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![Geometrical structure of the linear N 2 O molecule (in its electronic ground state) with nitrogen atoms depicted as the smaller (blue) balls and the oxygen atom as the larger (red) ball. Internuclear separations for the ground state are displayed as resulting from spectroscopy [37,38]. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)](profile/Wim-Ubachs/publication/320754691/figure/fig2/AS:614145091198985@1523435008479/Geometrical-structure-of-the-linear-N-2-O-molecule-in-its-electronic-ground-state-with.png)
Geometrical structure of the linear N 2 O molecule (in its electronic ground state) with nitrogen atoms depicted as the smaller (blue) balls and the oxygen atom as the larger (red) ball. Internuclear separations for the ground state are displayed as resulting from spectroscopy [37,38]. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
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High signal-to-noise and high-resolution light scattering spectra are measured for nitrous oxide (N$_2$O) gas at an incident wavelength of 403.00 nm, at 90$^\circ$ scattering, at room temperature and at gas pressures in the range $0.5-4$ bar. The resulting Rayleigh-Brillouin light scattering spectra are compared to a number of models describing in...
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... with m the mass, I the moment of inertia and d an effective diameter of the molecule. The moment of inertia I may be derived from the rotational constant as obtained in microwave spectroscopy of the molecule for which a value of B = 12561 MHz was reported [39], corresponding to a moment of inertia of I = 66.7 × 10 −47 kg·m 2 for N 2 O [37,38]. In Fig. 2 the geometrical structure of the N 2 O molecule is depicted with internuclear separations between nitrogen and oxygen atoms. The distance between outer atoms is 2.3 ˚ A, but the effective diameter d of the molecule is determined in a number of studies to be higher: d = 3.85Å 85Å [40] and d = 3.828Å828Å [41]. This results in a value of ...
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... the values obtained from the kinetic Tenti-S6 model, by a factor of six. Hence relaxation phenomena may be underestimated in the description. The relaxation phenomena are not well described by the assumptions made for collisions to occur between object of spherical nature. In view of the geometrical structure of the N 2 O molecule as displayed in Fig. 2 this is not surprising. Lastly, it is mentioned that the discrepancy resulting from the rough sphere model is not just based on the non-sphericity of the N 2 O geometrical structure. The model predicts a value for the heat capacity ratios of γ = 4/3, which is slightly smaller than the value γ = 7/5 for nitrous oxide. Therefore, the ...
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... the present study four of such prevailing models are applied to the scattering of the nitrous oxide molecule which is special for a number of reasons. N 2 O is a polyatomic molecule for which the linear N-N-O structure (see also Fig. 2) does not provide a symmetry point as is the case for CO 2 [31]. While a number of recent studies were performed to model RB-scattering in diatomic molecules [17,18,7,12] the quest is now to investigate RB-scattering in polyatomic molecules of different symmetry and sizes. N 2 O is a convenient target in view of its large scattering ...
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... a value for the shear viscosity of η s = 1 . 48 × 10 −5 Pa · s the rough sphere model derives a value for internal relaxation ef- fects, represented as a bulk viscosity via the relation [20] η b = η s 6 + 13 κ 60 κ (6) resulting in a value of η b = 0 . 92 × 10 −5 Pa · s. Model spectra for RB scattering in N 2 O were subsequently calculated using the for- malism presented by Marques et al. [25] , Marques and Kremer [42] . Results are displayed in Fig. 1 in terms of deviations be- tween experimental and modeled spectral profiles. Large discrep- ancies arise in particular at the high pressure values where relax- ation phenomena play an important role. Numerically the rough sphere model delivers a value for the bulk viscosity η b that is sig- nificantly smaller than the values obtained from the kinetic Tenti- S6 model, by a factor of six. Hence relaxation phenomena may be underestimated in the description. The relaxation phenomena are not well described by the assumptions made for collisions to oc- cur between object of spherical nature. In view of the geometrical structure of the N 2 O molecule as displayed in Fig. 2 capacity ratios of γ = 4 / 3 , which is slightly smaller than the value γ = 7 / 5 for nitrous oxide. Therefore, the rough sphere model pre- dicts a wrong value for the speed of sound and this is crucial in producing good agreement with ...
