Percolation of aligned rigid rods on two-dimensional square lattices

Area of Science:

• Statistical Physics
• Materials Science
• Computational Physics

Background:

• Percolation theory describes the formation of connected clusters in random systems.
• Understanding how particle shape and alignment influence network formation is crucial for materials design.

Purpose of the Study:

• To investigate the percolation behavior of aligned rigid rods (kmers) on 2D square lattices.
• To analyze the impact of kmer size and alignment on percolation thresholds and critical phenomena.

Main Methods:

• Numerical simulations were employed to study percolation.
• Finite-size scaling analysis was used to determine critical behavior.
• Irreversible deposition of aligned kmers on L×L lattices was simulated.

Main Results:

• The percolation threshold decreases as kmer size increases.
• Aligned rods show higher percolation thresholds compared to isotropic rods.
• The system belongs to the random percolation universality class for all kmer sizes.
• Aligned kmers exhibit nonuniversal critical behavior, unlike isotropic rods.

Conclusions:

• Kmer size and alignment significantly influence percolation thresholds and critical behavior.
• Aligned rod systems display distinct nonuniversal critical phenomena compared to isotropic systems.
• The findings contribute to understanding network formation in anisotropic systems.