Density of states of colloidal glasses and supercooled liquids

The glass transition is perhaps the greatest unsolved problem in condensed matter physics: the main question is how to reconcile the liquid-like structure with solid-like mechanical properties. In solids, structure and mechanics are related directly through the vibrational density of states of the material. Here, we obtain for the first time the density of states of colloidal glasses and supercooled liquids from a normal-mode analysis of particle displacements measured using confocal microscopy. We find that the spectrum of the (non-linear) vibrations has many ‘soft’, low-frequency modes, more abundant and very different in nature from the usual acoustic vibrations of ordinary solids. This results in an anomalous low-frequency peak in the density of states which approaches zero frequency as one goes deeper into the glass. The observed soft modes are due to collective ‘swirling’ particle motions, that extend over surprisingly long length scales.