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... this model, a simple relaxation term δ( f − f r ) is used to re- place the collision operator in Boltzmann equation with f ( r , v ) the six-dimensional position-velocity distribution and f r represent- ing a reference distribution function. Here the coefficients satisfy the conservation laws, while the collisional transfer of momentum and energy agree with the full Boltzmann description. The rough sphere model considers the interaction between the translational and rotational degrees of freedom and regards the collisions be- tween molecules as hard spheres, thereby ignoring the effect of vibrational relaxation. This model is built on a dimensionless mo- ment of inertia κ = 4 I/md 2 , with m the mass, I the moment of in- ertia and d an effective diameter of the molecule. The moment of inertia I may be derived from the rotational constant as obtained in microwave spectroscopy of the molecule for which a value of B = 12561 MHz was reported [39] , corresponding to a moment of inertia of I = 66 . 7 × 10 −47 kg · m 2 for N 2 O [37,38] . In Fig. 2 the ge- ometrical structure of the N 2 O molecule is depicted with inter- nuclear separations between nitrogen and oxygen atoms. The dis- tance between outer atoms is 2.3 ˚ A, but the effective diameter d of the molecule is determined in a number of studies to be higher: [41] . This results in a value ...
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... the present study four of such prevailing models are applied to the scattering of the nitrous oxide molecule which is special for a number of reasons. N 2 O is a polyatomic molecule for which the linear N-N-O structure (see also Fig. 2 ) does not provide a sym- metry point as is the case for CO 2 [31] . While a number of re- cent studies were performed to model RB scattering in diatomic molecules [7,12,17,18] the quest is now to investigate RB scattering in polyatomic molecules of different symmetry and sizes. N 2 O is a convenient target in view of its large scattering cross section [26] ...
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... For the internal heat capacity c i we adopt a result obtained in previous studies on the modeling of RB-scattering, where it was shown that the vibrational relaxation is frozen under the high-frequency conditions of Brillouin scattering. This was discussed in results for SF 6 [34], N 2 O [35] and CO 2 [32]. Hence, only rotational degrees of freedom are considered, and for SF 6 c i = 3R/2 is taken, and c i = R for N 2 O and CO 2 . ...
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... A celebrated example of a model representation of RBscattering profiles in the kinetic regime is the Tenti model [7,8], which was applied to describe the spectral profiles of a variety of gases, such as N 2 [9], CO 2 [10,11], and N 2 O [12]. However, the Tenti model was not developed for modeling the RB spectra of mixture gases. ...
... While for single-component gases the Brillouin side peaks become more pronounced when increasing the gas pressure, such as was observed for pure SF 6 gas [43], for CO 2 [11], and for N 2 O [12] in the present case with increasing pressure of the collisional partner in a mixture, the reverse is true. The addition of light-mass constituents to the gas causes the RBS profile to exhibit less pronounced Brillouin side peaks. ...
The spectral distribution of light scattered by microscopic thermal fluctuations in binary mixture gases was investigated experimentally and theoretically. Measurements of Rayleigh-Brillouin spectral profiles were performed at a wavelength of 532 nm and at room temperature, for mixtures of SF6−He,SF6−D2, and SF6−H2. In these measurements, the pressure of the gases with heavy molecular mass (SF6) is set at 1 bar, while the pressure of the lighter collision partner was varied. In view of the large polarizability of SF6 and the very small polarizabilities of He, H2, and D2, under the chosen pressure conditions these low mass species act as spectators and do not contribute to the light scattering spectrum, while they influence the motion and relaxation of the heavy SF6 molecules. A generalized hydrodynamic model was developed that should be applicable for the particular case of molecules with heavy and light disparate masses, as is the case for the heavy SF6 molecule, and the lighter collision partners. Based on the kinetic theory of gases, our model replaces the classical Navier-Stokes-Fourier relations with constitutive equations having an exponential memory kernel. The energy exchange between translational and internal modes of motion is included and quantified with a single parameter z that characterizes the ratio between the mean elastic and inelastic molecular collision frequencies. The model is compared with the experimental Rayleigh-Brillouin scattering data, where the value of the parameter z is determined in a least-squares procedure. Where very good agreement is found between experiment and the generalized hydrodynamic model, the computations in the framework of classical hydrodynamics strongly deviate. Only in the hydrodynamic regime both models are shown to converge.
... A celebrated example of a model representation of RB-scattering profiles in the kinetic regime is the Tenti-model [7,8], which was applied to describe the spectral profiles of a variety of gases, such as N 2 [9], CO 2 [10,11], and N 2 O [12]. However, the Tenti-model was not developed for modeling the RB-spectra of mixture gases. ...
... While for single-component gases the Brillouin side peaks become more pronounced when increasing the gas pressure, such as was observed for pure SF 6 gas [43], for CO 2 [11], and for N 2 O [12] in the present case with increasing pressure of the collisional partner in a mixture, the reverse is true. The addition of light-mass constituents to the gas causes the RBS-profile to exhibit less pronounced Brillouin side peaks. ...
