Dynamics of the rotational degrees of freedom in a supercooled liquid of diatomic molecules

Using molecular-dynamics computer simulations, we investigate the dynamics of the rotational degrees of freedom in a supercooled system composed of rigid, diatomic molecules. The interaction between the molecules is given by the sum of interaction-site potentials of the Lennard-Jones type. In agreement with mode-coupling theory (MCT), we find that the relaxation times of the orientational time correlation functions $C_1^{\mathrm{}\left(s\right)\mathrm{}}\mathrm{}\left(t\right),$ $C_2^{\mathrm{}\left(s\right)\mathrm{}}\mathrm{}\left(t\right),$ and $C_1\mathrm{}\left(t\right)\mathrm{}$ show at low temperatures a power law with the same critical temperature $T_c,$ which is also identical to the critical temperature for the translational degrees of freedom. In contrast to MCT, we find, however, that for these correlators the time-temperature superposition principle does not hold well and also the critical exponent γ depends on the correlator. For $C_l^{\mathrm{}\left(s\right)\mathrm{}}$ with $l=3,\dots ,6\mathrm{}$ this principle does hold. We also study the temperature dependence of the rotational diffusion constant $D_r$ and demonstrate that at high temperatures $D_r$ is proportional to the translational diffusion constant $D$ and when the system starts to become supercooled the former shows an Arrhenius behavior, whereas the latter exhibits a power-law dependence. We discuss the origin for the difference in the temperature dependence of $D$ (or the relaxation times of $C_l^{\mathrm{}\left(s\right)\mathrm{}}$) and $D_r.$ Finally, we present results that show that at low temperatures 180° flips of the molecule are an important component of the relaxation dynamics for the orientational degrees of freedom.