Marginal stability, heterogeneous force distribution and vibrational properties in hard sphere glasses

When the temperature of a liquid is decreased in such a way that crystallization is avoided, the resulting material is a glass or an amorphous solid. There are two sets of open questions concerning this subject. The first is a central problem in soft and condensed matter physics that aims understanding how a liquid becomes rigid at the glass transition. Although there are many scenarios to describe this transition, even in the simplest glasses - hard spheres -, what confers mechanical stability at large density is a matter of debate. The second set of questions is related to the properties of the amorphous material which is generated in this transition: when in the glass phase the material present different properties in respect to its crystal phase, as for example transport and vibrational properties.

In this work these two set of questions will be addressed. First, it will be shown that the glass of hard spheres can be mapped in a network of points connected with nonlinear springs [1]. Using this idea, it is shown that to understand quantitatively stability of a glass at a microscopic level, the presence of weakly interacting pairs of particles must be included. This approach allows us to predict various non-trivial scaling behaviour of the elasticity and vibrational properties of glasses. Some of these exponents are tested numerically and experimentally in colloidal glasses. It also gives a spatial interpretation to recent calculations in high-dimensions [2].

[1] C. Brito and M. Wyart, J. Chem. Phys. 131, 024504 (2009)

[2] E. DeGiuli, E. Lerner, C. Brito, M. Wyart , Proc. Natl. Acad. Sci. USA, 111, 17054 (2014)