Vapor-solid-solid growth of single-walled carbon nanotubes

TL;DR

The paper investigates vapor-solid-solid (VSS) growth of single-walled carbon nanotubes on solid rhenium catalysts using a neural-network–based interatomic potential (NEPRe-C) to enable microsecond-scale MD with near-DFT accuracy. It shows that solid Re nanoparticles persist above growth temperatures and that surface carbon concentrations typical of CCVD do not significantly depress the solid-state melting point, making VSS growth feasible. Growth is governed by facet-dependent surface diffusion, yielding a diffusion-limited carbon supply (e.g., ~44 carbon atoms μs⁻¹ for a 2.0 nm NP at 1500 K) and a narrow kinetic window around 1300–1400 K where single-cap nucleation and tubular elongation occur; higher temperatures promote encapsulation and low-curvature graphitic structures, while edge motifs become zigzag-rich with widespread Klein decoration. The findings highlight catalyst reconstruction via surface carbon adsorption and interfacial thermodynamics as central to VSS growth control, suggesting experimental tuning of temperature and feedstock partial pressure to balance diffusion delivery against encapsulation and competing nucleation pathways, with implications for achieving selective SWCNT growth on solid catalysts.

Abstract

Single-walled carbon nanotubes are one-dimensional $sp^2$ carbon materials whose electronic and optical properties are governed by their chirality. Catalytic chemical vapor deposition often uses transition-metal nanoparticles that liquefy at elevated temperature, and vapor-liquid-solid growth is commonly associated with broad chirality distributions. Improved selectivity has been reported for high-melting-point catalysts that remain solid, suggesting vapor-solid-solid growth, but the underlying kinetics and interface structure remain poorly resolved. The mechanisms that control carbon delivery and determine edge structure on solid catalysts are therefore unclear. Here it is shown, using microsecond-scale molecular dynamics driven by a neuroevolution machine-learning interatomic potential, that rhenium nanoparticles remain solid above 1123.15 K and that surface carbon at 5.0 to 6.0 nm$^{-2}$ does not appreciably depress melting. Carbon transport is dominated by facet-dependent surface diffusion, bounding sustainable supply on a 2.0 nm particle to $\sim 44$ carbon atoms per $μ$s on the slow $(10\bar{1}1)$ facet. Consistently, growth at 50 carbon atoms per $μ$s occurs only within a narrow window: multiple nucleation or encapsulation is promoted at 1300 K, tubular elongation is obtained at 1400 K, and low-curvature graphitic structures dominate at 1500 K and above. Non-hexagonal rings persist over 12 $μ$s, while zigzag-rich, strongly Klein-decorated edges are stabilized and deviate from configurational-entropy expectations for liquid catalysts. These results place catalyst reconstruction by surface carbon adsorption, facet-controlled diffusion, and crystalline interfacial thermodynamics at the center of vapor-solid-solid growth control, motivating experimental tuning of temperature and feedstock partial pressure to balance diffusion-limited supply against encapsulation pathways.

Figures (6)

• Figure 1: Sketch-map representation of the training data obtained via active learning. Total numbers of structures are 86 474 (training) and 9 549 (validation). Blue atoms indicate rhenium and gray atoms indicate carbon.
• Figure 2: The melting point, $T_\text{m}$, and facet dependent carbon diffusion on rhenium NPs. Wulff constructs of rhenium NPs, a without and b with surface carbon. c$T_\text{m}$ as a function of NP size, $N$, for $\bullet$ Wulff, $\bullet$ icosahedron and $\bullet$ polycrystalline NPs; $\bullet$ shows the experimental bulk melting point of rhenium. Here the solid, dash-dot and dashed lines are linear regressions fitted to $\bullet$ and $\bullet$ for $N < 455$ atoms, to $\bullet$ for $N > 2915$ and to $\bullet$ for $N > 2915$, respectively. d$T_\text{m}$ as a function of surface carbon concentration, $C_\text{C}$, for three different sized Wulff NPs $\bullet$ Re144CX, $\bullet$ Re330CX and $\bullet$ Re594CX. Here the solid, dash-dot and dashed lines are the trend line, $T_\text{m}(C_\text{C}=0) - \left(e^{a C_\text{C}} - 1\right)$, fitted to each NP size. e Temperature dependent carbon diffusion coefficient on rhenium facets; here the black line shows the carbon diffusion coefficient in liquid iron han1980determination. f Carbon diffusion coefficient on rhenium facets at 1500K normalized by the carbon diffusion coefficient in liquid iron at the same temperature. Here the inset shows the facet dependent activation energies for carbon diffusion obtained from e. In e and f the carbon concentration is $C_\text{C} = 5.5nm^{-2}$.
• Figure 3: The impact of temperature on the growth of SWCNTs on rhenium NPs. Growth was performed over 6µs at a rate of $k = 50$ carbon per µs on a Re594 NP. Blue atoms indicate rhenium and gray atoms indicate carbon.
• Figure 4: 12µs of SWCNT growth on a Re594 NP at 1400K and $k = 50$ carbon per µs. a Simulated transmission electron microscopy images of the structures in b obtained from the growth trajectory; blue atoms indicate Re and gray atoms indicate C. c Numbers of carbon atoms comprising each species during the early phases of growth. Transparent colored lines represent raw data and solid lines represent time averages. Dotted vertical lines demarcate cap nucleation from 2.16µs to 2.23µs. d Evolution of pentagons and heptagons (upper plot) and hexagons (lower plot). The shaded purple region marks where $N_5-N_7\geq 6$, where $N_5$ and $N_7$ are the numbers of pentagons and heptagons, respectively. $k_{5,6,7}$ denotes the average rate of formation of pentagons, hexagons, and heptagons, respectively, determined by the fitted dotted line. e Distribution of "free" carbon atoms (carbons not part of the tube). The inset shows the fraction of carbons on the surface.
• Figure 5: The structure of the SWCNT edge during growth and at equilibrium. a Time series of the edge length (top), the fractions of armchair (AC) pairs, $N_\text{AC}$, and zigzag (ZZ) sites, $N_\text{ZZ}$ (middle), and the fractions of Klein-decorated AC (KAC) and ZZ (KZZ) (bottom) for the growth simulation in Fig. \ref{['fig:growth']}. b AC-pair fraction, $\alpha_\text{AC}$, for SWCNTs on the $(0001)$ and $(10\bar{1}1)$ facets of a Re1356 nanoparticle, averaged over the final 500ns of a 1µs annealing run at 1600K. c Final structures obtained after annealing for each chirality for tubes on the $(0001)$ facet (blue: Re; gray: C). d Fraction of Klein-decorated edge sites averaged over the final 500ns of annealing.