept of isotopic thermal diffusion factor is introduced and calculated. The Chapman-Enskog method based on the 10th order approximation with respect to the Sonine polynomial expansion is applied. Ab initio potentials of interatomic interactions are employed to compute the transport cross-sections as they are part of the coefficient expressions. To study the influence of the isotopic composition, the same transport coefficients have been calculated for the single gases having an average atomic mass. The estimated numerical error of the present results is a function of the temperature and is different for each coefficient. At the room temperature, the relative numerical error of viscosity, thermal conductivity and diffusion coefficient is on the order of 10-6. The numerical error of the thermal diffusion factor affects the fifth decimal digit. The influence of the isotopic composition on viscosity and thermal conductivity depends on the gas species. It is negligible for argon and significant (about 0.02%) for xenon, while neon and krypton are weakly affected by the isotopic composition. The diffusion coefficient for each pair of isotopes differs from the corresponding self-diffusion coefficient by about 3%. The thermal diffusion factor of each isotope differs from the thermal self-diffusion factor in the third decimal digit.

Thermophysical properties of low-density neon gas from highly accurate first-principles calculations and dielectric-constant gas thermometry measurements

New interatomic potential energy and interaction-induced polarizability curves for two ground-state neon atoms were developed and used to predict the second density, acoustic, and dielectric virial coefficients and the dilute gas shear viscosity and thermal conductivity of neon at temperatures up to 5000 K. The potential energy curve is based on supermolecular coupled-cluster (CC) calculations at very high levels up to CC with single, double, triple, quadruple, and perturbative pentuple excitations [CCSDTQ(P)]. Scalar and spin-orbit relativistic effects, the diagonal Born-Oppenheimer correction, and retardation of the dispersion interactions were taken into account. The interaction-induced polarizability curve, which in this work is only needed for the calculation of the second dielectric virial coefficient, is based on supermolecular calculations at levels up to CCSDT and includes a correction for scalar relativistic effects. In addition to these first-principles calculations, highly accurate dielectric-constant gas thermometry (DCGT) datasets measured at temperatures from 24.5 to 200 K were analyzed to obtain the difference between the second density and dielectric virial coefficients with previously unattained accuracy. The agreement of the DCGT values with the ones resulting from the first-principles calculations is, despite some small systematic deviations, very satisfactory. Apart from this combination of two virial coefficients, the calculated thermophysical property values of this work are significantly more accurate than any available experimental data.

Effective hardness of interaction from thermodynamics and viscosity in dilute gases

The hardness of the effective inverse power law (IPL) potential, which can be obtained from thermodynamics or collision integrals, can be used to demonstrate similarities between thermodynamic and transport properties. This link is investigated for systems of increasing complexity (i.e., the EXP, square-well, Lennard-Jones, and Stockmayer potentials; ab initio results for small molecules; and rigid linear chains of Lennard-Jones sites). These results show that while the two approaches do not yield precisely the same values of effective IPL exponent, their qualitative behavior is intriguingly similar, offering a new way of understanding the effective interactions between molecules, especially at high temperatures. In both approaches, the effective hardness is obtained from a double-logarithmic temperature derivative of an effective area.

Entropy Scaling of Viscosity - I: A Case Study of Propane

In this work, a broadly-applicable and simple approach for building high accuracy viscosity correlations is demonstrated for propane. The approach is based on the combination of a number of recent insights related to the use of residual entropy scaling, especially a new way of scaling the viscosity for consistency with the dilute-gas limit. With three adjustable parameters in the dense phase, the primary viscosity data for propane are predicted with a mean absolute relative deviation of 1.38%, and 95% of the primary data are predicted within a relative error band of less than 5%. The dimensionality of the dense-phase contribution is reduced from the conventional two dimensional approach (temperature and density) to a one-dimensional correlation with residual entropy as the independent variable. The simplicity of the model formulation ensures smooth extrapolation behavior (barring errors in the equation of state itself). The approach proposed here should be applicable to a wide range of chemical species. The supporting information includes the relevant data in tabular form and a Python implementation of the model.

