Models and simulations of the growth of carbon nanotubesShaun Hendy

Carbon nanotubes

• Carbon nanotubes are one of the most important nanomaterials

• 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.

Source: Intel

Growth of carbon nanotubes

• Growth by Chemical Vapour Deposition (CVD) uses a metal particle catalyst (e.g. Fe or Ni).

• 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.

Amara et al, PRL 100, 056105 (2008)

Catalyst size vs. tube size

Nasibulin et al, Carbon 43 2251 (2005)

Fe catalysts, unsupported growth

6.1tr

r

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

CNT growth outcomes

• Cap lift-off (SWNT?)

• Catalyst withdrawal (MWNT?)

Yoshida et al, Nano Lett., 8, 2082–2086 (2008)

Metal particles in CNTs

Hsu et al, Thin Solid Films 471, 140 (2005)

Tsang et al, Nature 372, 159 (1994)

Question: How are metal catalyst particles being drawn into carbon nanotubes?

Metal qc

Ag 124o

Cu 120o

Ni-C 145o

Co 140o

Capillary forces?

If the droplets aresufficiently small:

they are be driven in by the Laplace pressure associated with their surface tension.

rrt

c 1cos0

Absorption of droplets

Schebarchov and SCH, Nano Letters 8 2253 – 2257 (2008)

Simulation shows Pd dropletwith qc=120o

Theory of absorption

Schebarchov and Hendy, Nanoscale 3, 134 (2011)

Edgar, Hendy et al, Small (2011)

Co has θc = 140° rt/rd = 0.45 < 0.77

• We can also evacuate a tube by immersing it in a droplet larger than the critical size threshold

Nanopipettery

• We can continue to fill tube by adding small droplets:

Edgar, Hendy, Schebarchov and Tilley, Small 7, 737–774 (2011)

Implications for CNT growth

• Capillary absorption places upper bound on radius of tube that can be grown from catalyst particle:

e.g. qc = 130o so

• Just consistent with Nasibulin et al (2005) as Fe3C has qc = 140o i.e. to avoid absorption

• Surface tension and adhesive forces are close to being in balance

ct rr cos

trr 6.1

trr 3.1

R

Energetics of graphitic cap

• Construct a simple expression model for CNT-catalyst energy assuming spheres and spherical caps

211

22

errAawAE

r = radius of curvature of cap, A is area of capl = line tension due to dangling or metal-carbon bondsk = elastic curvature modulus of capw = adhesion energy

re ra

h

Schebarchov, Hendy, Erterkin and Grossman PRL (2011)

Is lift-off trivial?

• Ni-C, R = 0.5 nm, re = 0,

• Lift-off stable only for range of catalyst sizes

R (A)

R

DE (eV)

qc=140o

qc=90o

Lifted cap stable

Collapsed cap stable

h

nm 1.3w

nm 5.0w

Lc

R (A)

Reduced model

• Set l=0 and use rigid catalyst approximation 2

112

errAwAE

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)

• Simple model can be adjusted to fit MD simulations

• Simulations reveal importance of cap geometry and edge termination

MD experiments

Schebarchov, Hendy, Erterkin and Grossman PRL (2011)

• Other cap geometries: (9,0)

MD experiments

Schebarchov, Hendy, Erterkin and Grossman PRL (2011)

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)

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)