  We investigate the translational and rotational relaxation dynamics of a
crowded two-dimensional system of monodisperse Penrose kites, in which
crystallization, quasi-crystallization, and nematic ordering are suppressed,
from low to high area fractions along the metastable ergodic fluid branch.
First, we demonstrate a decoupling between both the translational and the
rotational diffusion coefficients and the relaxation time: the diffusivities
are not inversely proportional to the relaxation time, neither in the
low-density normal liquid regime nor in the high-density supercooled regime.
Our simulations reveal that this inverse proportionality breaks in the normal
liquid regime due to the Mermin-Wagner long-wavelength fluctuations and in the
supercooled regime due to the dynamical heterogeneities. We then show that
dynamical heterogeneities are mainly spatial for translational degrees of
freedom and temporal for rotational ones, that there is no correlation between
the particles with the largest translational and rotational displacements, and
that different dynamical length scales characterize the translational and the
rotational motion. Hence, despite the translational and the rotational
glass-transition densities coincide, according to a mode-coupling fit,
translations and rotations appear to decorrelate via different dynamical
processes.
