Glass elasticity from particle trajectories

TL;DR

This paper uses particle trajectory data from experiments and simulations to analyze the elastic properties of colloidal glasses, clarifying rigidity emergence and defining the glass transition temperature through continuum elastic theory.

Contribution

It introduces a method to determine wave-vector-dependent spring constants and uses continuum elastic theory to identify the glass transition temperature from particle trajectories.

Findings

Rigidity emerges in colloidal glasses as temperature decreases.

The static shear modulus becomes finite at the glass transition.

A precise method to determine $T_g$ from elastic properties is proposed.

Abstract

Using positional data from video-microscopy of a two-dimensional colloidal system and from simulations of hard discs we determine the wave-vector-dependent normal mode spring constants in the supercooled fluid and glassy state, respectively. The emergence of rigidity and the existence of a displacement field in amorphous solids is clarified. Continuum elastic theory is used in the limit of long wavelengths to analyze the bulk and shear modulus of this amorphous system as a function of temperature. The onset of a finite static shear modulus upon cooling marks the fluid/solid transition. This provides an opportunity to determine the glass transition temperature $T_g$ in an intuitive and precise way.