Relationship between the Transport Coefficients of Polar Substances and Entropy

An expression is proposed that relates the transport properties of polar substances (diffusion coefficient, viscosity coefficient, and thermal conductivity coefficient) with entropy. To calculate the entropy, an equation of state with a good description of the properties in a wide region of the state is used. Comparison of calculations based on the proposed expressions with experimental data showed good agreement. A deviation exceeding 20% is observed only in the region near the critical point as well as at high pressures.

Eighth-order virial equation of state and speed-of-sound measurements for krypton

An eighth-order virial equation of state (VEOS) for krypton, valid for temperatures up to 5000 K, was developed using the accurate potential functions proposed by Jäger et al. [J. Chem. Phys. 144, 114304 (2016)] for the pair interactions and nonadditive three-body interactions between krypton atoms. While the second and third virial coefficients were already calculated by Jäger et al., the fourth- to eighth-order coefficients were determined in the present work. A simple analytical function was fitted individually to the calculated values of each virial coefficient to obtain the VEOS in an easy-to-use analytical form. To enable a stringent test of the quality of the new VEOS, we measured the speed of sound in krypton in the temperature range from 200 K to 420 K and at pressures up to 100 MPa with a very low uncertainty (at the 0.95 confidence level) of 0.005%-0.018% employing the pulse-echo technique. In order to verify that the isotopic composition of the krypton sample conforms to that of natural krypton in air, high-precision measurements of krypton isotope ratios using a high-sensitivity noble gas mass spectrometer were performed. The extensive comparison with the new speed-of-sound data as well as with experimental p-ρ-T and speed-of-sound data from the literature indicates that pressures and speeds of sound calculated using our new VEOS have uncertainties (at the 0.95 confidence level) of less than 0.1% at state points at which the VEOS is sufficiently converged.

Highly-accurate density-virial-coefficient values for helium, neon, and argon at 0.01 ○C determined by dielectric-constant gas thermometry

The dielectric-constant gas thermometer of Physikalisch-Technische Bundesanstalt (PTB) developed for measuring the Boltzmann constant with a relative uncertainty of 1.9 parts per million was used for determining the virial coefficients of the three noble gases, helium, neon, and argon, at the triple point of water (0.01 ^○C). For this purpose, isotherms were measured up to a maximum pressure of 7 MPa. The evaluation of the highly accurate data by fitting is required to derive an extended working equation for the dependence of the gas pressure on the dielectric constant. The following values have been obtained for the second B and third C virial coefficients, with the standard uncertainties given in parentheses as a multiple of the last digit, considering literature data for the dielectric virial coefficients: helium: B_DCGT ^He0.01 ^○C=11.925715 cm³/mol, C_DCGT ^He0.01 ^○C=113.4958 cm⁶/mol²; neon: B_DCGT ^Ne0.01 ^○C=10.994528 cm³/mol, C_DCGT ^Ne0.01 ^○C=215.815 cm⁶/mol²; argon: B_DCGT ^Ar0.01 ^○C=-21.233144 cm³/mol, C_DCGT ^Ar0.01 ^○C=1143.339 cm⁶/mol². These values are compared with the results of the latest ab initio calculations of the second and third virial coefficients.

Refractive-index gas thermometry

The principles and techniques of primary refractive-index gas thermometry (RIGT) are reviewed. Absolute primary RIGT using microwave measurements of helium-filled quasispherical resonators has been implemented at the temperatures of the triple points of neon, oxygen, argon and water, with relative standard uncertainties ranging from 9.1 × 10-6 to 3.5 × 10-5. Researchers are now also using argon-filled cylindrical microwave resonators for RIGT near ambient temperature, with relative standard uncertainties between 3.8 × 10-5 and 4.6 × 10-5, and conducting relative RIGT measurements on isobars at low temperatures. RIGT at optical frequencies is progressing, and has been used to perform a Boltzmann constant measurement at room temperature with a relative standard uncertainty of 1.2 × 10-5. Uncertainty budgets from implementations of absolute primary microwave RIGT, relative primary microwave RIGT and absolute primary optical RIGT are provided.

