Percolation thresholds of randomly rotating patchy particles on Archimedean lattices

Area of Science:

• Statistical Mechanics
• Materials Science
• Computational Physics

Background:

• Percolation theory describes the formation of connected clusters.
• Patchy particles offer tunable interaction sites for self-assembly.
• Understanding particle connectivity on lattices is crucial for designing materials.

Purpose of the Study:

• To investigate the percolation thresholds (χc) of randomly rotating patchy particles on 11 Archimedean lattices.
• To determine the influence of patch number and lattice geometry on percolation.
• To establish general rules for predicting percolation thresholds for particles with varying patch configurations.

Main Methods:

• Monte Carlo simulations were employed to model particle interactions and cluster formation.
• The critical polynomial method was used for precise estimation of percolation thresholds.
• Symmetry analysis was applied to understand the role of particle and lattice geometry.

Main Results:

• Percolation thresholds (χc) for one-patch particles correlate with site percolation thresholds, indicating lattice geometry dependence.
• For multi-patch particles, lattice symmetry significantly influences χc.
• Periodic patterns in χc were observed as the number of patches increases, with specific rules governing these relationships.

Conclusions:

• The study provides precise χc estimates for various patchy disk and sphere configurations on 11 lattices.
• General rules for predicting χc based on patch number and lattice symmetry were established.
• These findings offer valuable insights for the design and understanding of connected patchy particle systems.