Dynamic arrest in a liquid of symmetric dumbbells: reorientational hopping for small molecular elongations.

We present extensive equilibrium and out-of-equilibrium molecular-dynamics simulations of a liquid of symmetric dumbbell molecules, for constant packing fraction, as a function of temperature and molecular elongation. We compute diffusion constants as well as odd and even orientational correlators. The notations odd and even refer to the parity of the order l of the corresponding Legendre l polynomial, evaluated for the orientation of the molecular axis relative to its initial position. Rotational degrees of freedom of order l are arrested if, in the long-time limit, the corresponding orientational l correlator does not decay to zero. It is found that for large elongations translational and rotational degrees of freedom freeze at the same temperature. For small elongations only the even rotational degrees of freedom remain coupled to translational motions and arrest at a finite common temperature. On the contrary, the odd rotational degrees of freedom remain ergodic at all investigated temperatures. Hence, in the translationally arrested state, each molecule remains trapped in the cage formed by its neighboring molecules, but is able to perform 180 degrees rotations, which lead to relaxation only for the odd orientational correlators. The temperature dependence of the characteristic time of these residual rotations is well described by an Arrhenius law. Finally, we discuss the evidence in favor of the presence of the type-A transition for the odd rotational degrees of freedom, as predicted by mode-coupling theory for small molecular elongations. This transition is distinct from the type-B transition, associated with the arrest of the translational and even rotational degrees of freedom for small elongations, and with all degrees of freedom for large elongations. Odd orientational correlators are computed for small elongations at very low temperatures in the translationally arrested state. The obtained results suggest that hopping events restore the ergodicity of the odd rotational degrees of freedom at temperatures far below the A transition.