Theoretical characterization of the topology of connected carbon nanotubes in random networks

In recent years, a lot of attention has been paid to carbon nanotube (CNT) networks and their applications to electronic devices. Many studies concentrate on the percolation threshold and the characterization of the conduction in such materials. Nevertheless, no theoretical study has yet attempted to characterize the CNT features inside finite size CNT networks. We present a theoretical approach based on geometrical and statistical considerations. We demonstrate the possibility of explicitly determining some relations existing between two neighbor CNTs and their contact efficiency in random networks of identical CNTs. We calculate the contact probability of rigid identical CNTs and we obtain a probability of 0.2027, which turns out to be independent of the CNT density. Based on this probability, we establish also the dependence of the number of contacts per CNT as a function of the CNT density. All the theoretical results are validated by very good agreement with Monte Carlo simulations.