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 Gotze, Sjogren, 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[sub lm,l[sup (prime)]m[sup (prime)]]([bold q],t) of the tensorial one-particle density rho [sub lm]([bold q],t), which contains the orientational degrees of freedom for l(greater-than)0. Application of the mode coupling approximation to the memory kernel results into a closed set of equations for S[sub lm,l[sup (prime)]m[sup (prime)]]([bold q],t), which requires the static correlators S[sub lm,l[sup (prime)]m[sup (prime)]]([bold q]) as the only input quantities. The corresponding MCT equations for the nonergodicity parameters f[sub l][sup m](q)(equivalent)f[sub lm,lm](q[bold e][sub 3]) are solved for a system of dipolar hard spheres by restricting the values for l to 0 and 1. Depending on the packing fraction cursive-phi 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 f[sub 0][sup 0](q) and f[sub 1][sup 1](q) for q=0, we may conclude that the corresponding relaxation strength of the alpha peak of the compressibility can be much smaller than the corresponding strength of the dielectric function