Grüneisen approach for universal scaling of the Brillouin shift in gases

Abstract

A Grüneisen relationship is defined for gases, following the formulation of the original microscopic Grüneisen ratio γ = (dlnω)/(dlnV ) for solids. In the case of gases acoustic excitations represent the modes at frequency ω to be considered. By comparing to measured Brillouin shifts in various gases (SF6, N2O, and CO2) and under various conditions of pressure and temperature, a specific value of the defined ratio γ0 = 0.064±0.004 is found to provide a universal description of the active modes in a gas. This finding of such universal gas law may find application in extrapolation of properties of ideal gases to regimes where those cannot be measured easily, like the acoustics and shocks at extremely high temperatures.

Comment on ‘Gruneisen approach for universal scaling of the Brillouin shift in gases’

“…In solid-state lattices the Grüneisen effect is associated with the anharmonicity of the atomic interaction potential. Contrary to what is stated in [1] there is no such effect in gases. Real gas molecules engaged in a collision do indeed sense an anharmonic interaction potential (the van der Waals potential), but that only enters into the continuum behavior in the form of transport coefficients.…”

“…Dash-dotted line: Grüneisen model, v ′ s = 2π fB/ksc, fB = fB 0 exp (−γ0Vm/Vm0), with Vm0 the molar volume at T = 295 K and p = 1 bar, and fB 0 the corresponding ideal gas sound frequency. In agreement with [1], the parameter γ0 = 0.06. Gray line: vs from the CO2 van der Waals gas, p = RT/(Vm − b) − a/V 2 m , with a = 3.647 × 10 5 m 6 Pa kmol −1 and b = 0.04267 m 3 kmol −1 .…”

“…In a recent paper Liang et al [1] associate the Rayleigh-Brillouin spectrum of scattered light in dilute gases with the Grüneisen effect, a phenomenon rooted in solid state physics, which describes the change of phonon frequency due to compression. Alternatively, the Grüneisen effect is the change of specific heat with compression, as quantified by the Grüneisen ratio Γ,…”

“…The marriage between two contexts-the phonon dispersion relation and sound dispersion in a gas-led Liang et al [1] to propose equation ( 2) as a relation between the sound frequency and pressure in Rayleigh-Brillouin scattering. With the additional assumption that the Grüneisen ratio Γ itself is s from peak positions of the Tenti model for these spectra [3,5].…”

“…It agrees with the measured Brillouin shift f B , but it is consistent with the classic continuum equations, without invocation of anharmonicity, and without invocation of a pressure-dependent velocity of sound. As in [1], the peak positions f B were determined 'through peak reading' . A slightly more refined estimate of f B can be done through fitting an analytical model to the spectrum [4].…”