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 rigi d molecules. By use of the projection formalism of Zwanzig and Mori an equation of motion is derived for the correlators S-lm,S-l'm'(q,t) of the tensorial one-particle density rho(lm)(q,t), which contains the o rientational degrees of freedom for l>0. Application of the mode coupl ing approximation to the memory kernel results into a closed set of eq uations for S-lm,S-l'm'(q,t), which requires the static correlators S- lm,S-l'm'(q) as the only input quantities. The corresponding MCT equat ions for the nonergodicity parameters f(l)(m)(q)=f(lm,lm)(qe(3)) are s olved for a system of dipolar hard spheres by restricting the values f or t to 0 and 1. Depending on the packing fraction phi and on the temp erature T, three different phases exist: a liquid phase, where transla tional (TDOF's) (l = 0) and orientational (ODOF's) (l=1) degrees of fr eedom are ergodic, a phase where the TDOF are frozen into a (nonergodi c) glassy state, whereas the ODOF's remain ergodic, and finally a glas sy phase where both, TDOF's and ODOF's, are nonergodic. From the noner godicity parameters f(0)(0)(q) and f(1)(1)(q) for q = 0, we may conclu de that the corresponding relaxation strength of the apeak of the comp ressibility can be much smaller than the corresponding strength of the dielectric function.