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Connectedness percolation in polydisperse rod systems: A modified Bethe lattice approach
1Department of Chemistry, Edwin C. Jahn Laboratory, SUNY-ESF, One Forestry Drive, Syracuse, New York 13210, USA. apchatte@esf.edu
The Journal of Chemical Physics
|June 17, 2010
Summary
This study models percolation in rod-like particles with varying lengths. Results show length distribution impacts connectivity, while average length determines the percolation threshold.
Area of Science:
- Physics
- Materials Science
- Statistical Mechanics
Background:
- Percolation theory describes the formation of connected clusters in disordered systems.
- Understanding particle systems is crucial for materials design and fluid dynamics.
- Length polydispersity in rod-like particles introduces complexity to their collective behavior.
Purpose of the Study:
- To develop a mean-field theory for the percolation behavior of rod-like particles with length polydispersity.
- To analyze how particle length distribution affects percolation properties.
- To determine the relationship between system parameters and percolation characteristics.
Main Methods:
- A mean-field theory approach was employed.
- An analogy to site percolation on a modified Bethe lattice was utilized.
- Calculations estimated percolation threshold, probability, and backbone fraction.
Main Results:
- Percolation probability and backbone fraction are highly sensitive to the rod length distribution.
- The percolation threshold is primarily determined by the weight-averaged rod length.
- Model calculations provide quantitative predictions for these properties.
Conclusions:
- The developed mean-field theory effectively captures percolation phenomena in polydisperse rod systems.
- Rod length distribution significantly influences the connectivity and structural properties of particle clusters.
- Weight-averaged rod length is a key parameter for predicting the onset of percolation.
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