Molecular-shape- and size-independent power-law dependence of percolation thresholds on radius of gyration in ideal molecular systems

TL;DR

This study demonstrates that in ideal molecular systems, the percolation threshold depends on the radius of gyration through a power-law relation, independent of molecular shape, and is governed by a scale-free parameter.

Contribution

It introduces a universal power-law relation for percolation thresholds based on radius of gyration, regardless of molecular shape, and identifies a key scale-free parameter.

Findings

Percolation thresholds decrease as a power-law function of radius of gyration.

Molecular shape does not affect the percolation threshold when volume and radius are fixed.

A scale-free parameter (ratio of radius of gyration to cube root of volume) determines the threshold.

Abstract

Three-dimensional single-component ideal gas systems composed of model homogeneous rigid molecules in various molecular shapes and sizes are simulated by a molecular Monte Carlo simulation technique. We reveal that percolation thresholds of such single-component systems result in, when the molecular volume is fixed, power-law decreasing functions of the radius of gyration (gyradius) of the molecules. The systems with the same parameter set of the molecular volume and radius of gyration, but in different molecular shapes, show the identical value of the percolation threshold. Moreover, we also reveal that a dimensionless scale-free parameter, which is the ratio between the radius of gyration and real cube root of the molecular volume, uniquely determines the percolation threshold.