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Quantum chemical molecular dynamics (QM/MD) simulations of ensembles of C2 molecules on the Ni(111) terrace show that, in the absence of a hexagonal template, hydrogen, or step edge, Haeckelite as a metastable intermediate is preferentially nucleated over graphene [1]. The nucleation process is dominated by the swift transition of long carbon chains towards a fully connected sp2 carbon network. Starting from a pentagon as nucleus, pentagons and heptagons condense during ring collapse reactions, which results in zero overall curvature. To the contrary, in the presence of a coronene-like C24 template, hexagonal ring formation is clearly promoted, in agreement with recent suggestions from experiments. In the absence of step edges or molecular templates, graphene nucleation follows Ostwald’s ‘rule of stages’ cascade of metastable states, from linear carbon chains, via Haeckelite islands that finally anneal to graphene. Furthermore, we found similarities between graphene nucleation and other critical phase transition phenomena [2]. Our analysis confirms the existence of a critical nC-C/NC value close to 1.0 (‘H’ model) and 1.1 (‘G’ model), where nC-C is the number of C-C bonds and NC is the number of carbon atoms. As in random graph theory, above this critical value, the further conversion of linear carbon chains to sp2 carbon polygons leads to the emergence of a fully networked carbon structure. Thus we find the theory of selforganized criticality [2] applicable to discuss the sp2 network formation from sp chains in the formation mechanism of graphenes. References: [1] Wang, Y.; Page, A. J.; Nishimoto, Y.; Qian, H.-J.; Morokuma, K., Irle, S.; JACS (just accepted) (2011). [2] Bak, P.; Tang, C.; Wiesenfeld, K., Phys. Rev. Lett. 1998, 59, 381.
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Haeckelite and Graphene Formation on a Metal Surface: Evidence for a Phase Transition at the Edge of Criticality
Ying Wang, Alister J. Page, Yoshio Nishimoto, Hu-Jun Qian, Keiji Morokuma, Stephan Irle
Department of Chemistry, Graduate School of Science, Nagoya University, JapanFukui Institute for Fundamental Chemistry, Kyoto University, Japan
.
Kyoto University Nagoya University
http://kmweb.fukui.kyoto-u.ac.jp/nano http://qc.chem.nagoya-u.ac.jp
Talk XX5.62012 Materials Research Society Spring Meeting, San Francisco, CA
April 11, 2012
2
Haeckelite
Overview
Crespi et al. Phys. Rev. B 53, R13303 (1996); Terrones et al. Phys. Rev. Lett. 84, 1716 (2000); Rocquefelte et al. Nano Lett. 4, 805 (2004)
DE(TB) (meV/C atom)DE(PBE) (meV/C atom)
00
307261
304246
408375
419380
C60:
Ernst Haeckel(1834-1919)
Thrower-Stone-Wales Transformation
Radiolara
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Haeckelite
Overview
Rocquefelte et al. Nano Lett. 4, 805 (2004) a) graphite b) rectangular
c) oblique d) hexagonal
& Haeckelite Nanotubes
4
Overview Experiments
Graphene CVD SynthesisNagashima et al. Phys. Rev. B 4, 17487 (1994)
• “monolayer graphite (MG)”
• C2H4 decomposition on Ni(111) at 600°C
• No bulk carbide
Graphene Formation from Ni-C AlloyShelton et al. Surf. Sci. 43, 493 (1974)
• “graphitic monolayer” = modern picture
• Carbon doping of Ni(111) with CO at 1200°C
• Phase transition: Carbon segregationGrüneis et al. Phys. Rev. B 77, 193401 (2008)
Overview Theoretical Studies
How Does Graphene Form on Ni(111)?Gao et al. J. Am. Chem. Soc. 133, 5009 (2011)
• GGA PW91/UPP-PW (VASP) geometry optimizations• individual clusters on Ni(111) C1-C24
5
Geometries and energetics only
No information on structure evolution with time (growth)!
Want QM/MD Simulations!
6
Self-consistent-charge density-functional tight-binding (SCC-DFTB)
12
2tot i i repi
E f E q q
0vi iv
c H S Second order-expansion of DFT total energy with respect to charge fluctuation
TB-eigenvalue equation
Method SCC-DFTB
Single-zeta STO basis set
Finite temperature approach (Mermin free energy EMermin)
1
exp / 1ii B e
fk T
2 ln 1 ln 1e B i i i ii
S k f f f f
Te: electronic temperatureSe: electronic entropy
0 1
2N
repi i i i
i
EH H SF f c c q q
SR R R R
0 1if
Atomic force
M. Weinert, J. W. Davenport, Phys. Rev. B 45, 13709 (1992)
EMermin = Etot - TeSe
E
2fi0 1 2
m
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DFTB/MD Results H model
QM/MD of 30 C2 on Ni(111), 1180 KY. Wang, A. J. Page, Y. Nishimoto, H.-J. Qian, K. Morokuma, SI, JACS (2011)
Haeckelite!
