George Birnbaum

Far‐Infrared Collision‐Induced Absorption in CO2. I. Temperature Dependence

Accurate measurements of collision‐induced absorption in CO2 are made at a number of temperatures in the range from −u200940 to 60°C in the wavelength region 7–250 cm−1. Direct evidence for the separation of the pure translational band from the rotational–translational band is obtained at all temperatures. This and other aspects of the band shape are discussed. Over the entire temperature range, the experimentally determined Kramers–Kronig integral is found to be in good agreement with the theoretical value, i.e., the static dielectric constant. This agreement is achieved only when the contribution of the quadrupole–quadrupole energy in the radial distribution function, of particular importance for CO2 because of its large quadrupole moment, is calculated accurately. A value of the quadrupole moment is obtained, (4.5u2009±u20090.2)10−26 esu, which is in satisfactory agreement with that obtained by the method of Buckingham and Disch, which does not depend on a knowledge of intermolecular force constants. Induction due...

Determination of Models for Collision‐Induced Polarizability by the Method of Moments

The form of the function giving the variation of the induced anisotropic polarizability with interatomic separation in a pair of interacting atoms is obtained by the method of moments. The spectrum of depolarized light in gaseous Ar, Kr, and Xe and the second Kerr virial coefficient of Ar, used to convert relative to absolute scattered light intensities, are used in this analysis. The coefficients in the model for the induced anisotropy, β (x)=(6A2σ−3)u2009[x−3+(y/6) x−p], where A is the polarizability of a single isolated atom, σ is the atomic diameter, and x=r/σ, are for Xe, for example, p=9.6 and y/6=−0.957. These results clearly demonstrate that short‐range interactions have an important effect on the induced anisotropy.

Far infrared collision‐induced absorption in gaseous methane. II. Determination of the octupole and hexadecapole moments

The octupole and hexadecapole moments of methane are obtained by comparing the experimental and theoretical zeroth spectral moment and the integrated absorption coefficient of the collision‐induced far infrared rotation–translation spectrum. The data presented in Part I of this series and the theory summarized in this paper give the values Ω2/σ7 = 4.67×10−16 erg and Φ2/σ9 = 1.56×10−16 erg, from which we obtain the octupole and hexadecapole moments, respectively, ‖Ω‖ = (2.22±0.12) ×10−34 esu⋅cm3 and ‖Φ‖ = (4.8±0.5) ×10−42 esu⋅cm4 for σ=3.758 A. An argument is advanced as to why it is preferable to report these results in the form Ω2/σ7 and Φ2/σ9, where σ is the molecular diameter parameter appearing in the potential function.

Far-infrared absorption in H2 and H2-He mixtures

Abstract Collision-induced absorption in the translation-rotation band of H 2 and H 2 -He mixtures has been measured from 20 to 900 cm -1 at 77.4, 195 and 292 K. To establish the accuracy of the results, various sources of error are investigated. The zeroth and first spectral moments are evaluated from experiment and theory for H 2 at the various temperatures. To obtain theoretical moments consistent with the experimental values, the quantum pair-distribution function must be used. The major portion of the experimental moments can be accounted for by quadrupole-induced dipoles in H 2 pairs. The remaining portion is attributable to an anistropic overlap interaction, although its magnitude depends on the value of the molecular parameters required to calculate the quadrupole contribution.

Pure rotational spectrum of HCl and DCl in liquid SF6

Abstract The far infrated spectrum of dilute solutions of HCl and DCl dissolved in liquid SF 6 at 0°c is observed in the frequency region 30 cm −1 . A broad absorption band is obtained for DCl which is in excellent agreement with the band envelope defined by the relative integrated intensity of each of the pure rotational transitions in the gas phase. The HCl spectrum, however, shows clearly resolved lines superimposed on a broad absorption band. These lines are readily identifiable with the pure rotational lines in the gas phase.

