3-D Percolative Model-Based Multiscale Simulation of Randomly Aligned Networks of Carbon Nanotubes

A carbon nanotube (CNT) network is an aggregate of nanotubes with different properties, which is randomly deposited over a certain substrate. The way the CNTs are physically arranged gives the electrical behavior of the film that can be described by the percolation theory. However, due to the statistical nature of the problem, many aspects about the transport are still unknown. Here, we present a model based on a stochastic algorithm that can generate nonrigid solid objects in a 3-D space, emulating the typical fabrication processes involved with high fidelity. The properties of the nanotubes are extracted according to some probability distributions inferred from experimental measurements. The transport mechanisms are modeled according to the theory of 1-D ballistic channels based on the computation of the density-of-states. The behavior of the entire network is then simulated by coupling a SPICE program with an iterative algorithm that self-consistently calculates the electrostatic potential and the current flow in each node of the network. We performed several simulations of the conductivity of different networks and validated the model with experimental measurements. Our results suggest that the observed spread of the results between nominally identical networks is due to border effects, which are more pronounced in films close to their percolation threshold. We, furthermore, performed a study on the percolation threshold of different networks, finding good agreement with previous studies on the percolation theory.