Ideal glass transitions for hard ellipsoids

For hard ellipsoids of revolution we calculate the phase diagram for the idealized glass transition. Our equations cover the glass physics in the full phase space, for all packing fractions and all aspect ratios $X_0.$ With increasing aspect ratio we find the idealized glass transition to become primarily driven by orientational degrees of freedom. For needlelike or platelike systems the transition is strongly influenced by a precursor of a nematic instability. We obtain three types of glass transition line. The first one $\left({\phi }_c^{\mathrm{}\left(B\right)\mathrm{}}\right)$ corresponds to the conventional glass transition for spherical particles which is driven by the cage effect. At the second one $\left({\phi }_c^{{(B}^{\prime })}\right),$ which occurs for rather nonspherical particles, a glass phase is formed that consists of domains. Within each domain there is a nematic order where the center of mass motion is quasiergodic, whereas the interdomain orientations build an orientational glass. The third glass transition line $\left({\phi }_c^{\mathrm{}\left(A\right)\mathrm{}}\right)$ occurs for nearly spherical ellipsoids where the orientational degrees of freedom with odd parity, e.g., $180°$ flips, freeze independently from the positions.