Dynamics of Liquid CD4from Cold-Neutron Scattering

The scattering of 4.1 Å neutrons by liquid C${\mathrm{D}}_4$ at 95°K has been studied at several angles of scattering covering the first liquid diffraction peak. The spectra are strikingly different from those observed in liquid C${\mathrm{H}}_4$ with the quasielastic peak being very much more prominent than in liquid C${\mathrm{H}}_4$ at large scattering angles. The width of the quasielastic peak shows an oscillatory behavior as a function of momentum transfer, with a minimum at the diffraction peak. Expressions are derived for the scattering of slow neutrons by a monomolecular system under the assumption of no vibrational scattering and weak anisotropic forces. In applying the theory to liquid C${\mathrm{D}}_4$, two models (A and B) are considered. In both models, the single-particle translational motions are assumed to have a simple diffusion behavior, while collective motions are described by an intermediate scattering function with a structure-dependent damping. The rotations are treated as free in model A and as hindered in model B. The first- and second-order relaxation functions for the hindered rotator, are derived from infrared and Raman data, respectively, as suggested by Sears. Both models make essentially the same predictions for the quasielastic widths, and these are found to be in fair agreement with experiment. Examination of the various contributions to the total spectrum in both models shows that the differences in the spectra for C${\mathrm{D}}_4$ and C${\mathrm{H}}_4$ are partly due to intramolecular effects which reduce the rotational inelastic intensity and enhance the quasielastic, and partly due to intermolecular effects which also boost the quasielastic intensity. It is further found that spectra predicted by the two models are very nearly the same, unlike the case of liquid C${\mathrm{H}}_4$, where hindering of the rotation influences the spectrum considerably. This is a consequence of the fact that rotational effects appear mainly via incoherent scattering, which is small in the case of C${\mathrm{D}}_4$. Comparison with experiment shows that our models are able to explain qualitatively the important differences between the spectra for C${\mathrm{H}}_4$ and C${\mathrm{D}}_4$. Quantitative agreement is, however, lacking, and this indicates the need for improved models for the center-of-mass motions.