QM/MD Simulation of SWNT Nucleation on Transition-Metal

Carbide NanoparticlesStephan Irle,1 Alister J. Page,2 Honami Yamane,2 Yasuhito

Ohta,2 Keiji Morokuma2

1Institute for Advanced Research and Department of Chemistry, Nagoya University2Fukui Institute for Fundamental Chemistry, Kyoto University

The 40th Commemorative Fullerene-Nanotubes General Symposium

9 March, 2011

SWNT Synthesis: The Vapour-Liquid-Solid Mechanism

Gavillet et al., J. Nanosci. Nanotech. (2004)

Yoshida et al., Nano. Lett. (2004) Zhu et al., Small (2004) Zhang et al., Appl. Phys. A (2005)

• 1-electron matrix integrals tabulated using spline functions of interatomic distances.

• Repulsive term fitted against B3LYP dissociation curves of training set species.

• Finite electronic temperature (Te) employed.

• MO occupations:

• Variational quantity:

SCC-DFTB:

NCC-DFTB SCC-DFTB AM1 PM3

C20-C36 0.025 0.019 0.035

0.030

C60-C86 0.014 0.014 0.016

0.015

Geometry RMS Errors (Å), Relative to B3LYP/6-31G(d)

NCC-DFTB SCC-DFTB AM1 PM3

C20-C36 0.88 0.93 0.77 0.73

C60-C86 0.97 0.98 0.86 0.84

Relative Energy R2 values, Relative to B3LYP/6-31G(d)

(a) (b) (c)

PW91 0.88 0.93 0.7

7

SCC-DFTB 0.97 0.98 0.8

6

Adhesion Energies (eV/atom) for

Fen-(5,5) SWNT Complexes

SCC-DFTB: M. Elstner et al., Phys. Rev. B, 58, 7260, (1998)(Sc,Co,Ti,Fe,Co,Ni)-C DFTB parameters: G. Zheng et al., J. Chem. Theor. Comp. 3, 1349, (2007)

Density-Functional Tight-Binding Method

NCC-DFTB: 100 atoms, 1 ns

SCC-DFTB: 100 atoms, 0.1 ns

NCC-DFTB:

• SCC-DFTB; Te = 10,000 K.

• MD; ∆t=1 fs.

• NVT ensemble; Tn= 1,500 K.

• Nosé-Hoover-Chain thermostat.

• 30 C2 deposited onto fcc-Fe38 surface (1/ps).

• NVT thermal annealing for 400 ps.

SCC-DFTB/MD Simulation of SWNT Nucleation Fe38 Catalyst

Y. Ohta et al., ACS Nano 3, 3413 (2009)

Yasuhito Ohta

SCC-DFTB/MD Simulation of SWNT Nucleation Fe38 Catalyst

Y. Ohta et al., ACS Nano 3, 3413 (2009)

Yoshida et al., Nano. Lett. (2008)

SCC-DFTB/MD Simulation of SWNT Nucleation Fe38 Catalyst

Y. Ohta et al., ACS Nano 3, 3413 (2009)

SWNT nucleation: driven by 5-/6-membered ring

formation

Fe3C nanoparticle

SWNT ‘cap’ formed without carbide phase...

Ni116 Ni39C77Ni77C39 Ni58C58

SCC-DFTB/MD Simulation of SWNT Nucleation Ni-Carbide Nanoparticle PrecursorPage et al. J. Am. Chem. Soc. 132, 15699

(2010).

Metal-carbide phase ➛ metal/carbon system.

Precipitation of carbon (bulk ➛ surface): < 50 ps.

SWNT Nucleation: < 150 ps.

Fe77C59@1400K-5

Fe77C59@1400K-5

SWNT nucleation mechanism independent of:

• Catalyst Composition (type of transition metal).• Catalyst Size.

• Reaction Temperature.• [C] & carbon source.

Carbide phase ➛ Catalyst/Cap structure in < 300 ps!

Fe/Ni-carbide nanoparticles thermodynamically unstable

at these conditions.

Ni58C58 @ 800 K

Ni58C58 @ 1400 K

Ni58C58 @ 2000 K

SCC-DFTB/MD Simulation of SWNT Nucleation Page et al. J. Am. Chem. Soc. 132, 15699 (2010).

Average SWNT ‘Nucleation Times’ (ps) from Fe/Ni-Carbide Nanoparticles

SCC-DFTB/MD Simulation of SWNT Nucleation Page et al. J. Am. Chem. Soc. 132, 15699 (2010).

Ni-Carbide

Fe-Carbide

Average ‘Carbon Precipitation Times’

(ps),Fe/Ni-Carbide Nanoparticles

SCC-DFTB/MD Simulation of SWNT Nucleation Page et al. J. Am. Chem. Soc. 132, 15699 (2010).

Carbon Precipitation Dynamics @ 800 K

(Ni58C58, Fe58C58)

Ni-Carbide

Fe-Carbide

Liquid

1400 K

2000 KSolid

800 K

Avera

ge L

IAvera

ge L

IAvera

ge L

I

Phase of Catalyst during Nucleation:Fe: liquid > 800 K;

Ni: solid at 800 K, liquid at 1400 K.

SCC-DFTB/MD Simulation of SWNT Nucleation Page et al. J. Am. Chem. Soc. 132, 15699 (2010).

Ding, Eur. Phys. J. D (2005)

Departure from linearity in L.I.

Melting of Nanoparticles: The Lindemann Index

•SWNT nucleation dynamics: •Driven by ‘catalyst-carbon’ interaction strength. •Catalyst-carbon interactions: Ni-C=1.06 eV; Fe-C=1.78 eV.•Fe-carbide: SWNT nucleation impeded (destruction of C-C bonds).•Ni-carbide: SWNT nucleation enhanced by presence of long carbyne chains

•Catalytically active state of metal particles:•metallic phase, cf. Anisimov et al. Carbon 48, 380 (2010)

•carbide phase not necessary for nucleation•carbide phase not stable for small particles, cf. Harutyunyan et al.

“Reduced carbon solubility in Fe Nanoclusters and Implications for Carbon Nanotube Growth”, Phys. Rev. Lett. 100, 195502 (2008)

ConclusionsPage et al. J. Am. Chem. Soc. 132, 15699 (2010).