Carbon nanotubes are grown using chemical vapor deposition with a metal catalyst particle. Simulations show the carbon nanotube cap controls the chirality and diameter of the grown nanotube. For a nanotube to lift off and grow, the radius of the catalyst particle must be within a specific range determined by the particle's contact angle. The energetics of cap formation and lift off can be modeled and show good agreement with molecular dynamics simulations. Understanding how the cap detaches from the particle may allow controlling the chirality of the grown carbon nanotube.

1. Models and simulations of the
growth of carbon nanotubes
Shaun Hendy

2. Carbon nanotubes
• Carbon nanotubes are one of the most important
nanomaterials
Source: Intel
• For applications, one would like to be able to grow CNTs
of specific chiralities and diameters (which control the
band gap), in place, in devices.

3. Growth of carbon nanotubes
• Growth by Chemical Vapour Deposition (CVD) uses a
metal particle catalyst (e.g. Fe or Ni).
Amara et al, PRL 100, 056105 (2008)
• In small catalyst particles (<5nm) cap nucleates and then
lifts off, resulting in growth of single wall tube.
• Simulating CNT growth is challenging due to timescales
involved – limited success so far.

4. Catalyst size vs. tube size
Fe catalysts, unsupported growth
r
1 .6
rt
Nasibulin et al, Carbon 43 2251 (2005)

5. Focus on cap
• Geometrically, there is a 1:1 relationship
between the cap structure and the tube
chirality
• Hypothesis: CNT cap controls CNT chirality
(Reich et al., Chem. Phys. Lett. 421, 469 (2006))
• If we can understand formation of cap and transition to
tube growth, we may learn how to control chirality

6. CNT growth outcomes
• Cap lift-off (SWNT?)
• Catalyst withdrawal (MWNT?)
Yoshida et al, Nano Lett., 8, 2082–2086 (2008)

7. Metal particles in CNTs
Tsang et al, Nature 372, 159 (1994)
Hsu et al, Thin Solid Films
471, 140 (2005)
Question: How are metal catalyst particles
being drawn into carbon nanotubes?
Metal c Capillary forces?
Ag 124o
Cu 120o
Ni-C 145o
Co 140o

8. Absorption of droplets
Simulation shows Pd droplet
with c=120o
If the droplets are
sufficiently small:
cos c 1
0
rt r
they are be driven in by the
Laplace pressure associated
with their surface tension.
Schebarchov and SCH, Nano Letters 8 2253 – 2257 (2008)

9. Theory of absorption
Co has θc = 140° rt/rd =
0.45 < 0.77
Edgar, Hendy et al, Small (2011)
Schebarchov and Hendy, Nanoscale 3, 134 (2011)

10. Nanopipettery
• We can continue to fill tube by adding small droplets:
• We can also evacuate a tube by immersing it in a droplet
larger than the critical size threshold
Edgar, Hendy, Schebarchov and Tilley, Small 7, 737–774 (2011)

11. Implications for CNT growth
• Capillary absorption places upper bound on radius of
tube that can be grown from catalyst particle:
rt r cos c
e.g. c = 130o so r 1.6rt
• Just consistent with Nasibulin et al (2005) as Fe3C has
c = 140o i.e. r 1.3rt to avoid absorption
• Surface tension and adhesive forces are close to being
in balance

12. Energetics of graphitic cap
• Construct a simple expression model for CNT-catalyst
energy assuming spheres and spherical caps
R re r h
a
2
1 1
E wA 2 a 2 A
r re
r = radius of curvature of cap, A is area of cap
= line tension due to dangling or metal-carbon bonds
= elastic curvature modulus of cap
w= adhesion energy
Schebarchov, Hendy, Erterkin and Grossman PRL (2011)

13. Is lift-off trivial?
• Ni-C, R = 0.5 nm, re = 0, Lc 0.5 nm 3.1 nm
w w
E (eV)
h
Collapsed cap
stable
R (A)
c=90
o
c=140
o
R Lifted cap stable
R (A)
• Lift-off stable only for range of catalyst sizes

14. Reduced model
• Set =0 and use rigid catalyst approximation
2
1 1
E wA 2 A
r re

15. MD experiments
• Cap is slowly
stretched on uniform
catalyst particle
• Lift-off occurs for
some Rcrit that can
be compared with
the reduced model
Schebarchov, Hendy, Erterkin and Grossman PRL (2011)

16. MD experiments
• Simple model can be adjusted to fit MD simulations
• Simulations reveal importance of cap geometry and edge
termination
Schebarchov, Hendy, Erterkin and Grossman PRL (2011)

17. MD experiments
• Other cap geometries:
(9,0)
Schebarchov, Hendy, Erterkin and Grossman PRL (2011)

18. Conclusions
• Lift-off is a non-trivial process in CNT growth: catalyst-
graphite contact angle is a key parameter
• These ideas are consistent with the experimental
correlation between catalyst size and tube size
• Cap geometry is also important for details of lift-off
process; possible that chirality could be controlled
Schebarchov, Hendy, Erterkin and Grossman PRL (2011)

19. Acknowledgements
• Coworkers:
– Aruna Awasthi, Nicola Gaston,
Dmitri Schebarchov,
Nagesh Longanathan
• Collaborators:
– Theory: Barry Cox (Wollongong),
Elif Erterkin (UC Berkeley),
Jeff Grossman (MIT)
– Experiments:
Richard Tilley & Kirsten Edgar (VUW)