Site-Percolation Threshold of Carbon Nanotube Fibers: Fast Inspection of Percolation with Markov Stochastic Theory

Abstract

We present a site-percolation model based on a modified FCC lattice, as well as an efficient algorithm of inspecting percolation which takes advantage of the Markov stochastic theory, in order to study the percolation threshold of carbon nanotube (CNT) fibers. Our Markov-chain based algorithm carries out the inspection of percolation by performing repeated sparse matrix-vector multiplications, which allows parallelized computation to accelerate the inspection for a given configuration. With this approach, we determine that the site-percolation transition of CNT fibers occurs at p_c =0.1533+-0.0013, and analyze the dependence of the effective percolation threshold (corresponding to 0.5 percolation probability) on the length and the aspect ratio of a CNT fiber on a finite-size-scaling basis. We also discuss the aspect ratio dependence of percolation probability with various values of p (not restricted to p_c).

21 pages, 6 figures

References in corpus (4)

• Quantum thermal transport in nanostructures
• Scaling of Resistance and Electron Mean Free Path of Single-Walled Carbon Nanotubes
• Weighted percolation on directed networks
• Stacked triangular lattice: Percolation properties

Cited by in corpus (4)

• Percolation thresholds on triangular lattice for neighbourhoods containing sites up-to the fifth coordination zone
• Universality of random-site percolation thresholds for two-dimensional complex non-compact neighborhoods
• Lower limit of percolation threshold on a square lattice with complex neighborhoods
• Percolation thresholds for discrete-continuous models with non-uniform probabilities of bond formation