The spectral distribution of light scattered by microscopic thermal fluctuations in binary mixture gases was investigated experimentally and theoretically. Measurements of Rayleigh-Brillouin spectral profiles were performed at a wavelength of 532 nm and at room temperature, for mixtures of SF$_6-$He, SF$_6-$D$_2$ and SF$_6-$H$_2$. In these measurements, the pressure of the gases with heavy molecular mass (SF$_6$) is set at 1 bar, while the pressure of the lighter collision partner was varied. In view of the large polarizability of SF$_6$ and the very small polarizabilities of He, H$_2$ and D$_2$, under the chosen pressure conditions these low mass species act as spectators and do not contribute to the light scattering spectrum, while they influence the motion and relaxation of the heavy SF$_6$ molecules. A generalized hydrodynamic model was developed that should be applicable for the particular case of molecules with heavy and light disparate masses, as is the case for the heavy SF$_6$ molecule, and the lighter collision partners. Based on the kinetic theory of gases, our model replaces the classical Navier-Stokes-Fourier relations with constitutive equations having an exponential memory kernel. The energy exchange between translational and internal modes of motion is included and quantified with a single parameter $z$ that characterizes the ratio between the mean elastic and inelastic molecular collision frequencies. The model is compared with the experimental Rayleigh-Brillouin scattering data, where the value of the parameter $z$ is determined in a least-squares procedure. Where very good agreement is found between experiment and the generalized hydrodynamic model, the computations in the framework of classical hydrodynamics strongly deviate. Only in the hydrodynamic regime both models are shown to converge.
... One approach is the Tenti-model [3,47] providing a rather straightforward representation of the scattering profile in terms of six moments connected to transport coefficients. The Tenti approach has been shown to work well in the case of diatomic and linear molecules [14,17,40,51], where usually the bulk viscosity is included in the model as a fit parameter. Another approach for the kinetic regime dealt with collisions of molecules treated as rough spheres, which well described the RB-spectrum of SF 6 [52]. ...
... This holds in particular for the bulk viscosity, which was found to deviate by some four orders of magnitude for the case of CO 2 between measurements performed at acoustic frequencies, i.e. in the MHz range, or light scattering experiments for GHz scattering frequencies [17,36,53]. Also for the case of the thermal conductivity such a frequency dependence was found, specifically for N 2 O [51]. This phenomenon is associated with relaxation of the internal degrees of freedom of the molecule, i.e., rotations and vibrations [5,53]. ...
Spontaneous Rayleigh-Brillouin scattering (RBS) experiments have been performed in air for pressures in the range 0.25 - 3 bar and temperatures in the range 273 - 333 K. The functional behaviour of the RB-spectral profile as a function of experimental parameters, such as the incident wavelength, scattering angle, pressure and temperature is analyzed, as well as the dependence on thermodynamic properties of the gas, as the shear viscosity, the thermal conductivity, the internal heat capacity and the bulk viscosity. Measurements are performed in a scattering geometry detecting at a scattering angle $\theta=55.7^\circ$ and an incident wavelength of $\lambda_i=532.22$ nm, at which the Brillouin features become more pronounced than in a right angles geometry and for ultraviolet light. For pressure conditions of 1 - 3 bar the RB-spectra, measured at high signal-to-noise ratio, are compared to Tenti-S6 model calculations and values for the bulk viscosity of air are extracted. Values of $\eta_b$ are found to exhibit a linear dependence on temperature over the measurement interval in the range $1.0 - 2.0 \times 10^{-5}$ Pa$\cdot$s. A temperature dependent value is deduced from a collection of experiments to yield: $\eta_{\rm b} = (0.86 \times 10^{-5}) + 1.29 \times 10^{-7} \cdot (T - 250)$. These results are implemented in model calculations that were verified for the low pressure conditions ($p < 1$ bar) relevant for the Earth's atmosphere. As a result we demonstrate that the RB-scattering spectral profiles for air under sub-atmospheric conditions can be generated via the Tenti-S6 model, for given gas-phase and detection conditions ($p$, $T$, $\lambda_i$, and $\theta$), and for values for the gas transport coefficients.
... Since the vibrational relaxation is "frozen" in RBS experiments, the internal degrees of freedom only correspond to the rotational degrees of freedom. Similarly, in the determination of effective thermal conductivity κ e the contribution from vibrational degrees of freedom should be subtracted (Wang et al. 2017(Wang et al. , 2018: ...
