Discontinuous Shear Modulus Determines the Glass Transition Temperature

A solid-amorphous or crystalline-is defined by a finite shear modulus while a fluid lacks such. We thus experimentally investigate the elastic properties of a colloidal glass former near the glass transition: Spectroscopy of vibrational excitations yields the dispersion relations of longitudinal and transverse phonons in the glassy state. From the long-wavelength limit of the dispersion relation, we extract the bulk and the shear modulus. As expected, the latter disappear in a fluid and we measure a clearly resolved discontinuous behavior of the elastic moduli at the glass transition. This not only determines the transition temperature T-G of the system but also directly addresses recent discussions about elasticity during vitrification. We show that low-frequency excitations in our system are plane waves such that continuum elasticity theory can be used to describe the macroscopic behavior.