STOCHASTIC MODEL FOR CONSTRUCTING A CONDUCTIVE CLUSTER FORMED BY CARBON NANOTUBES ON A COMPOSITE GRID
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Abstract
A two-dimensional stochastic model has been developed for constructing and investigating the percolation threshold of a conductive cluster. The cluster is formed by carbon nanotubes embedded in a polymer dielectric matrix.
In this work, a two-dimensional stochastic model was developed, which, based on an analogy with Buffon's needle problem, simulates the random distribution of carbon nanotubes in the polymer matrix and detects the formation of conductive clusters on a planar grid. A systematic analysis of the influence of key parameters on the probability of percolation was carried out: it was shown that increasing the number of nanotubes accelerates the transition to a conductive state, while elongation of the nanotubes reduces the critical filler concentration required to form a continuous path. The size effect was also investigated: as the grid size increases, the transition from non-conductive to conductive state becomes smoother. For the analytical description of the percolation curve, the approximation using the hyperbolic tangent was replaced with a logistic function, which simplifies the estimation of the system’s threshold parameters.
The obtained results make it possible to evaluate the critical parameters necessary for the emergence of electrical conductivity in composite nanomaterials based on carbon nanotubes.
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References
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