What do we learn from the local geometry of glass-forming liquids?

We examine the local geometry of a simulated glass-forming polymer melt. Using the Voronoi construction, we find that the distributions of Voronoi volume $P({v}_{V})$ and asphericity $P(a)$ appear to be universal properties of dense liquids, supporting the use of packing approaches to understand liquid properties. We also calculate the average free volume $⟨{v}_{f}⟩$ along a path of constant density and find that $⟨{v}_{f}⟩$ extrapolates to zero at the same temperature ${T}_{0}$ that the extrapolated relaxation time diverges. We relate $⟨{v}_{f}⟩$ to the Debye-Waller factor, which is measurable by neutron scattering.