Abstract
Multiple distinct glass states with different dynamic and mechanical properties occur in binary hard-sphere mixtures with constituents of very disparate sizes according to the mode-coupling theory of the glass transition (MCT), distinguished by considering whether small particles remain mobile or not, and whether small particles contribute significantly to perturb the big-particle structure or not. In the idealized case, the four different glasses are separated by well-defined glass and localization transitions that give rise to higher-order singularities involving logarithmic decay laws, and to anomalous power-law–like diffusion.