... Therefore, this example further confirms that, when applying the gas kinetic model, the internal degrees of freedom should be the rotational degrees of freedom d r , and the total thermal conductivity should only take into account the contribution from the translational and rotational motions. Indeed, in the analysis of experimental RBS spectra it was concluded that the vibrational relaxation was found to be frozen in various molecular gases (Wang et al. 2017(Wang et al. , 2018. ...
... In this case, even at relatively large values of y, different values of f tr lead to different RBS spectra (the difference is most prominent at the relative intensity of the central Rayleigh peak), see Figure 5. This is because only the translational and rotational heat conductivities are reflected in RBS spectra (Wang et al. 2017(Wang et al. , 2018, and their sum varies with f tr even when f u is fixed. ...
Although the thermal conductivity of molecular gases can be measured straightforwardly and accurately, it is difficult to experimentally determine its separate contributions from the translational and internal motions of gas molecules. Yet this information is critical in rarefied gas dynamics as the rarefaction effects corresponding to these motions are different. In this paper, we propose a novel methodology to extract the translational thermal conductivity (or equivalently, the translational Eucken factor) of molecular gases from the Rayleigh-Brillouin scattering (RBS) experimental data. From the numerical simulation of the Wu et al. (2015b) model we find that, in the kinetic regime, in addition to bulk viscosity, the RBS spectrum is sensitive to the translational Eucken factor, even when the total thermal conductivity is fixed. Thus it is not only possible to extract the bulk viscosity, but also the translational Eucken factor of molecular gases from RBS light scattering spectra measurements. Such experiments bear the additional advantage that gas-surface interactions do not affect the measurements. By using the Wu et al. model, bulk viscosities (due to the rotational relaxation of gas molecules only) and translational Eucken factors of N 2 , CO 2 and SF 6 are simultaneously extracted from RBS experiments.
... One approach is the Tenti-model [20,21] providing a rather straightforward representation of the scattering profile in terms of six moments connected to transport coefficients. The Tenti approach has been shown to work well in the case of diatomic and linear molecules [16,[22][23][24], where usually the bulk viscosity is included in the model as a fit parameter. Another approach for the kinetic regime dealt with collisions of molecules treated as rough spheres, which well described the RB-spectrum of SF 6 [25]. ...
... This holds in particular for the bulk viscosity, which was found to deviate by some four orders of magnitude for the case of CO 2 between measurements performed at acoustic frequencies, i.e. in the MHz range, or light scattering experiments for GHz scattering frequencies [17,22,40]. Also for the case of the thermal conductivity such a frequency dependence was found, specifically for N 2 O [23]. This phenomenon is associated with relaxation of the internal degrees of freedom of the molecule, i.e. rotations and vibrations [17,41]. ...
Spontaneous Rayleigh-Brillouin (RB) scattering experiments have been performed in air for pressures in the range 0.25–3 bar and temperatures in the range 273–333 K. The functional behaviour of the RB-spectral profile as a function of experimental parameters, such as the incident wavelength, scattering angle, pressure and temperature is analysed, as well as the dependence on thermodynamic properties of the gas, as the shear viscosity, the thermal conductivity, the internal heat capacity and the bulk viscosity. Measurements are performed in a scattering geometry detecting at a scattering angle θ = 55.7 ∘ and an incident wavelength of λ i = 532.22 nm , at which the Brillouin features become more pronounced than in a right angles geometry and for ultraviolet light. For pressure conditions of 1–3 bar the RB-spectra, measured at high signal-to-noise ratio, are compared to Tenti-S6 model calculations and values for the bulk viscosity of air are extracted. Values of η b are found to exhibit a linear dependence on temperature over the measurement interval in the range 1.0 -- 2.0 × 10 − 5 Pa ⋅ s . A temperature dependent value is deduced from a collection of experiments to yield: η b = ( 0.86 × 10 − 5 Pa ⋅ s ) + 1.29 × 10 − 7 ⋅ ( T − 250 ) . These results are implemented in model calculations that were verified for the low pressure conditions (p<1 bar) relevant for the Earth's atmosphere. As a result we demonstrate that the RB-scattering spectral profiles for air under sub-atmospheric conditions can be generated via the Tenti-S6 model, for given gas-phase and detection conditions (p, T, λ i , and θ), and for values for the gas transport coefficients. Spectral profiles for coherent RB-scattering in air are also computed, based on the Tenti-S6 formalism, and the predictions are compared with profiles of spontaneous RB-scattering. Finally data on RB-scattering in air, obtained under a variety of pressure, temperature, wavelength and scattering angles, are analysed in terms of universal scaling, involving the dimensionless uniformity parameter y and the dimensionless frequency x. Such scaling behaviour is shown to be well behaved for a wide parameter space and implies that RB-scattering spectra can be generated for a wide range of atmospheric applications of RB-scattering. The verification of this dimensionless scaling also shows that air can be treated as an ideal gas in the atmospheric regime, where y ≤ 1 .
