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

TL;DR

This study uses molecular dynamics simulations to test mode coupling theory predictions for q-dependent orientational correlators in a supercooled diatomic liquid, revealing both agreements and deviations across different angular momentum indices.

Contribution

It provides a detailed comparison of mode coupling theory with simulation data for orientational correlators, highlighting the theory's validity range and specific behaviors for different angular momentum modes.

Findings

Mode coupling theory's first scaling law holds for l>=2 but not for l=1.

A single critical temperature T_c influences the dynamics significantly.

The second scaling law is reasonably valid for l≠1 but not for l=1.

Abstract

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 depend on l, l' and m. The time dependent correlators are calculated for l=l'. A thorough test of the predictions of mode coupling theory (MCT) is performed for S_{ll}^m(q,t) and its self part S_{ll}^{(s)m}(q,t), for l=1,..,6. We find a clear signature for the existence of a single temperature T_c, at which the dynamics changes significantly. The first scaling law of MCT, which involves the critical correlator G(t), holds for l>=2, but no critical law is observed. Since this is true for the same exponent parameter lambda as obtained for the TDOF, we obtain a consistent description of both, the TDOF and ODOF, with the exception of l=1. This different behavior for l \ne 1 and l=1 can also be seen from the corresponding susceptibilities (chi'')_{ll}^m(q,omega) which exhibit a minimum at about the same frequency omega_{min} for all q and all l \ne 1, in contrast to (chi'')_{11}^m(q,omega) for which omega'_{min} approx 10 omega_{min} . 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 \ne 1 but not for l=1. Furthermore we show that the q- and (l,m)-dependence of the self part approximately factorizes, i.e. S_{ll}^{(s)m}(q,t) \cong C_l^{(s)}(t) F_s(q,t) for all m.