Local Anisotropy of Fluids using Minkowski Tensors

TL;DR

This paper demonstrates that Minkowski tensors effectively quantify local anisotropy in various fluid models, revealing how anisotropy varies with free volume and structural transitions.

Contribution

It introduces Minkowski tensors as a robust tool to measure local anisotropy in simple fluids, extending their application beyond granular systems.

Findings

Local anisotropy increases from vapor to solid phases.

Anisotropy decreases monotonously with increasing free volume.

Indices are sensitive to structural transitions in fluids.

Abstract

Statistics of the free volume available to individual particles have previously been studied for simple and complex fluids, granular matter, amorphous solids, and structural glasses. Minkowski tensors provide a set of shape measures that are based on strong mathematical theorems and easily computed for polygonal and polyhedral bodies such as free volume cells (Voronoi cells). They characterize the local structure beyond the two-point correlation function and are suitable to define indices $0\leq \beta_\nu^{a,b}\leq 1$ of local anisotropy. Here, we analyze the statistics of Minkowski tensors for configurations of simple liquid models, including the ideal gas (Poisson point process), the hard disks and hard spheres ensemble, and the Lennard-Jones fluid. We show that Minkowski tensors provide a robust characterization of local anisotropy, which ranges from $\beta_\nu^{a,b}\approx 0.3$ for vapor phases to $\beta_\nu^{a,b}\to 1$ for ordered solids. We find that for fluids, local anisotropy decreases monotonously with increasing free volume and randomness of particle positions. Furthermore, the local anisotropy indices $\beta_\nu^{a,b}$ are sensitive to structural transitions in these simple fluids, as has been previously shown in granular systems for the transition from loose to jammed bead packs.