Raman and infrared study of vibrational and rotational relaxations

Abstract

Our data on the area-ratio of the split components of the Ag Raman line in potash alum show a clear departure from the Boltzmann distribution at temperatures below 150 K. Modification of the phonon-induced transition rates by a temperature-independent rate ? (see (20)), explains our observations quite well. It is suggested that ? has its origin in the cooperative behaviour of the reorientation of sulphate ions, specifically a cooperation of the 'flip-flop' type. The small value of ? implies that the coupling between sulphate ions is weak but is nevertheless important in deciding the population ratio below 150 K. The downward trend of the theoretical curve in figure 4 at the low-temperature end is noteworthy. It would be interesting to extend the present measurements down to liquid helium temperatures to see if such a trend is actually observed; such experiments are currently under planning. It is also pertinent to mention that orientational disorder similar to that in X-alums is seen in a large number of nitrates, nitrites and carbonates (Brooker 1978a, b and references therein). In the case of KNO?, Brooker (1978b) has specifically noted a discrepancy similar to that observed by us (see our figure 4) in regard to the area-ratio of the split components. Quite possibly our model may apply to KNO? also. For a quantitative assessment, however, more accurate experimental data is necessary. In analyzing infrared and Raman experiments on rotational relaxation in fluids, one often finds the data to lie close to the predictions of the M-model than that of the J-model but the behaviour is sufficiently complex, and a scheme which interpolates smoothly between the J- and M-limits (Chapter 6) is not adequate for a satisfactory understanding of the data. In such cases one normally resorts to either the M-prescription or certain memory function schemes. I consider both these routes unsatisfactory from a fundamental point of view as no reasonable basis can be provided either for the ansatz used in the M-model or for the construction of the memory kernels. The analysis proposed here lends a basic meaning to the M-ansatz with the aid of a simple-minded but plausible extension of the ordinary M-model. Quite recently, there has been renewed activity in the area of rotational diffusion of molecules based on Langevin equation for the angular coordinates of a rotor (Ornstein and Hiller 1930). In this connection, it has been speculated that it may be possible to simulate the behaviour of the M-model by means of certain nonlinear Langevin equations. We have restricted our treatment in this paper to the dipole correlation function. The extension needed to compute the Raman correlation function (U?u, U?u) is straightforward. One has to deal now with the rotational operator associated with angular momentum L = 2. Equation (8) is still valid except that the exponent on the right-hand side is a 5 × 5 matrix in the Raman case. The extensions for the Raman correlation function in the generalized model as well as extension of the present analysis to molecules of other symmetries (e.g., symmetrical and spherical rotors) will be carried out in future.