IOP PUBLISHING NANOTECHNOLOGY
Nanotechnology 18 (2007) 105702 (7pp) doi:10.1088/0957-4484/18/10/105702
A molecular dynamics study of the
nucleation, thermal stability and
nanomechanics of carbon nanocones
Ping-Chi Tsai
1and Te-Hua Fang
2,31Institute of Mechanical and Electromechanical Engineering, National Formosa University, Chia-Yi 621, Taiwan
2Department of Mechanical and Electromechanical Engineering, National Formosa University, Yunlin 632, Taiwan
E-mail:[email protected]
Received 4 October 2006, in final form 4 December 2006
Published 31 January 2007
Online at
stacks.iop.org/Nano/18/105702
Abstract
In this study, the nucleation mechanism of carbon nanocones is investigated
using molecular dynamics (MD) simulations and structural analyses and is
compared with that of carbon nanotubes. It is shown that the structural
stability of carbon nanocones is sensitive to the cone apex angle. Specifically,
an increase in the conical angle results in a moderate improvement in the
structural stability of the nanocone as a result of a lower strain energy in the
capped mantle. The simulation results also show that the melting temperature
of the nanocone increases with increasing conical angle. Furthermore, it is
observed that a metastable tube-like structure is formed in carbon nanocones
with a lower conical angle at temperatures ranging from 2400 to 3600 K.
Finally, the numerical simulations reveal that the mechanical properties of
carbon nanocones under nanoindentation are strongly dependent on the
conical angle. For carbon nanocones with a large conical angle, the high
deformation-promoted reactivity and reversible mechanical response have
been performed due to highly symmetrical networks.
(Some figures in this article are in colour only in the electronic version)
1. Introduction
Nanotubes made from carbon atoms are perhaps one of the greatest scientific success stories of recent years [1]. Researchers have proposed various novel methods for the fabrication of atomic-scale tubes, including chemical vapour deposition (CVD) [2], arc-discharge schemes [3], and so forth. Recently, innovative techniques for efficiently patching and jointing arrangements of sp2-bonded carbon atoms have
also been demonstrated [4–7]. It is well known that a curved graphitic surface can be created by inserting pentagons into a planar graphite surface consisting solely of hexagons. Introducing regular arrangements of pentagons into the hexagon structure facilitates the formation of such nanoscale
3 Author to whom any correspondence should be addressed.
structures as fullerenes [8] and caps on the ends of straight tubular forms [9–11]. As expected, the transient and extreme growth conditions of these species of significant derivatives, such as nanofoams [12] and nanocones [13, 14], obscure the mechanism of nucleation and self-scrolling because more significant strain energies and thermal loads invoke self-scrolling to produce a constant diameter for nanotechnology applications.
Carbon nanocones have been ideally suited for use as scanning probe tips and electron field emitters [14], due to their small size and high stiffness [15]. In general, the favourable characteristics of carbon nanocones for such applications, including a low field-emission turn-on field and a high scanning resolution, improve as the cone apex angle of the nanocone reduces. Identifying the nature of the relationship between the mechanical properties of nanocones and their
Nanotechnology 18 (2007) 105702 P-C Tsai and T-H Fang conical angle is essential because potential applications depend
on the nanocone having sufficient stability and stiffness [16]. However, a review of the available literature reveals that relatively few studies have investigated the full range of mechanical properties of carbon nanocones. Specifically, it appears that no studies have considered the structural stability characteristics of carbon nanocones under significant thermal treatments.
Accordingly, this study performs molecular dynamics (MD) simulations based on the Tersoff many-body poten-tial [17,18] to investigate how the local symmetry of grapheme sheets combine to produce unique nanostructures such as nanocones and nanotubes. In the simulations, the grapheme sheet is subjected to internal stress, detaches itself from the supporting substrate, and then rolls itself up into either tubular or conical structures. The simulations systematically exam-ine the nucleation mechanism, thermal stability and mechani-cal properties of carbon nanocones with various cone apex an-gles. To the best of the current authors’ knowledge, this study represents the first reported attempt to use MD simulations to investigate the formation of derivative nanostructures via the self-rolling process.
