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

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