Mean-field theory of orientational ordering in rigid rotor models with identical atoms: spin conversion and thermal equilibration

Abstract

In coupled rotor models which describe identical rotating nuclei the nuclear spin states restrict the possible angular momenta of each molecule. There are two mean-field approaches to determining the orientational phase diagrams in such systems. In one the nuclear spin conversion times are assumed to be instantaneous in the other infinite. In this paper the intermediate case, when the spin conversion times are significantly slower than those of rotational time scales, but are not infinite on the time-scale of the experiment, is investigated. Via incorporation of the configurational degeneracy it is shown that in the thermodynamic limit the mean-field approach in the intermediate case is identical to the instantaneous spin conversion time approximation. The total entropy can be split into configurational and rotational terms. The mean-field phase diagram of a model of coupled rotors of three-fold symmetry is also calculated in the two approximations. It is shown that the configurational entropy has a maximum as a function of temperature which shifts to lower temperatures with increasing order.