Motional Narrowing in Rotational Raman Spectra of Gaseous Nitrogen, Carbon-Monoxide Carbon-Dioxide and Hydrochloric Acid.
Abstract
The evolution of the depolarized Rayleigh and rotational Raman spectrum of gaseous N(,2), CO, CO(,2) and HCl with increasing density was studied up to almost twice liquid density. Among them, only CO(,2) showed a total collapse of the rotational structure to a single Lorentzian profile at high densities. Except for HCl, the experimental spectra of all these gases could be described reasonably well by the motional narrowing theory of McClung. However, several mathematical difficulties of this extended diffusion model were discovered. The relaxation times (tau)(,J) obtained from fitting the theory to the experimental spectra are found to be very close to the mean relaxation time obtained from the broadening coefficients of individual lines measured at low densities. A simple picture is developed based on Anderson's motional narrowing for a two-line spectrum which possesses many of the characteristics of the observed spectra and which shows us that motional narrowing of the rotational Raman bands occurs when the O and S branches overlap. This is contrary to the generally held view that one needs only adjacent lines overlapped. The fact that (tau)(,J) may be estimated from broadening coefficients and the need to overlap bands allows us to predict that motional narrowing will not occur in CO, N(,2) or HCl except at densities well beyond those reached in these experiments. This is consistent with the observations. For CO(,2), a single Lorentzian profile is obtained at high densities as predicted by classical hydrodynamics. However, our results and the very general behaviour they display due to motional narrowing clearly show that the motion of small molecules in dense fluids cannot be described in terms of classical (Debye) rotational diffusion. This too is contrary to the view generally expressed in the literature. For HCl, the anomalously large intensity at the laser frequency is explained in terms of collision induced scattering. The contribution of induced scattering to the spectrum of CO, N(,2) and CO(,2) is also estimated and found to be negligible. A second moment analysis of the observed spectra of N(,2), CO and CO(,2) was performed. While the second moments of N(,2) and CO spectra (up to 400 Amagat) stay constant and close to their corresponding low density theoretical values, the second moment of CO(,2) at 528 Amagat drops by 30% from its low density value. This indicates appreciable orientational correlation between CO(,2) molecules at this density.
- Publication:
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Ph.D. Thesis
- Pub Date:
- December 1983
- Bibcode:
- 1983PhDT........38T
- Keywords:
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- Physics: Molecular