Far‐Infrared Collision‐Induced Absorption in CO2. II. Pressure Dependence in the Gas Phase and Absorption in the Liquid

The pressure dependence of the collision‐induced spectrum in CO2 at room temperature in the frequency region 7–250 cm−1 is measured throughout this region as a function of density, ρa, from 0–85 amagat. At each frequency the density variation of the absorption is fitted by α(ν, ρa)u2009=u2009ρa2α2(ν)u2009+u2009ρa3α3(ν) to obtain values of α2(ν) and α3(ν). The coefficient α2(ν) and its temperature dependence is discussed in the previous paper of this series. The coefficient α3(ν) is negative in sign and has a band shape considerably sharper than that found for α2(ν). The Kramers–Kronig integral π−2∫α3(ν)ν−2dν is in reasonable agreement with the theoretical value of the third dielectric virial coefficient. Absorption in liquid CO2 is measured at 0°C and compared with the band spectrum obtained in the gas phase at the same temperature. The peak intensity in the liquid spectrum occurs at a frequency 25 cm−1 higher than in the gas phase. The integrated intensity ρa−2∫α(ν)dν in the liquid is 3.2u2009±u20090.1u2009×u200910−4 cm−2·amagat−2, whe...

Far‐Infrared Spectra of Gaseous and Liquid SF6

The far‐infrared absorption spectrum of SF6 in the gaseous state was measured at 25°C at pressures from 3 to 19 atm in the wavelength region 12–250 cm−1. The absorption of liquid SF6 in this region was measured at 0°C and −40°C. The strongest bands in the gas phase are centered roughly at 50 cm−1, and approximately at 94 and 173 cm−1. Bands centered at approximately 55, 90, and 150 cm−1 were observed in the liquid phase. Since the intensity of the band at 50 cm−1 varies as density squared, it is ascribed to collision induction. The bands at 94 and 173 cm−1 in the gas phase (considered to be the same bands at 90 and 150 cm−1 in the liquid phase) vary linearly with density and are ascribed to the difference vibrations, respectively, ν4u2009−u2009ν5 and ν5u2009−u2009ν6. The hexadecapole moment of SF6 was estimated from the integrated intensity of the collision‐induced band in the gas.

Pure Rotational Spectrum and Electric Dipole Moment of CH3D

The pure rotational spectrum of CH3D in the ground vibrational and electronic state has been observed using a far‐infrared grating spectrometer. This spectrum is of particular interest because the electric dipole moment μ arises entirely from an isotopic substitution. Ten distinct lines have been observed in the frequency range from 40 to 120 cm−1, and have been identified with the (Ju2009→u2009Ju2009+u20091) transitions for the rotational levels Ju2009=u20095u2009−u200914. For the (6u2009→u20097) line, the absolute intensity and the linewidth were determined by a curve of growth method. It was found that, for this line, the dipole moment μu2009=u2009(5.68u2009±u20090.30)u2009×u200910−3D and the broadening parameter γ0u2009=u2009(0.075u2009±u20090.012) cm−1/amagat. This measurement constitutes the first correct experimental determination of the dipole moment of CH3D. By making further intensity measurements on other lines, it was shown that, to within 6%, μ is independent of J in the range 5u2009≤u2009Ju2009≤u200912. A detailed account of the experimental methods used to make the intensity measureme...

Constant Acceleration Approximation in Collision‐Induced Absorption

In terms of the constant acceleration approximation, introduced by Oppenheim and Bloom in 1961, the line shapes occurring in collision‐induced absorption have a simple form that is suitable for numerical calculation. To test the reliability of the constant acceleration approximation in describing the appropriate time dependent distribution function, we compare a particular line shape in this approximation with the direct computer calculation of McQuarrie and Bernstein. A similar comparison with the experimental results of Bosomworth and Gush is also made. From both comparisons it follows that the constant acceleration approximation, as applied to a short range intermolecular interaction, is poor at all frequencies.

Dielectric Relaxation at High Frequencies

A theory of dielectric relaxation is presented which is based on using an interpolation function to represent a classical correlation function which is analytic at the origin and becomes exponential at sufficiently long times. The Fourier transform of this interpolation function is a relatively simple analytical function of frequency which has the Debye character at low frequencies but decreases essentially exponentially in the high‐frequency wing. The parameters in the correlation function are discussed in terms of relaxation due to reorientational diffusion. Our model predicts practically the same absorption in the microwave region and somewhat more absorption in the far‐infrared region as theories of dielectric relaxation which include the effect of rotational inertia, but in agreement with experiment predicts very much smaller absorption in the infrared region.