Abstract
Understanding the mechanical properties of glasses remains elusive since
the glass transition itself is not fully understood, even in well studied
examples of glass formers in two dimensions. In this context we demonstrate:
(i) a direct evidence for a fast increase of a typical length scale as the
glass transition is approached. (ii) an identification of the glass
transition with the disappearance of fluid-like regions and (iii) the
appearance in the glass state of fluid-like regions when mechanical strain
is applied. These fluid-like regions are associated with the onset of
plasticity in the amorphous solid. The relaxation time which increases
enormously upon the approach to the glass transition is related
quantitatively to the increasing length scale. The relaxation mechanisms
upon quenching from high temperatures are also studied where the aging
occurs via events which are localized in time and space. A statistical
mechanics model is worked out where the glass disorder is encoded via the
Voronoi tessellation. The theory provides, without free parameters, an
explanation of the glass transition phenomenology, including the
identification of jamming and and the appearance of a low temperature
crystalline phase.
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