Free energy of the solid C ₆₀ fullerene orientational order-disorder transition

The free energies of the orientationally ordered crystal phase of C ₆₀ at low temperatures and the disordered crystal phase at high temperatures are calculated to an accuracy of ±0.05 kJ/mol using the expanded ensemble Monte Carlo method with the potential model of Sprik et al. [J. Phys. Chem. 96, 2027 (1992)]. The order-disorder transition temperature at zero pressure is determined directly from these free energies, and is found to be consistent with the abrupt changes in configurational energy and unit cell size also found in simulation. A modification of the potential results in predictions of the transition temperature of 257 K and the entropy change of 18.1 J/mol K at this transition, which are in good agreement with the experimental values of 260 K and 19 J/mol K, respectively. The orientational distinguishability in the ordered phase and the indistinguishability in the disordered phase lead to a contribution to the entropy difference of k In 60, with 60 being the symmetry number of C ₆₀. This quantum mechanical correction is important for the accurate prediction of the phase transition properties of the C ₆₀ crystals.