Test of mode coupling theory for a supercooled liquid of diatomic molecules. II.q-dependent orientational correlators

Using molecular-dynamics computer simulations, we study the dynamics of a molecular liquid by means of a general class of time-dependent correlators S_ll^'ᵐ(q,t), which explicitly involve translational (TDOF) and orientational degrees of freedom (ODOF). The system is composed of rigid, linear molecules with Lennard-Jones interactions. The q dependence of the static correlators S_ll^'ᵐ(q) strongly depends on $l,$ l^', and $m.$ The time-dependent correlators are calculated for l=l^'. A test of some of the predictions of mode coupling theory (MCT) is performed for Sₗₗᵐ(q,t) for $l=1,2$ and its self-part Sₗₗ⁽ˢ⁾ᵐ(q,t), for l=1,,6. We find a clear signature for the existence of a single temperature Tc, at which the nature of the dynamics changes significantly. In the first scaling law regime of MCT it is found that the various correlators can be fitted with the {β} correlator $G(t),$ with the exception of those with $l=1.$ Since this is true for the same exponent parameter {λ} as obtained for the TDOF, we thus find that MCT gives a consistent description of the dynamics of the TDOF as well as the one of the ODOF, with the exception of $l=1.$ This different behavior for l≠1 and $l=1$ can also be seen from the corresponding susceptibilities (χ^'')ₗₗᵐ(q,ω), which exhibit a minimum at about the same frequency ωₘᵢₙ for all q and all l≠1, in contrast to (χ^'')₁₁ᵐ(q,ω) for which ωₘᵢₙ^'≈10ωₘᵢₙ. The asymptotic regime, for which the first scaling law holds, shrinks with increasing $l.$ The second scaling law of MCT (time-temperature superposition principle) is reasonably fulfilled for l≠1 but not for $l=1.$ Furthermore, we show that the q and $(l,m)$ dependence of the self-part approximately factorizes, i.e., Sₗₗ⁽ˢ⁾ᵐ(q,t) Cₗ⁽ˢ⁾(t)Fₛ(q,t) for all $m.$