Reference measurements of hydrogen's dielectric permittivity

Abstract

We used a quasi-spherical cavity resonator to measure the relative dielectric permittivity ε _r of H₂ at frequencies from 2.4 to 7.3 GHz, at pressures up to 6.5 MPa, and at the temperatures 273 K and 293 K. The resonator was calibrated using auxiliary measurements of ε _r(p, T) for helium together with the accurate ab initio values of helium's dielectric permittivity. The measurements determine accurate values of hydrogen's molecular electric polarizability and its temperature dependence. At 273 K, we obtained = (8.9568 ± 0.0008) × 10⁻⁴¹ F m² (all uncertainties reported here are one standard uncertainty), which agrees with the value (8.9566 ± 0.0026) × 10⁻⁴¹ F m² that was obtained by combining Rychlewski's ab initio calculations with estimates of rotational level populations. Our results yield the temperature dependence = × (1.1 ± 0.3) × 10⁻⁵ K⁻¹, which agrees with the calculated value × 1.0 × 10⁻⁵ K⁻¹. Our data also determine hydrogen's second dielectric virial coefficient, = (0.03 ± 0.05) cm³ mol⁻¹, a property that has not yet been calculated.

Keywords:

• hydrogen
• dielectric permittivity
• polarizability
• ab initio
• microwave resonator

Acknowledgements

The authors thank John Hurly for his thermophysical property calculations, Jim Mehl and Allan Harvey for calculations of the ab initio values of hydrogen's second virial coefficient, and Laurent Pitre for assistance with the measurements. We thank Allan Harvey and Robert Berg for reading the manuscript and we appreciate their comments and suggestions. While at NIST, E.F.M. was supported in part by the American Australian Association.