Edge Dynamics in Iron-Cluster Catalyzed Growth of Single-Walled Carbon Nanotubes Revealed by Molecular Dynamics Simulations based on a Neural Network Potential

TL;DR

The paper addresses chirality control in SWCNT growth by developing a carbon–Fe neural network potential (NNP) to enable long-timescale MD simulations of Fe-catalyzed growth. The NNP is trained on ~44,000 structures and validated against graphene defect energies, graphene edge energetics, and Fe thermodynamics, achieving higher accuracy than conventional potentials and enabling reliable C–Fe simulations. Using MD with the NNP, defect-free, chirality-definable SWCNT growth is observed, characterized by dynamic edge rearrangements and an entropy-driven edge-stability model based on the interfacial energy $E_ ext{Int}(n,m,i)$ and the associated partition function $Z(n,m)$ that yields the edge-configuration probabilities $P(n,m,i)$. The study also identifies vacancy formation at antiarmchair/antizigzag sites and adatom diffusion healing as key mechanisms for minimizing defects, providing a thermodynamic–kinetic framework to guide chirality-controlled synthesis. Together, these findings connect edge thermodynamics to experimental chirality trends and demonstrate how tuning catalyst state and temperature can steer edge dynamics toward desired SWCNT chiralities.

Abstract

Given the high potential for applications utilizing the unique properties of single-walled carbon nanotubes (SWCNTs), there is considerable enthusiasm for addressing the challenges associated with synthesizing SWCNTs with specific chirality. To elucidate the mechanisms that determine the chirality of SWCNTs during growth, intensive efforts have been devoted to classical molecular dynamics (MD) simulations. However, the mechanism of chirality determination has not been fully clarified, which can partly be attributed to the limited accuracy of empirical interatomic potentials in reproducing the behavior of carbon and metal atoms. In this work, we develop a neural network potential (NNP) for carbon-metal system to accurately describe the SWCNT growth, and perform MD simulations of SWCNT growth using the NNP. The MD simulations illustrate the defect-free, chirality-definable growth of SWCNTs, highlighting the dynamic rearrangement of edge configurations and the consistency between the probability of edge configuration appearance and the entropy-driven edge stability model proposed here. It is also shown that the edge defect formation is induced by vacancy and suppressed by vacancy healing through adatom diffusion on the SWCNT edges. These results provide insights into the edge formation thermodynamics and kinetics of SWCNTs, an important clue to the chirality-controlled synthesis of SWCNTs.

Figures (8)

• Figure 1: Comparison of (a) defect formation energy of graphene and (b) edge energy of graphene as a function of chiral angle between DFT with GGA, the developed NNP, Tersoff-type potentialdoi:10.1021/acs.jpcc.7b12687, and ReaxFFdoi:10.1021/jp004368udoi:10.1021/jp9035056. The edge energies of graphene were directly computed (dots) and fitted with Eq. \ref{['eq:edge']} (lines).
• Figure 2: Thermodynamic behaviors of Fe nanoparticles. (a-c) Snapshots of cross sectional views of annealed structures of Fe$_{200}$, Fe$_{600}$ and Fe$_{2000}$ nanoparticles. The blue and red balls denote atoms in bcc and Ih structure, respectively. The white balls denote atoms out of bcc and Ih structures. The structures were categorized by the common neighbor analysisdoi:10.1021/j100303a014. (d) Melting point of Fe nanoparticles as a function of inverse diameter. The red line is linear fits to data points for bcc Fe nanoparticles. (e) Melting points of Fe$_{120}$C$_{n}$ nanoparticles obtained by adding up to 17.5 % of carbon atoms.
• Figure 3: Snapshots of the initial stages of SWCNT growth at (a) 1100 K and (b) 1500 K. The blue and green atoms denote iron and carbon, respectively.
• Figure 4: (8,7) SWCNT growth on Fe$_{120}$ at 1500 K. Snapshots in the (a-b) saturation, (c-g) cap formation, and (h) sidewall elongation stage. The red-colored rings denote the pentagons. (i) Time evolution of the number of C atoms belonging to monomers, dimers, trimers, and rings. The circled numbers denote the growth stages. 1, 2, and 3 are saturation stage, cap formation stage, and sidewall elongation stage, respectively. (j) Radial distribution function of C atoms in monomers, dimers, and trimers from the center of mass of the Fe nanoparticles. The radial distribution is averaged over the sidewall elongation stage. Two C atoms within 2.0 Å are regarded as being bonded.
• Figure 5: (a) Time evolution of the numbers of hexagons, pentagons, and heptagons. (b) An enlarged view of (a). (c) Reformation of a pentagon into a hexagon on the (8,7) SWCNT. (d) Reformation of a heptagon into a hexagon on the (8,7) SWCNT. The red and blue polygons denote the pentagon and heptagon, respectively. The dotted lines indicate the bonds that are about to break.