ESPCI web site
Elastic Behavior and Homogeneous Melting of a Hard-Sphere Crystal
In this theoretical work, the elastic and dynamical properties of a solid are studied with the aim to draw the links between a perfect crystal and a glassy state. Recently, experimental groups observed a slice in a colloidal glass under a confocal microscope, in order to study its local elastic properties.
This work proves analytically that, even in the case of a crystal, observing only a slice does not lead to the elastic constants and dispersion relation of the three-dimensional solid. Molecular dynamic simulations performed on a hard-sphere crystal are consistent with the analytical results.
Moreover, this work shows numerical evidence that adding polydispersity in the sphere radii causes the elastic constants of the crystal to grow and create localized elastic modes correlated with the positions of the particles of largest and smallest cage.
Furthermore, the elastic and dynamical properties of a superheated crystal are studied. A minimal model, in the form of a reaction-like mechanism, is proposed to describe the dynamics of homogeneous melting.
The model is used to set a mean-field approach that predicts macroscopic properties of the metastable and equilibrium states. The predictions are successfully compared with molecular dynamics results.
The minimal model is also used to design kinetic Monte Carlo simulations that account for the fluctuations at the particle scale and reproduce the existence of a critical liquid droplet, defined in the same way as in molecular dynamics simulations, without having to resort to the full particle dynamics.