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Explosive percolation in a nanotube-based system.

Using the percolation theory, we study the underlying mechanism in the formation of single-walled nanotube bundles with uniform diameter. By applying the cluster repulsion process to stick percolation, we find that the transition becomes explosive. To understand the transition nature, we first investigate the scaling behavior of transition interval Δ. By comparing the results with loopless and loop-allowed bond percolations, we find that the loops crucially affect the scaling behavior of Δ, and Δ is not universal. Moreover, the scaling behavior of Δ for the present nanostick systems is the same as that for loopless bond percolation. For more systematic studies on the transition nature, we also measure the changes in order parameter during the stick removal process and show that there exists a hysteresis. The results more clearly show that the transition of the stick system with cluster repulsion is discontinuous.