The Zero-Density Limit of the Residual Entropy Scaling of Transport Properties

The modified residual entropy scaling approach has been shown to be a successful means of scaling dense phase transport properties. In this work, we investigate the dilute-gas limit of this scaling. This limit is considered for model potentials and highly accurate results from calculations with ab initio pair potentials for small molecules. These results demonstrate that with this approach, the scaled transport properties of noble gases can be collapsed without any empirical parameters to nearly their mutual uncertainties and that the scaled transport properties of polyatomic molecules are qualitatively similar, and for sufficiently high temperatures they agree with "universal" values proposed by Rosenfeld in 1999. There are significant quantitative differences between the model potentials and real fluids in these scaled coordinates, but this study provides a thorough coverage of model fluids and simple real fluids, providing the basis for further study. In the supporting information we provide the collected calculations with ab initio pair potentials from the literature, as well as code in the Python language implementing all aspects of our analysis.

Predicting vapor liquid equilibria using density functional theory: A case study of argon

Predicting vapor liquid equilibria (VLE) of molecules governed by weak van der Waals (vdW) interactions using the first principles approach is a significant challenge. Due to the poor scaling of the post Hartree-Fock wave function theory with system size/basis functions, the Kohn-Sham density functional theory (DFT) is preferred for systems with a large number of molecules. However, traditional DFT cannot adequately account for medium to long range correlations which are necessary for modeling vdW interactions. Recent developments in DFT such as dispersion corrected models and nonlocal van der Waals functionals have attempted to address this weakness with a varying degree of success. In this work, we predict the VLE of argon and assess the performance of several density functionals and the second order Møller-Plesset perturbation theory (MP2) by determining critical and structural properties via first principles Monte Carlo simulations. PBE-D3, BLYP-D3, and rVV10 functionals were used to compute vapor liquid coexistence curves, while PBE0-D3, M06-2X-D3, and MP2 were used for computing liquid density at a single state point. The performance of the PBE-D3 functional for VLE is superior to other functionals (BLYP-D3 and rVV10). At T = 85 K and P = 1 bar, MP2 performs well for the density and structural features of the first solvation shell in the liquid phase.

State-of-the-art ab initio potential energy curve for the xenon atom pair and related spectroscopic and thermophysical properties

A new ab initio interatomic potential energy curve for two ground-state xenon atoms is presented. It is based on supermolecular calculations at the coupled-cluster level with single, double, and perturbative triple excitations [CCSD(T)] employing basis sets up to sextuple-zeta quality, which were developed as part of this work. In addition, corrections were determined for higher coupled-cluster levels up to CCSDTQ as well as for scalar and spin-orbit relativistic effects at the CCSD(T) level. A physically motivated analytical function was fitted to the calculated interaction energies and used to compute the vibrational spectrum of the dimer, the second virial coefficient, and the dilute gas transport properties. The agreement with the best available experimental data for the investigated properties is excellent; the new potential function is superior not only to previous ab initio potentials but also to the most popular empirical ones.

Accurate virial coefficients of gaseous krypton from state-of-the-art ab initio potential and polarizability of the krypton dimer

We have developed a new krypton-krypton interaction-induced isotropic dipole polarizability curve based on high-level ab initio methods. The determination was carried out using the coupled-cluster singles and doubles plus perturbative triples method with very large basis sets up to augmented correlation-consistent sextuple zeta as well as the corrections for core-core and core-valence correlation and relativistic effects. The analytical function of polarizability and our recently constructed reference interatomic potential [J. M. Waldrop et al., J. Chem. Phys. 142, 204307 (2015)] were used to predict the thermophysical and electromagnetic properties of krypton gas. The second pressure, acoustic, and dielectric virial coefficients were computed for the temperature range of 116 K-5000 K using classical statistical mechanics supplemented with high-order quantum corrections. The virial coefficients calculated were compared with the generally less precise available experimental data as well as with values computed from other potentials in the literature {in particular, the recent highly accurate potential of Jäger et al. [J. Chem. Phys. 144, 114304 (2016)]}. The detailed examination in this work suggests that the present theoretical prediction can be applied as reference values in disciplines involving thermophysical and electromagnetic properties of krypton gas.

