Idealized glass transitions for a system of dumbbell molecules

The mode-coupling theory for ideal glass transitions in simple systems is generalized to a theory for the glassy dynamics of molecular liquids using the density fluctuations of the sites of the molecule’s constituent atoms as the basic structure variables. The theory is applied to calculate the liquid-glass phase diagram and the form factors for the arrested structure of a system of symmetric dumbbells of fused hard spheres. The static structure factors, which enter the equations of motion as input, are calculated as function of the packing fraction $\phi$ and the molecule’s elongation $\zeta$ within the reference-interaction-site-model and Percus-Yevick theories. The critical packing fraction ${\phi }_c$ for the glass transition is obtained as nonmonotone function of $\zeta$ with a maximum near $\zeta =\mathrm{0.43.}\mathrm{}$ A transition line is calculated separating a small-$\zeta$-glass phase with ergodic dipole motion from a large-$\zeta$-glass phase where also the reorientational motion is arrested. The Debye-Waller factors at the transition are found to be somewhat larger for sufficiently elongated systems than those for the simple hard-sphere system, but the wave-number dependence of the glass-form factors is quite similar. The dipole reorientations for $\zeta >~0.6$ are arrested as strongly as density fluctuations with wave vectors at the position of the first sharp diffraction peak.