Researchers from the University of Strasbourg, France, are using a theoretical approach based on geometrical and statistical considerations to characterize two-dimensional random networks. The study examines the existing relationship between two neighbouring NTs and their contact efficiency within a random network of identical NTs.

Determining the probability of contact

First, the team focused on extracting the average probability of contact Pcont between two identical NTs starting from the geometrical parameters that define the relationship between two neighbouring NT. Pcont is evaluated to the value 0.2027 by integrating the contact probability density over the surrounding area of a NT. This quantity, together with the average values of the geometrical parameters of the problem, is found to be independent of the density D0 of NT network.

Further investigations have shown that, on the contrary, the probability of multiple contacts per NT is found to be highly dependent of the NT density D0 within the network. Indeed, the number of contacts per NT follows a two-dimensional Poissonian process of parameter λc = Pcont D0. Despite that dependency, the number of contacts per NT does not show any discontinuity around the critical density associated with the percolation threshold. The analytical calculations have been confronted to Monte Carlo simulations with very good agreement.

Understanding how clusters evolve

All of these considerations provide the basics for determining how NT clusters evolve with the density of NT within a random network and their relationship to the occurrence of percolation and on the performance of the final device. Such information should help developers to understand more about the conductive properties of devices based on two-dimensional NT networks. It's worth noting that the current model can be extended to three-dimensional networks provided that the thickness of the NT is taken into account.

The researchers presented their results in the journal Nanotechnology.