Fast hopping of deuterated methyl groups

Abstract

Methyl groups in solids reorientate at high temperature in a manner that is essentially dependent on the temperature of the host lattice but not on its phonon spectrum. The reorientation rate of CH3 groups can be easily predicted by evaluating a thermal average over all excited torsional states of the expectation values of the angular momentum, thus making it a calculable function of the hindering potential barrier V and temperature T. The aim of the experiments described was to extend the theory for fully deuterated compounds containing methyl groups; and consequently see how the temperature dependent reorientation rates of CD3 could be predicted from measurements of CH3 tunnel splittings of the analogous compound at low temperature. Theory-and the subsequent experiments-show how it is not necessary to carry out the full calculation again; instead, it is sufficient to calculate the energy levels of a CH3 group in a potential of height 2V and then divide these energies by two. The expectation values of the angular velocities are also reduced by a factor of two. The above can be summarised into what the authors call the 'rule of two', which may be stated by saying that a CD3 group hops at half the rate of a CH3 group of twice the barrier height at twice the temperature. The result is that the same set of curves of hopping rate ( tau -1) against inverse temperature (T-1) and potential barrier height VH of CH3, can be used for CD3 of one halves the ( tau -1) and doubles the (T-1) scales and replaces VH by 2VH. Agreement with this theory is shown to be satisfactory; the data were obtained using the time-of-flight (IN5) and back-scattering (IN10) spectrometers of the Institute Laue-Langevin, Grenoble, for four fully deuterated samples (acetone, nitromethane, iodoethane and toluene). The measurements fall in a region of very fast hopping motion.