**Self-Assembly of Graphene Nanoribbons Induced by the Carbon Nanotube**

Hui Li, Yifan Li and Wei Chen

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/67413

#### **Abstract**

In this chapter, a series of molecular dynamics simulations have been carried out to explore the self‐assembly of graphene nanoribbons (GNRs) induced by the single‐walled carbon nanotubes (SWCNTs). Simulation results show that GNRs can insert and wrap SWCNTs spontaneously, forming helical configurations and maximizing the π‐π stacking area between graphene and SWCNT. The helical configuration takes the least amount of energy and achieves the maximum occupancy. The size and function group of GNR and SWCNT should meet the required conditions to guarantee the self‐assembly in insertion and wrapping processes. Several GNRs can spiral in an SWCNT simultaneously, and two formulas have come up in this study to estimate the quantity threshold for multiple GNR spiralling. The rolled GNRs can also spontaneously insert into SWCNTs, forming a DNA‐like double helix, or collapsing to a linked double graphitic nanoribbon and wrap‐ ping in a helical manner around the tube.

**Keywords:** molecular dynamics simulation, graphene nanoribbon, structural evolution, helical configuration, self‐assembly

### **1. Introduction**

Carbon materials, especially the carbon nanotube and graphene, have attracted tremendous attention on the theoretical research and the potential applications because of their unique configurations and excellent performances. The cylindrical SWCNT possessing a large spe‐ cific surface area and hollow interior could act as 'molecular straws' capable of absorbing dipolar molecules by capillary action [1]. Over the past decade, the self‐assembled systems [2, 3] relied on the special hollow structure of cylindrical SWCNTs, are an attractive class of new bio‐inspired nanomaterial for biologists and material scientists, because the self‐assembled

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materials may not only be designed to be highly dynamic, displaying adaptive and self‐heal‐ ing properties, but could also help gain an understanding of the rules that govern biomolecule assembly processes [4]. In the self‐assembly process, the hollow interior of SWCNT can serve as nanometre‐sized moulds and templates [5] to control the configuration of other materi‐ als, or as a protective layer [6] to prevent the filler from oxidation and shape fragmentation. The physical and chemistry properties of the heterostructure are expected to be modified due to the interaction between SWCNT and exotic materials [7]. Thus, filling SWCNTs with chosen fillers can produce one‐dimensional nanostructures with exciting new applications [8]. A wide array of fillers, including various metal atoms [9], halides [10], C60 [11, 12] and polyacetylene [13], were found to be filled into the SWCNT, with novel configurations and properties. Strano et al. [14] found that water molecules displayed different phase transition temperatures when confined in the nanotube. C60 [15] or other spherical metallofullerenes [16] were distributed evenly along the axial direction after self‐assembling into the SWCNT just as beans distributed in pod, while those linear fillers such as DNA [17] and polyacetylene [13] were easy to insert into or wrap the SWCNT spontaneously with an interesting helical configuration.

Recently, our studies [18, 19] indicated that GNRs, the material with unique optical, mag‐ netic and electrical properties [20–23], have been succeeded in spontaneously and spirally wrapping and inserting into the SWCNT. GNRs possess intriguing electronic structures ranging from semiconducting to half‐metallic, depending on their geometry and dimen‐ sions. Thus, the helical composite structures formed by two novel carbon materials are expected to have excellent properties, such as high carrier mobility and high mechanical strength, to be used in microcircuit interconnectors, nanoelectronic devices and nanosen‐ sors [24–26]. And a convincing model on the interaction between the GNR and SWCNT may inspire great efforts in theoretical studies, synthesis and chemical modifications which focus on their electronic, biological, chemical and even magnetic properties. In this chap‐ ter, the self‐assembly behaviour of GNRs, especially multiple GNRs, induced by SWCNT is studied in detail, while the mechanism and influencing factors of self‐assembly are also described, providing an opportunity for a comprehensive and satisfactory understanding of how to control the composite structure of this SWCNT‐GNR nanomaterial hybrid. This discovery is of great significance in the exploration of the properties of the GNR‐SWCNT system and may expand the applications of GNR and SWCNT in extensive fields involving medicine, chemistry, biology and even fuel cells. The perfect GNR helix in SWCNT may be used to control the band gap of various GNT‐based nanodevices, which will pave the way for the progress of nanoelectronics.

#### **2. Simulation method**

Molecular dynamics method is used to study the self‐assembly behaviour of GNRs induced by SWCNTs. The force field of condensed‐phase optimized molecular potentials for atomistic simulation studies (COMPASS) [27] is applied to model the atomic interaction. COMPASS is an ab initio force field which has been parameterized and validated using condensed‐phase properties, various ab initio calculations and experimental data, with a functional form that includes covalent terms, van der Waals interactions and electrostatic forces. The aim of the force field is to achieve high accuracy in predicting the properties of complex mixtures [28] and it has been widely used due to its potential to obtain reasonable results in terms of the mechanical properties of CNTs [29, 30]. The van der Waals energy is described by LJ‐96 function [28] in COMPASS force field, the functional forms of which is listed as: *<sup>E</sup>* <sup>=</sup> *<sup>D</sup>* <sup>0</sup>[<sup>2</sup> ( *R* \_0 *R* ) 9 <sup>−</sup> <sup>3</sup> ( *R* \_0 *R* ) 6 ], where *D*<sup>0</sup> = 0.064 Kal/mol and *R*<sup>0</sup> = 4.01Å [31, 32]. The temperature in this paper is chosen as 298 K in the NVT canonical ensemble (number of particles, vol‐ ume and temperature are constant). Andersen thermostat [33] is employed to control the thermodynamic temperature and generate the correct statistical ensemble by allowing the simulated system to exchange energy with a 'heating bath'. The speed of atoms follows the Maxwell‐Boltzmann distribution and the time integration is undertaken using the velocity Verlet algorithm. The simulation time step is 1.0 fs. Each system is simulated for sufficient time to reach equilibrium. Trajectory is recorded every 5.0 ps for further analysis. The GNR with the opening edge is prepared by cutting the parallel sheet of block graphite.