2. Methodology
Using molecular dynamics (MD) simulations, this study investigates the formation of carbon nanocones and nanotubes via a self-scrolling process. Subsequently, the structural properties and thermal stability of these nanostructures are examined. The simulations use the Tersoff many-body potential [17, 18] to describe the inter-atomic forces, molecular bond energies, and bond lengths. Although originally developed to study the chemical vapour deposition of diamond, the Tersoff many-body potential also provides a simple and computationally inexpensive method for modelling fullerenes [19,20] and generating accurate predictions of the structural properties of carbon nanotubes [21,22]. In exploring the thermal stability of the current nanocones, the structural changes are examined under constant volume and temperature conditions (i.e. a canonical NVT ensemble) using the Nos´e– Hoover thermostat [23, 24]. Furthermore, to ensure the optimal integration of the Newtonian equations of motion with the equations of energy conservation, the simulations apply Gear’s fifth predictor–corrector algorithm with a neighbour list technique and a time step of 1 fs. The MD simulations commence by applying an initial time step of 105 fs to
bring the nanocones into equilibration at a temperature of 300 K. The constant-temperature MD simulations start from a low temperature (300 K for nanocones). The temperature gradually increases towards high temperature (6000 K) in 50 K steps. At each temperature, 106 MD annealing steps are recorded to give the thermodynamic average of the physical properties. To assess the influence of the conical angle upon the structural properties and thermal stabilities of the nanocones, the simulations consider a series of nanocones with various conical angles (θ), where 30◦ n 120◦, at various temperatures in the range of 1000–4000 K.
A B
C
A B
Figure 1. Schematic of MD simulation model for self-rolling nucleation. (Note: ‘A’ denotes the artificial scroll region, ‘B’ denotes the thermostat region, and ‘C’ indicates the Newton-atom region.)
3. Results and discussion
3.1. Growth mechanism and structural properties of carbon nanocones
Single-walled carbon nanotubes (SWCNTs) comprise a single graphite sheet that is wound to make a seamless cylinder, in which these carbon nanotube scrolls provide a new type of actuation (scroll unwinding), so these results are of interest for possible nanoscale actuator applications. Although self-scrolling likely exists in many other pathways based on the spiral wrapping of a few stacked sheets of graphite, here we consider only the principal case, namely that flat and curled regions of the sheet simultaneously exist, as shown in figure1. Based on the basic structural features, the single-walled carbon nanocone (SWCNC) is a new material with a structure similar to that of SWCNTs. SWCNCs are shaped in the form of a horn or an ampoule rather than a simple tube-like form. To explore the nucleation mechanisms and configurations of the SWCNC and SWCNT, this study performed MD simulations to compare the energy characteristics of a SWCNC with that of a SWCNT and to examine the dynamic changes which occur as the original flat surfaces of the two structures self-roll into a curved configuration under the effect of significant strains. In the simulations, the grapheme sheet is divided into three distinct regions, namely the artificial-atom zone, the thermostat-atom zone, and the Newton-atom zone, as shown in figure 1. The artificial atoms are located at either end of the unwrapped grapheme sheet, and then the curved-sheet angle can be addressed by the initial setting of artificially scrolled region (labelled as A in figure 1). The curved-sheet angle between the neighbouring atom and the origin atom on the same layer is rolled-up to 360◦ by 1◦ with a fixed C–C bond length of 1.42 ˚A. The purpose of these atoms is to ensure that atomic motion at the ends of the grapheme sheet is completely rolled-up. The thermostat regions of the grapheme sheet (labelled as B in figure1) each contain 220 thermostat atoms and are designed to simulate thermostatic effects in the grapheme sheet and to guarantee that the equilibrium temperature approaches the desired value in an efficient manner. Finally, the Newton-atom region of the 2
Nanotechnology 18 (2007) 105702 P-C Tsai and T-H Fang the apex of the nanocone (snapshot (c) in figure 5(b)). This
geometrical transition relaxes the strain energy. However, it should be noted that this relaxation mechanism is different from the constant-force mode of a buckled nanotube [39], which follows the theory of buckled beams [40]. The formation of the circular concave is accompanied by the onset of an sp3
type bonding arrangement in the folding process. Finally, the nanocone abruptly truncates, producing a prominent circular fold at the transition between the upward and downward sloping sidewalls (snapshot (d) in figure5), where it again acts as a secondary metastable until the nanocone attains complete inversion. For nanocones with larger conical angles, the high deformation-promoted reactivity and reversible mechanical response can be attributed to the highly symmetrical geometry and lower strain energy of the nanocone. Conversely, in nanocones with a smaller cone apex angle, the mechanical energy is concentrated in the cone apex, resulting in early degeneracy.
4. Conclusion
This study has performed MD simulations based on the Tersoff potential to investigate the nucleation mechanism, thermal stability and mechanical properties of carbon nanocones with various cone apex angles. The results have shown that the nanocones may have a lower cohesive energy than the precursor grapheme sheet. Furthermore, it has been shown that the structural stability of carbon nanocones is sensitive to the cone apex angle. The simulations have also investigated the thermal characterization and melting behaviour of carbon nanocones. During thermal processing, a metastable tube-like structure is formed from carbon nanocones with a low cone apex angle. The simulation results have also shown that the melting temperature of carbon nanocones is significantly dependent on the cone apex angle. Finally, the mechanical properties of carbon nanocones under nanoindentation have been investigated. It has been shown that an increase in the conical angle results in an improved resistance to higher loads and that a deformation-promoted reactivity and reversible mechanical response have been performed due to its high symmetry.
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