Percolation probability in a system of cylindrical particles

Area of Science:

• Materials Science
• Statistical Physics
• Chemical Engineering

Background:

• Cylindrical particles like carbon nanotubes are crucial in composites, nano-fluids, and electrodes.
• These particles significantly alter material properties by forming conductive networks.
• Existing theories struggle to accurately model the complex microstructure and percolation behavior.

Purpose of the Study:

• To develop an analytical, probabilistic model for the microstructure of randomly dispersed cylindrical particles.
• To accurately predict particle contact number distribution and percolation probability.
• To establish a foundation for analytical composition-structure-property relationships in heterogeneous materials.

Main Methods:

• Developed an analytical framework for soft-core, cylindrical particles of finite aspect ratio.
• Calculated particle contact number distribution and percolation probability.
• Compared model predictions with excluded volume theory and numerical simulations.

Main Results:

• The analytical model accurately captures microstructure at arbitrary concentrations.
• The model precisely predicts percolation probability and contact number distribution.
• The developed model outperforms excluded volume theory for spherocylinders and matches numerical results.

Conclusions:

• The analytical model provides an accurate and efficient method for understanding particle network formation.
• This framework enhances predictions of material transport properties based on microstructure.
• The study lays the groundwork for developing advanced heterogeneous materials with tailored properties.