A
t = 0
100 ps 410 ps
0 50 100 150 200 250 300 350 4000
1
2
3
4
5
6
7
8
Num
ber
of poly
gonal rings
Time [ps]
five-membered ring six-membered ring seven-membered ring
200 ps 300 ps
0 50 100 150 200 250 300 350 4000
1
2
3
4
5
6
7
8
Num
ber
of poly
gonal rings
Time [ps]
five-membered ring six-membered ring seven-membered ring
5
Average 5- and 6-ring counts over 10 annealing
trajectories
Formation of first condensed 2-ring
system (5/5 or 5/6)
Always pentagon first!
Hollow in Fe is required
Y. Ohta, Y. Okamoto, A. J. Page, SI, K. Morokuma, ACS Nano 3, 3413 (2009)
Nanotube cap nucleation
DFTB/MD Results Why Pentagons?
8
9
DFTB/MD Results H model
QM/MD of 30 C2 on Ni(111), 1180 KY. Wang, A. J. Page, Y. Nishimoto, H.-J. Qian, K. Morokuma, SI, JACS (2011)
top side
10
DFTB/MD Results G Model
QM/MD of 18 C2 + C24 on Ni(111), 1180 KY. Wang, A. J. Page, Y. Nishimoto, H.-J. Qian, K. Morokuma, SI, JACS (2011)
• Pentagon-first vs. template effect.• Suppression of heptagons and
pentagons
Wang et al., Nano Lett., (2011)
Graphene!
11
DFTB/MD Results G Model
QM/MD of 18 C2 + C24 on Ni(111), 1180 KY. Wang, A. J. Page, Y. Nishimoto, H.-J. Qian, K. Morokuma, SI, JACS (2011)
• Pentagon-first vs. template effect.• Suppression of heptagons and
pentagons
Wang et al., Nano Lett., (2011)
Graphene!
12
DFTB/MD Results G Model
QM/MD of 18 C2 + C24 on Ni(111), 1180 KY. Wang, A. J. Page, Y. Nishimoto, H.-J. Qian, K. Morokuma, SI, JACS (2011)
top side
DFTB/MD Results Templating effect
Ring count analysis(average over 10 trajectories)
13
Our “haeckelite index” h
Y. Wang, A. J. Page, Y. Nishimoto, H.-J. Qian, K. Morokuma, SI, JACS (2011)
Haeckelite is a Metastable Phase
DFTB/MD Results Ostwald’s rule
14
F. W. Ostwald, Z. Phys. Chem. 22, 289 (1897)
MC Study: Karoui et al., ACS Nano 4, 6114 (2010)
Self-Organized Criticality Random Graph Theory
15
S. Kauffman, At Home in the Universe (1996)
Phase Transformation in Random Graph Theory
20 nodesedgesnodes
= 520
largest cluster:
3
1020
5
1520
15
2020
18
2520
20
largest cluster:
edgesnodes
x x
xx x
Self-Organized Criticality Random Graph Theory
16
S. Kauffman, At Home in the Universe (1996)
Edges Number of BondsNodes Number of Atoms
Phase transition!
Self-Organized Criticality Carbon phase transition
17
Haeckelite/Graphene Formation: Carbon spsp2 Phase Transition?
18
Self-Organized Criticality Carbon phase transition
What is Self-Organized Criticality (SOC)?P. Bak, C. Tang, K. Wiesenfeld (BTW), Phys. Rev. Lett. 59, 381 (1987)
Avalanche sizes (time)
frequency P over size x
P(x) x∝ -α (x>1)
19
Self-Organized Criticality Carbon phase transition
What is Self-Organized Criticality (SOC)?P. Bak, C. Tang, K. Wiesenfeld (BTW), Phys. Rev. Lett. 59, 381 (1987)
Universality of self-organized critical state and 1/f noise:Gutenberg-Richter Law N/NTOT = 10-bM
(Earthquake probability vs magnitude)
Source: wikipedia
Marine extinction on geological time scale
Source: wikipedia
time (Ma)
Others: Stock market, epidemics, solar flares, rivers, mountain ranges, etc. etc. = FRACTALS!
20
Self-Organized Criticality Carbon phase transition
Michael Hilke, McGill Universityhttp://www.physics.mcgill.ca/webgallery/michael1/
• Universality of pentagon-first mechanism in carbon condensation
• Possibility to synthesize Haeckelite: fast carbon supply, rapid cooling
• Graphene nucleation follows pentagon-first mechanism; subsequent annealing required (Ostwald’s rule of stages)
• C24 template imprints hexagonal structure on growing flat carbon network: suggestion to experiment
• spsp2 condensation at high [C] is a phase transition with fractal characteristics of self-organized criticality (SOC)
Summary http://qc.chem.nagoya-u.ac.jp
21
22
Acknowledgements
July 8, 2011
The Group:
Dr. Oraphan Saengsawang (Visitor)Dr. Ying WangDr. Hu-Jun QianDr. Matt Addicoat (JSPS)Dr. Cristopher CamachoMs. Lili Liu (D3)Mr. Yoshifumi Nishimura (D1)Ms. Elena Vyshnyakova (D1, visitor)Mr. Yoshio Nishimoto (M2)Undergraduates
CREST “Multiscale Physics” (2006-2011)CREST “Soft -p materials: (2011-2015)
SRPR tenure track program (2006-2011) JSPS KAKENHI
Funding: