Local anisotropy of fluids using Minkowski tensors

Abstract

Statistics of the free volume available to individual particles have previously beenstudied for simple and complex fluids, granular matter, amorphous solids, andstructural glasses. Minkowski tensors provide a set of shape measures that arebased on strong mathematical theorems and easily computed for polygonal andpolyhedral bodies such as free volume cells (Voronoi cells). They characterize the localstructure beyond the two-point correlation function and are suitable to define indices0 ≤ βνa, b ≤ 1 of local anisotropy. Here, we analyze the statistics of Minkowski tensors for configurationsof simple liquid models, including the ideal gas (Poisson point process), the hard disks andhard spheres ensemble, and the Lennard-Jones fluid. We show that Minkowskitensors provide a robust characterization of local anisotropy, which ranges fromβνa, b≈0.3 for vapor phases to for ordered solids. We find that for fluids, local anisotropy decreases monotonically with increasingfree volume and randomness of particle positions. Furthermore, the local anisotropy indicesβνa, b are sensitive to structural transitions in these simple fluids, as has been previously shown ingranular systems for the transition from loose to jammed bead packs.