Nearest-neighbor connectedness theory: A general approach to continuum percolation

Area of Science:

• Materials Science
• Physics
• Statistical Mechanics

Background:

• Electrical percolation is crucial for thin film composites with nanofillers.
• Existing theories accurately predict percolation for 3D systems but fail in 2D.
• Standard contact volume arguments and Percus-Yevick approximations are insufficient for 2D geometric percolation.

Purpose of the Study:

• Introduce a novel method for estimating continuum percolation thresholds.
• Validate the method using geometric percolation of line segments and disks in 2D.
• Address the limitations of conventional approaches in 2D systems.

Main Methods:

• Developed a new method based on simple geometric considerations and nearest-neighbor distribution.
• Investigated geometric percolation of noninteracting line segments and disks in two spatial dimensions.
• Compared results with Monte Carlo simulations.

Main Results:

• The new method accurately predicts percolation thresholds for line segments (ρc*l² ≈ 5.83 vs. simulation ≈ 5.64).
• The method also provides accurate predictions for disks (ρc*a ≈ 1.00 vs. simulation ≈ 1.13).
• Conventional methods showed significant shortcomings in predicting these thresholds.

Conclusions:

• The proposed method offers a more accurate and robust approach to estimating percolation thresholds in 2D systems.
• The nearest-neighbor distribution is key to overcoming the limitations of traditional methods.
• This work has implications for designing thin film composites with controlled electrical properties.