Molecular dynamics simulation of carbon nanotube growth under a tensile strain

www.nature.com/scientificreports OPEN Molecular dynamics simulation of carbon nanotube growth under a tensile strain Ayaka Yamanaka 1*, Ryota Jono 1, Syogo Tejima 1 & Jun‑ichi Fujita 2 We performed molecular dynamics simulations of carbon nanotube (CNT) to elucidate the growth process in the floating catalyst chemical vapor deposition method (FCCVD). FCCVD has two features: a nanometer-sized cementite (Fe3C) particle whose melting point is depressed because of the larger surface-to-volume ratio and tensile strain between the growing CNT and the catalyst. The simulations, including these effects, demonstrated that the number of 6-membered rings of the (6,4) chiral CNT constantly increased at a speed of 1 mm/s at 1273 K , whereas those of the armchair and zigzag CNTs were stopped in the simulations and only reached half of the numbers for chiral CNT. Both the temperature and CNT chirality significantly affected CNT growth under tensile strain. Carbon nanotubes (CNTs) are one-dimensional carbon allotropes comprising sp 2 carbon networks with unique properties1–4. Based on their unique structure, which is a rolled-up two-dimensional graphene to cylinder, they have many favorable characteristics, including mechanical strength, and thermal and electrical conductivity. CNTs have attracted much attention of many researchers since their s ynthesis5 and identification6 due to these properties. For example, the tensile strength of CNTs is more than 80 GPa7, while that of stainless steel is only 1 GPa8, and the thermal conductivity of CNTs is 6000 W/m K, while that of copper metal is 500 W/m K9. Various synthesis methods have been developed so far, including laser ablation10, arc discharge11, and chemical vapor deposition (CVD)12–14. Substrate-based CVD is widely used because of its low-cost and scalable methods for mass production of CNTs. Another type of the CVD, floating catalyst CVD (FCCVD) have also attracted many researchers because of its high-speed CNT g rowth15–21. The reported growth speed of CNT in FCCVD is from 0.1 to 100 μm/s22,23 and sometimes reaches 1 mm/s24, and is faster than that in substrate-based CVD whose speed is from 1 nm/s to 10 μm/s25,26. The CNT grows on the flying nm size cementite (Fe 3 C) particles in the FCCVD method, while it grows on a substrate in substrate-based CVD. The dynamics of carbon in cementite nanoparticles are faster than those on the substrate because of the melting-point depression from the larger surface-to-volume ratio, and the growing CNT may be pulled and feel tensile strain by the interaction with flying nanoparticles in the FCCVD process. It is necessary to elucidate these effects on the high-speed growth mechanism of CNT in the FCCVD method for more efficient production of CNT; however, there are no experimental reports owing to the difficulty in directly observing the CNT growth progress using floating catalysts. Molecular dynamics (MD) simulations are powerful methods for investigating the growth of CNTs at the atomic level. Many MD simulations of CNT growth have been reported thus far. However, most of these studies involved CNT formation via natural deposition on saturated carbon atoms from the catalyst27,28. In this study, we calculated the dynamics of carbon in cementite nanoparticles and introduced tensile strain to the CNT growth simulation to reveal its effects on CNT growth in the FCCVD process. Methods We focused on the CNT-catalyst interface and modeled the initial stage of CNT growth on a cementite (Fe3 C) (001) surface, as shown in Fig. 1. The sizes of the simulation boxes were determined from the reported s tructure29 as 2.54 × 2.61 × 8.00 nm. The bottom of the 1 nm layers for cementite was fixed in space. To obtain the equilibrium state of the cementite structure at 1073 K , 1273 K , and 1473 K , which are below, above, and much above the melting point of cementite, respectively, we performed the NVT simulations under Nosé-Hoover t hermostat30–32 for 100 ns. The positions and velocities are time-integrated by using velocity Verlet method with 1.0 fs for time step. To introduce the tensile strain, the top 0.4 nm of the CNT was pulled up at a constant velocity during the simulations, which was set to 1 mm/s to attempt the experimentally reported upper limit of the growth speed24. 1 Research Organization for Information Science and Technology, 7F, Sumitomo‑Hamamatsucho Building, 1‑18‑16, Hamamatsucho, Minato‑ku, Tokyo 105‑0013, Japan. 2Graduate School of Pure and Applied Science, University of Tsukuba, 1‑1‑1 Ten‑nodai, Tsukuba, Ibaraki 305‑8573, Japan. *email: Scientific Reports | (2024) 14:5625 | https://doi.org/10.1038/s41598-024-56244-6 1 Vol.:(0123456789) www.nature.com/scientificreports/ ↑ 1 mm/s z ↑→x fixed Figure 1.  Simulation models of the CNT on cementite (Fe3C). The total MD simulation time was 500 ns, i.e., the CNT was pulled up for 0.5 nm , which is correspond to the length of the two 6-membered rings. We considered CNTs with diameters of 0.7 nm and the chirality of the armchair (5,5), chiral (6,4), and zigzag (9,0) CNTs to compare the differences in the growth processes depending on the CNT structure. All calculations were performed using the LAMMPS p ackage33. There are many kinds of force fields for the mixture of iron and carbon systems, but almost all of them are not suitable for simulating the cementite structure, which is considered as the basic structure in the high-temperature FCCVD process. The previous study reported that only the embedded atom method (EAM) by Lau et al.34 and Ruda et al.35 and the short-range Tersoff-Brenner-type analytical bond order potential (ABOP) by Henriksson et al.29 are the reliable potentials to describe the properties of c ementite36. Among them, Henriksson’s ABOP can reproduce the 6-membered ring structure of carbon a llotropes37 because it uses Brenner’s reactive bond-order (REBO) potential38 for carbon-carbon interaction, whose accuracy is well tested by comparison with density functional theory. It should be noted that the development of ReaxFF to simulate the mixture of iron and carbon system is continuing, but the simulation by ReaxFF potential takes much longer time than that by ABOP. Based on these references and our preliminary tests, we used the Henriksson’s ABOP to simultaneously describe the interaction of atoms in the cementite and CNT in this work. Results and discussions Figure 2 shows the z-oriented trajectories of carbon and iron atoms in the cementite nanostructure at 1073 K , 1273 K , and 1473 K . The dynamics of the carbon atoms above the melting points (1273 K and 1473 K ) are well activated, and the carbon atoms are freely exchanged in their positions. The average velocity of the carbon in the direction normal to the surface was estimated using the following expression: v̄ = 100 ns |z(t + �t) − z(t)|/�t (1) t=50 The average velocities were 5.4 mm/s at 1073 K , 126 mm/s at 1273 K , and 143 mm/s at 1473 K , and all v (...truncated)