Percolation thresholds for polydisperse circular disks: a lattice-based exploration.

Area of Science:

• Physics
• Materials Science
• Statistical Mechanics

Background:

• Understanding percolation phenomena is crucial in various scientific fields.
• The influence of particle shape, size distribution, and orientation on percolation is complex.
• Previous studies often focused on simpler geometries or monodisperse systems.

Purpose of the Study:

• To calculate the percolation threshold for polydisperse systems of circular disks.
• To investigate the effects of isotropic and perfectly aligned (nematic) orientations.
• To compare results with existing theoretical approaches like integral equations.

Main Methods:

• Utilizing an analogy to a lattice model for percolation calculation.
• Expressing results in terms of moments of the distribution function of disk radii.
• Comparing findings with integral equation approaches.

Main Results:

• Percolation threshold is highly sensitive to polydispersity in disk radii.
• For monodisperse systems, the threshold plateaus at large aspect ratios.
• Percolation threshold for aligned disks consistently exceeds that for isotropic disks.

Conclusions:

• Polydispersity and orientational order are critical factors determining percolation thresholds.
• The lattice model analogy provides a robust framework for analyzing these systems.
• Findings offer insights into the behavior of complex particulate materials.