Reference Values and Reference Correlations for the Thermal Conductivity and Viscosity of Fluids

In this paper, reference values and reference correlations for the thermal conductivity and viscosity of pure fluids are reviewed. Reference values and correlations for the thermal conductivity and the viscosity of pure fluids provide thoroughly evaluated data or functional forms and serve to help calibrate instruments, validate or extend models, and underpin some commercial transactions or designs, among other purposes. The criteria employed for the selection of thermal conductivity and viscosity reference values are also discussed; such values, which have the lowest uncertainties currently achievable, are typically adopted and promulgated by international bodies. Similar criteria are employed in the selection of reference correlations, which cover a wide range of conditions, and are often characterized by low uncertainties in their ranges of definition.

The Boltzmann project

The International Committee for Weights and Measures (CIPM), at its meeting in October 2017, followed the recommendation of the Consultative Committee for Units (CCU) on the redefinition of the kilogram, ampere, kelvin and mole. For the redefinition of the kelvin, the Boltzmann constant will be fixed with the numerical value 1.380 649 × 10-23 J K-1. The relative standard uncertainty to be transferred to the thermodynamic temperature value of the triple point of water will be 3.7 × 10-7, corresponding to an uncertainty in temperature of 0.10 mK, sufficiently low for all practical purposes. With the redefinition of the kelvin, the broad research activities of the temperature community on the determination of the Boltzmann constant have been very successfully completed. In the following, a review of the determinations of the Boltzmann constant k, important for the new definition of the kelvin and performed in the last decade, is given.

Similarity Laws for the Lines of Ideal Free Energy and Chemical Potential in Supercritical Fluids

We have found the curves on the density-temperature plane, along which the values of free energy and chemical potential correspond to ideal gas quantities. At first, we have applied the van der Waals equation to construct them and to derive their equations. Then we have shown that the same lines for real substances (Ar, N₂, CH₄, SF₆, H₂, H₂O) and for the model Lennard-Jones system constructed on the basis of the measurements data and calculations are well matched with the derived equations. The validity and deviations from the obtained similarity laws are discussed.

Energy accommodation coefficient extracted from acoustic resonator experiments

We review values of the temperature jump coefficient ζT determined from measurements of the acoustic resonance frequencies facoust of helium-filled and argon-filled, spherical cavities near ambient temperature. We combine these values of ζT with literature data for tangential momentum accommodation coefficient (TMAC) and the Cercignani-Lampis model of the gas-surface interaction to obtain measurement-derived values of the normal energy accommodation coefficient (NEAC). We found that NEAC ranges from 0 to 0.1 for helium and from 0.61 to 0.85 for argon at ambient temperature for several different surfaces. We suggest that measurements of facoust of gas-filled, cylindrical cavities and of the non-radial modes of quasi-spherical cavities might separately determine TMAC and NEAC. Alternatively, TMAC and NEAC could be determined by measuring the heat transfer and momentum transfer between parallel rotating discs at low pressure.

Beyond Born-Mayer: Improved Models for Short-Range Repulsion in ab Initio Force Fields

Short-range repulsion within intermolecular force fields is conventionally described by either Lennard-Jones (A/r(12)) or Born-Mayer (A exp(-Br)) forms. Despite their widespread use, these simple functional forms are often unable to describe the interaction energy accurately over a broad range of intermolecular distances, thus creating challenges in the development of ab initio force fields and potentially leading to decreased accuracy and transferability. Herein, we derive a novel short-range functional form based on a simple Slater-like model of overlapping atomic densities and an iterated stockholder atom (ISA) partitioning of the molecular electron density. We demonstrate that this Slater-ISA methodology yields a more accurate, transferable, and robust description of the short-range interactions at minimal additional computational cost compared to standard Lennard-Jones or Born-Mayer approaches. Finally, we show how this methodology can be adapted to yield the standard Born-Mayer functional form while still retaining many of the advantages of the Slater-ISA approach.

