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Explosive percolation in a nanotube-based system.

Yup Kim¹, Yeo-kwang Yun, Soon-Hyung Yook

¹Department of Physics and Research Institute for Basic Sciences, Kyung Hee University, Seoul 130-701, Korea.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|January 15, 2011

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The formation of single-walled nanotube bundles involves explosive transitions, influenced by loop structures in percolation theory. These loops critically affect the transition interval, indicating a discontinuous process in nanotube bundle formation.

Area of Science:

Materials Science
Condensed Matter Physics
Nanotechnology

Background:

Understanding the formation mechanisms of single-walled nanotube (SWNT) bundles is crucial for their applications.
Percolation theory provides a framework for studying phase transitions in disordered systems.
Previous studies have not fully elucidated the role of specific processes like cluster repulsion in SWNT bundle formation.

Purpose of the Study:

To investigate the underlying mechanism governing the formation of uniform diameter single-walled nanotube bundles.
To analyze the transition nature during bundle formation using percolation theory and cluster repulsion.
To determine the influence of loops on the scaling behavior of the transition interval.

Main Methods:

Application of the cluster repulsion process to stick percolation models.

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Investigation of the scaling behavior of the transition interval (Δ).

Comparison with loopless and loop-allowed bond percolation models.

Measurement of order parameter changes during stick removal to identify hysteresis.

Main Results:

The transition during SWNT bundle formation with cluster repulsion is found to be explosive.
The scaling behavior of the transition interval (Δ) is significantly affected by loops and is not universal.
The scaling behavior of Δ for nanostick systems mirrors that of loopless bond percolation.
Hysteresis is observed in the order parameter changes, confirming a discontinuous transition.

Conclusions:

The formation of single-walled nanotube bundles via stick percolation with cluster repulsion exhibits a discontinuous, explosive transition.
The presence and nature of loops in the percolation model critically influence the transition dynamics and scaling properties.
The findings provide a deeper understanding of the self-assembly mechanisms in nanomaterials.