Curviness Percolation Threshold in Transparent, Conductive 2D Networks Consisting of Curvy Nanotubes

Two-dimensional (2D) networks consisting of one-dimensional (1D) nanoelements, such as carbon nanotubes, metal nanowires, and graphene nanoribbons, are promising candidates for next-generation flexible and transparent conductors in organic light-emitting diodes (OLEDs), solar cells, touch screens, smart windows, transparent heaters, and liquid crystal displays. They offer a replacement for indium tin oxide (ITO), a critical raw material which suffers from brittleness, scarcity, high cost, and slow deposition. Nanotube or nanowire networks also have applications in flexible electronics, such as thin film transistors, wearables, electronic skin, and internet of things (IoT) sensors, as well as memristors for neuromorphic computation.<br/> <br/>The electrical transport in nanotube networks is governed by percolation, which deals with the formation of long-range connectivity in random networks. As a result, Monte Carlo simulations need to be employed in order to compute the electrical properties of these networks. In most Monte Carlo studies, nanotubes in these networks have been modeled as straight “sticks”. However, nanotubes deposited experimentally always exhibit some degree of curviness. There has been some computational work on the density percolation threshold of carbon nanotube/nanofiber networks and nanocomposites at fixed curviness, showing that curviness increases the critical density of randomly oriented networks. However, a systematic study of the curviness percolation threshold at fixed density and its interaction with nanotube alignment is currently lacking.<br/> <br/>In this work, we utilize Monte Carlo simulations to compute the curviness percolation threshold in 2D networks consisting of curvy nanotubes. We generate curvy nanotubes using third order Bezier curves characterized by the curviness angle. We also introduce the concept of curl ratio, which is the ratio of the actual length of the nanotube to the effective straight length between its two ends. Using Monte Carlo simulations, we establish an empirical relationship between the curviness angle and the curl ratio.<br/> <br/>In order to extract the critical curviness angle and the critical curl ratio, where the 2D network undergoes an insulator-to-conductor phase transition, we first compute the percolation probability as a function of the curviness angle at fixed nanotube density. We then extract the curviness percolation threshold at different nanotube densities using finite-size scaling analysis. We find that the critical curviness angle and curl ratio increase with increasing density. We also find that there is a nanotube density below which the percolation probability is 0 regardless of the curviness angle and there is a density above which it is always 1.<br/> <br/>Alignment of nanotubes in the network, characterized by the alignment angle, is found to significantly change the curviness percolation threshold, resulting in a reversal of the percolation probability versus curviness angle curve. We find that, at a fixed intermediate density, random networks exhibit a conductor-to-insulator transition as the curviness is increased, whereas well-aligned networks exhibit an insulator-to-conductor transition.<br/> <br/>These results, which can be explained by the two competing effects of curviness, provide important insights into the electronic properties of 2D networks, films, or nanocomposites consisting of 1D nanoelements such as carbon nanotubes, metal nanowires, and graphene nanoribbons. These results also show that computational studies are an essential tool for studying the insulator-to-conductor transition in nanotube/nanowire networks, which are promising candidates for a wide range of applications such as flexible transparent conductors, thin film transistors, and resistive switching memory.