... Pressure fluctuations, which can be regarded as acoustic waves, lead to Brillouin scattering, while entropy fluctuations give rise to Rayleigh-center scattering [1,2]. Many gaseous parameters can be got from SRBS spectral profile, such as temperature [3,4], pressure (density) [5], bulk viscosity [6][7][8] and so on. Coherent Rayleigh-Brillouin scattering (CRBS), which was first proposed by She et al. [9] and measured by Pan et al. [10], is stimulated by density variation from dipole forces by crossing laser beams. ...
... The gaseous bulk viscosity measured by the traditional method of ultrasonic determination is not suited for hypersound frequencies, such as CO 2 [6,11]. Therefore, SRBS or CRBS combined with related models [7,8,14,15], which can describe the Rayleigh-Brillouin scattering (RBS) spectrum, provides an alternative method to measure the gaseous bulk viscosity at hypersound frequencies. ...
In this paper, the spontaneous Rayleigh-Brillouin scattering spectra of air are simulated to study the effect of uncertainties of pressure, temperature, scattering angle and the characteristic parameter uncertainty of the Fabry-Perot interferometer on the accurate measurement of the bulk viscosity. It is found that those uncertainties have an obvious impact on the bulk viscosity measurement deviation and the bulk viscosity can be measured accurately under higher pressures (.3.0 bar). In order to obtain the accurate bulk viscosity of nitrogen, oxygen and air, the spontaneous Rayleigh-Brillouin scattering spectra are measured with the wavelength of 532 nm under pressure of 4.0-7.0 bar and at temperature from 289.0 K to 400.0 K. The linear relation between the measured bulk viscosity and temperature is established with R2 being above 0.99 for nitrogen, oxygen and air respectively. By comparison, it is found that our measured bulk viscosities mostly agree with the reported values obtained by spontaneous Rayleigh-Brillouin scattering, coherent Rayleigh-Brillouin scattering, ultrasonic determination or theoretical calculation for nitrogen, oxygen and air within 3≥P results at the same temperature. The factors arousing the differences between them are attributed to the obvious measurement error and the measured uncertainty of the bulk viscosity under low pressures and the defects in the theoretical model itself. The empirical formula for calculating the bulk viscosity for air from pure components is proposed and it can match our measured result well.
... I can be used as a means to extract the value of transport coefficients from experimental data. 5,6,26,27 The models take these transport coefficients as parameters and can be evaluated extremely quickly as the used eigensystems have only dimension 6 or 7. In fact, this procedure is the only means to obtain a value of the bulk viscosity η b at the GHz frequencies of light scattering. ...
Rayleigh-Brillouin light scattering spectra of CO2 at ultraviolet wavelengths are computed from molecular dynamics which depends on intermolecular potentials only. We find excellent agreement with state of the art experimental data. This agreement was reached in a minimal computational box with sides one scattering wavelength long and integrating the classical trajectories over 20 ns. We also find complete consistency with models based on kinetic theory, which take known values of the transport coefficients as input.
... 29 It can also be retrieved from the light scattering spectrum of molecular gases. This was demonstrated by Pan et al. 2 and recently for N 2 , O 2 , and air by Gu and Ubachs 30 and for N 2 O gas by Wang et al. 31 In light scattering, the frequencies f s involved are those of sound with wavelengths comparable to that of light, three orders of magnitude larger than the frequencies used to measure η b from ultrasound experiments. The bulk viscosity of CO 2 ...
Rayleigh-Brillouin scattering spectra of CO 2 were measured at pressures ranging from 0.5 to 4 bars and temperatures from 257 to 355 K using green laser light (wavelength 532 nm, scattering angle of 55.7°). These spectra were compared to two line shape models, which take the bulk viscosity as a parameter. One model applies to the kinetic regime, i.e., low pressures, while the second model uses the continuum, hydrodynamic approach and takes the rotational relaxation time as a parameter, which translates into the bulk viscosity. We do not find a significant dependence of the bulk viscosity with pressure or temperature. At pressures where both models apply, we find a consistent value of the ratio of bulk viscosity over shear viscosity η b /η s = 0.41 ± 0.10. This value is four orders of magnitude smaller than the common value that is based on the damping of ultrasound and signifies that in light scattering only relaxation of rotational modes matters, while vibrational modes remain "frozen."
