12.45 o14 s hendy
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Research 14: S HendyTRANSCRIPT
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Models and simulations of the growth of carbon nanotubesShaun Hendy
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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
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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)
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Catalyst size vs. tube size
Nasibulin et al, Carbon 43 2251 (2005)
Fe catalysts, unsupported growth
6.1tr
r
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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
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CNT growth outcomes
• Cap lift-off (SWNT?)
• Catalyst withdrawal (MWNT?)
Yoshida et al, Nano Lett., 8, 2082–2086 (2008)
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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?
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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
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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
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• 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)
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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
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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)
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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)
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Reduced model
• Set l=0 and use rigid catalyst approximation 2
112
errAwAE
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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)
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• 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)
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• Other cap geometries: (9,0)
MD experiments
Schebarchov, Hendy, Erterkin and Grossman PRL (2011)
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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)
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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)