Topological Characterization of Rigid-Nonrigid Transition across the Frenkel Line

TL;DR

This paper provides a topological and geometrical analysis of the Frenkel line in supercritical fluids, revealing how structural percolation relates to the transition from rigid to non-rigid states.

Contribution

It introduces a topological framework to interpret the Frenkel line, linking structural percolation to the rigid-nonrigid transition in supercritical fluids.

Findings

Percolation of solid-like structures occurs above the crossover densities.

Structural interpretation of the Frenkel line is achieved through topological classification.

The transition is explained via instantaneous configurations, not just atomic dynamics.

Abstract

The dynamics of supercritical fluids, a state of matter beyond the gas-liquid critical point, changes from diffusive to oscillatory motions at high pressure. This transition is believed to occur across a locus of thermodynamic states called the Frenkel line. The Frenkel line has been extensively investigated from the viewpoint of the dynamics, but its structural meaning is not still well understood. This letter interprets the mesoscopic picture of the Frenkel line entirely based on a topological and geometrical framework. This discovery makes it possible to understand the mechanism of rigid/non-rigid transition based not on the dynamics of individual atoms, but on their instantaneous configurations. The topological classification method reveals that the percolation of solid-like structures occurs above the rigid-nonrigid crossover densities.