Mode coupling approach to the ideal glass transition of molecular liquids: Linear molecules

The mode coupling theory (MCT) for the ideal liquid glass transition, which was worked out for simple liquids mainly by G\"otze, Sj\"ogren, and their co-workers, is extended to a molecular liquid of linear and rigid molecules. By use of the projection formalism of Zwanzig and Mori an equation of motion is derived for the correlators S_lm,l^'m^'(q,t) of the tensorial one-particle density ρₗₘ(q,t), which contains the orientational degrees of freedom for $l>0.$ Application of the mode coupling approximation to the memory kernel results into a closed set of equations for S_lm,l^'m^'(q,t), which requires the static correlators S_lm,l^'m^'(q) as the only input quantities. The corresponding MCT equations for the nonergodicity parameters fₗᵐ(q)≡flm,lm(qe₃) are solved for a system of dipolar hard spheres by restricting the values for l to 0 and 1. Depending on the packing fraction {φ} and on the temperature $T,$ three different phases exist: a liquid phase, where translational (TDOF's) $(l=0)$ and orientational (ODOF's) $(l=1)$ degrees of freedom are ergodic, a phase where the TDOF are frozen into a (nonergodic) glassy state, whereas the ODOF's remain ergodic, and finally a glassy phase where both, TDOF's and ODOF's, are nonergodic. From the nonergodicity parameters f₀⁰(q) and f₁¹(q) for $q=0,$ we may conclude that the corresponding relaxation strength of the {α} peak of the compressibility can be much smaller than the corresponding strength of the dielectric function.