Rotational Diffusion and Reorientations in Molecular Crystals

In plastic crystals (“rotary phases”) there is a dynamic disorder of the orientations of the molecules. But reorientations can exist without disorder (jumps between equivalent orientations, e.g. benzene), and on the other hand frozen disorder can be found (exceptions to Nernst principle, e.g. CO). The rate of the motion is relatively easy to measure thanks to several techniques, but its precise nature is harder to determine; this is because distance‐sensitive methods are few. Numerous types of models for the motion have been proposed. Most of those designed for liquids can be envisaged, with the probable exception of the free volume models (numerical illustration). It is stressed that an Arrhenius law for the rate is not really a proof of the physical existence of potential barriers. An inevitably arbitrary classification of models is discussed as follows: Free rotation: at the classical limit the rate should be of the order of ( k T/I ) 1/2 . It is doubtful if this can be found in nature, because usually the molecular largest “diameter” is slighly greater than the intermolecular distance. Collision‐interrupted rotations (e.g. J‐diffusion). This situation is unlikely, because at solid densities the interactions are continuously acting. Classical rotational diffusion: the necessary fast fluctuating random torques would be provided by numerous phonon interactions via large anharmonicities. Here the molecules are most of the time trapped in potential wells, with large‐angle jumps inbetween. They perform more or less damped librations in each well (this can be detected through far IR absorption or neutron inelastic scattering whereas the jump rate can be obtained by numerous methods, including neutron quasi‐elastic scattering which provide also informations on jump angles). In case 4) the wells are randomly oriented, whereas they are fixed and are more or less related by the lattice site symmetry‐group in case 5). The two cases can be distinguished by time‐averaging methods, i.e. diffraction experiments. Case 5), the site model, seems often valid, and has been unambigously verified in at least two instances. Composite models have also been proposed. Group theory is useful for computing the decay rates of various pertinent correlation functions. Finally an important but hardly touched upon question is evoked: that of the correlation of the orientational motion of neighbouring molecules. The process for group‐theoretically computing pertinent time correlation functions, in the site model, together with results for three situations of cubic symmetry, are given in an Appendix.