Hierarchical glass transition of hard hemidisks with local assemblies

Using computer simulation, we investigate the glass transition of a two-dimensional hard-hemidisk system. Upon increasing the packing fraction of the system, we find that the system vitrifies into a glass with local assembled discal "dimers", which are free to rotate in a collective way. The rotational mean square displacement does not exhibit the typical plateau (slowdown) like what occurs in the translational mean square displacement. This effect induces a pronounced violation of the rotational Stokes-Einstein relationship compared with the translational degree of freedom at the supercooled region. However, the obtained glass transition points in these two freedom degrees are found to be the same within the numerical accuracy, which is due to the strong positive spatial and dynamic correlation between translational and rotational slow-moving particles. Moreover, we find that the locally assembled dimers can serve as fast rotating gears facilitating the orientational relaxation in the system, and this suggests that the locally favored finite structures play an important role in the hierarchical glass transition of anisotropic colloids.