  Systems with a high degree of size polydispersity are becoming standard in
the computational study of deeply supercooled liquids. In this work we perform
a systematic analysis of continuously polydisperse fluids as a function of the
degree of polydispersity within the framework of the Mode-Coupling Theory of
the glass transition (MCT). Our results show that a high degree of
polydispersity tends to stabilize the liquid phase against vitrification, the
magnitude of which depends on the shape of the polydispersity distribution.
Further, we report on a separation between the localization lengths of the
smallest and largest particles. A diameter-resolved analysis of the
intermediate scattering functions reveals that this separation significantly
stretches the relaxation patterns, which we quantitatively study by an analysis
of the dynamical exponents predicted by the theory. Our observations have
strong implications for our understanding of the nature of dynamical
heterogeneities and localization lengths in continuously polydisperse systems.
These results suggest that the dynamics of the smallest particles is of central
importance to understand structural relaxation of continuously size
polydisperse fluids, already in the mildly supercooled regime where MCT is
usually applicable.
