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 T0 that the extrapolated relaxation time diverges. We relate <v(f)> to the Debye-Waller factor, which is measurable by neutron scattering.