Calculation of the thermal conductivity of low-density CH4-N2 gas mixtures using an improved kinetic theory approach

The thermal conductivity of low-density CH4-N2 gas mixtures has been calculated by means of the classical trajectory method using state-of-the-art intermolecular potential energy surfaces for the CH4-CH4, N2-N2, and CH4-N2 interactions. Results are reported in the temperature range from 70 K to 1200 K. Since the thermal conductivity is influenced by the vibrational degrees of freedom of the molecules, which are not included in the rigid-rotor classical trajectory computations, a new correction scheme to account for vibrational degrees of freedom in a dilute gas mixture is presented. The calculations show that the vibrational contribution at the highest temperature studied amounts to 46% of the total thermal conductivity of an equimolar mixture compared to 13% for pure nitrogen and 58% for pure methane. The agreement with the available experimental thermal conductivity data at room temperature is good, within ±1.4%, whereas at higher temperatures, larger deviations up to 4.5% are observed, which can be tentatively attributed to deteriorating performance of the measuring technique employed. Results are also reported for the magnitude and temperature dependence of the rotational collision number, Z(rot), for CH4 relaxing in collisions with N2 and for N2 relaxing in collisions with CH4. Both collision numbers increase with temperature, with the former being consistently about twice the value of the latter.

Acoustic and microwave tests in a cylindrical cavity for acoustic gas thermometry at high temperature

Relative primary acoustic gas thermometry (AGT) determines the ratios of thermodynamic temperatures from measured ratios of acoustic and microwave resonance frequencies in a gas-filled metal cavity on isotherms of interest. When measured in a cavity with known dimensions, the frequencies of acoustic resonances in a gas determine the speed of sound, which is a known function of the thermodynamic temperature T. Changes in the dimensions of the cavity are measured using the frequencies of the cavity's microwave resonances. We explored techniques and materials for AGT at high temperatures using a cylindrical cavity with remote acoustic transducers. We used gas-filled ducts as acoustic waveguides to transmit sound between the cavity at high temperatures and the acoustic transducers at room temperature. We measured non-degenerate acoustic modes in a cylindrical cavity in the range 295 K Collapse

Key Words

• acoustic resonator
• cylindrical acoustic gas thermometer
• microwave resonator
• thermodynamic temperature
• waveguide

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MESH Headings Collapse

Grants

• 9999-NIST Intramural NIST DOC

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Affiliation(s)

K Zhang Department of Thermal Engineering, Tsinghua University, Beijing 100084, People's Republic of China Division of Thermophysics and Process Measurements, National Institute of Metrology, Beijing 100029, People's Republic of China
X J Feng Division of Thermophysics and Process Measurements, National Institute of Metrology, Beijing 100029, People's Republic of China
K Gillis National Institute of Standards and Technology, Gaithersburg, MD 20899, USA
M Moldover National Institute of Standards and Technology, Gaithersburg, MD 20899, USA
J T Zhang Division of Thermophysics and Process Measurements, National Institute of Metrology, Beijing 100029, People's Republic of China
H Lin Division of Thermophysics and Process Measurements, National Institute of Metrology, Beijing 100029, People's Republic of China
J F Qu Division of Thermophysics and Process Measurements, National Institute of Metrology, Beijing 100029, People's Republic of China
Y N Duan Division of Thermophysics and Process Measurements, National Institute of Metrology, Beijing 100029, People's Republic of China

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Transport coefficients of helium-argon mixture based on ab initio potential

The viscosity, thermal conductivity, diffusion coefficient, and thermal diffusion factor of helium-argon mixtures are calculated for a wide range of temperature and for various mole fractions up to the 12th order of the Sonine polynomial expansion with an ab initio intermolecular potential. The calculated values for these transport coefficients are compared with other data available in the open literature. The comparison shows that the obtained transport coefficients of helium-argon mixture have the best accuracy for the moment.

Using a two-capillary viscometer with preheating to measure the viscosity of dilute argon from 298.15 K to 653.15 K

Currently, there exists only one set of experimental results at temperatures up to 680 K with the claimed relative standard uncertainty of (0.15-0.20)%. This paper reports new experimental results using the two-capillary viscometer in the temperature range from 298.15 K to 653.15 K with the claimed relative standard uncertainty of 0.062%. The new measurements agree with the existing high accuracy measurements and ab initio calculations in the overlapping temperature range within the extraordinary low relative differences of ±0.08%. The good agreement represents a robust proof of the potential models derived from the ab initio calculations, which play the powerful means in obtaining the thermophysical properties of dilute monoatomic gases over wide temperature ranges. In the experiments, the authors observed the occurrence of insufficient preheating existing with the two-capillary viscometer at high temperature.