Meier, Karsten

The method of Lustig [J. Chem. Phys. 100, 3048–3059 (1994)] is applied to the path integral formulation of the quantum-mechanical canonical ensemble to derive equations for the calculation of all common thermodynamic properties in a rigorous and systematic way. Using these equations, thermodynamic properties such as the pressure, the isochoric and isobaric heat capacity, the speed of sound, or the Joule–Thomson coefficient can be calculated in path integral Monte Carlo simulations, fully incorporating quantum effects without uncontrolled approximations. The equations are derived for primitive and virial estimators. For the virial estimators, we generalize the finite-difference approach of Yamamoto [J. Chem. Phys. 123, 104101 (2005)] to arbitrary thermodynamic properties. We verify the derived equations by Monte Carlo simulations of supercritical helium-4 above the vapor–liquid critical point at selected state points on the 80 K isotherm using recent, highly accurate ab initio pair and nonadditive three-body potentials. The results of these simulations agree with our previous simulation results in the isobaric-isothermal ensemble, a virial equation of state of metrological quality, and the most accurate experimental data for the speed of sound in helium within their mutual uncertainties. We suppose that our results for the density are more accurate than the available experimental data in this region of the phase diagram.

This paper reports comprehensive and accurate measurements of the speed of sound in liquid n-heptane and 2,2,4-trimethylpentane (isooctane). The measurements were carried out by a double-path-length pulse-echo technique and cover the temperature range between 200 K and 420 K with pressures up to 100 MPa. The expanded uncertainties (coverage factor 𝑘 = 2) amount to 2.1 mK in temperature, 0.005% in pressure, 0.02% in speed of sound in 𝑛-heptane, and 0.015% in speed of sound in isooctane, with the exception of a few state points at low pressures, where it increases up to 0.03% for 𝑛-heptane and up to 0.035% for isooctane. Our data are more accurate than previously published data for both fluids. The measurements for isooctane extend the range in which the speed of sound had been measured before from 293 K down to 200 K and from 373 K up to 420 K. We also provide accurate correlations for the speed of sound as a function of temperature and pressure in the range of our measurements. Our data can contribute to developing new, more accurate equations of state for both fluids.

In the project H2MIXPROP, highly accurate data for several thermophysical properties of gaseous mixtures containing molecular hydrogen are obtained by state-of-the-art theoretical approaches and experimental methods. Such data are required for many technical applications in the transition of the energy supply system to renewable energy sources, in which hydrogen is expected to play a prominent role. This contribution describes theoretical results for cross second virial coefficients of several binary mixtures, the development and validation of a path integral Monte Carlo code for the simulation of quantum gases, and the current status of the experimental tasks.

We apply the methodology of Lustig, with which rigorous expressions for all thermodynamic properties can be derived in any statistical ensemble, to derive expressions for the calculation of thermodynamic properties in the path integral formulation of the quantum-mechanical isobaric–isothermal (NpT) ensemble. With the derived expressions, thermodynamic properties such as the density, speed of sound, or Joule–Thomson coefficient can be calculated in path integral Monte Carlo simulations, fully incorporating quantum effects without uncontrolled approximations within the well-known isomorphism between the quantum-mechanical partition function and a classical system of ring polymers. The derived expressions are verified by simulations of supercritical helium above the vapor–liquid critical point at selected state points using recent highly accurate ab initio potentials for pairwise and nonadditive three-body interactions. We observe excellent agreement of our results with the most accurate experimental data for the density and speed of sound and a reference virial equation of state for helium in the region where the virial equation of state is converged. Moreover, our results agree closer with the experimental data and virial equation of state than the results of semiclassical simulations using the Feynman–Hibbs correction for quantum effects, which demonstrates the necessity to fully include quantum effects by path integral simulations. Our results also show that nonadditive three-body interactions must be accounted for when accurately predicting thermodynamic properties of helium by solely theoretical means.

This report describes how the insights from the two previous studies led to a newly designed viscosity sensor that centers around a torsionally vibrating piezoelectric quartz cylinder. The main features of the sensor are line conductor electrodes for improved piezoelectric excitation of the torsional vibration of the quartz cylinder and a novel suspension of the cylinder with significantly reduced vibrational losses. The quartz cylinder itself was machined with higher accuracy and much reduced surface roughness than before. The resulting sensor is more compact, easier to assemble, and offers greater access to the liquid whose viscosity is to be determined. The sensor was incorporated and calibrated in an experimental manifold for automated measurements in a wide temperature range from 200 to 420 K with pressures up to 100 MPa. The performance of the sensor is assessed by a detailed uncertainty analysis and validated by measurements of the aromatic hydrocarbon toluene, whose viscosity is considered to be known at standard reference quality. Representative measurement results for most of the experimental temperature range are presented at standard atmospheric pressure, while results for the entire pressure range are reported at two temperatures, 303.15 and 393.15 K, at which comparisons with literature data are possible. They confirm that with an achieved 0.2% the uncertainty development goal of the sensor of less than 1% has been exceeded and is approximately by an order of magnitude improved over previous such sensors, while the repeatability of the new sensor is 0.02%.

We report comprehensive and accurate measurements of the speed of sound in neon. These measurements were carried out by a double-path-length pulse-echo technique and cover the temperature range between 200 K and 420  K with pressures up to 100 MPa. The standard uncertainties are 1.9 mK in temperature, 22 parts in 10^6 in pressure and 35 parts in 10^6 in speed of sound. The third and fourth acoustic virial coefficients of neon were derived from the speed of sound data in the temperature range of the measurements by fitting a fourth-order acoustic virial expansion in pressure with the second acoustic virial coefficient constrained from first-principles calculations. To support our claimed uncertainty, we determined the ratio M/γ_0 between the molar mass M and the ideal-gas heat capacity ratio γ_0 of the neon sample with a relative standard uncertainty of 7.7 parts in 10^6 by additional speed of sound measurements using a spherical resonator at 273.16 K.

Vapor–liquid equilibria and thermodynamic properties of saturated argon and krypton were calculated by semi-classical Monte Carlo simulations with the NpT + test particle method using ab initio potentials for the two-body and nonadditive three-body interactions. The NpT + test particle method was extended to the calculation of second-order thermodynamic properties, such as the isochoric and isobaric heat capacities or the speed of sound, of the saturated liquid and vapor by using our recently developed approach for the systematic calculation of arbitrary thermodynamic properties in the isothermal–isobaric ensemble. Generally, the results for all simulated properties agree well with experimental data and the current reference equations of state for argon and krypton. In particular, the results for the vapor pressure and for the density and speed of sound of the saturated liquid and vapor agree with the most accurate experimental data for both noble gases almost within the uncertainty of these data, a level of agreement unprecedented for many-particle simulations. This study demonstrates that the vapor–liquid equilibrium and thermodynamic properties at saturation of a pure fluid can be predicted by Monte Carlo simulations with high accuracy when the intermolecular interactions are described by state-of-the-art ab initio pair and nonadditive three-body potentials and quantum effects are accounted for.