005 keiji morokuma

7/27/2019 005 Keiji Morokuma

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Density-Functional Tight-Binding Molecular

Dynamics Simulation of Growth of Single-WalledCarbon Nanotubes from Metal Cluster

1Kyoto University 2Nagoya University

http://kmweb.fukui.kyoto-u.ac.jp/nano http://qc.chem.nagoya-u.ac.jp

The Fourth NASA-Rice-AFOSR Workshop on Nucleation and Growth

Mechanisms of Single Wall Carbon NanotubesTierra Sagrada, TX April 17-21, 2009

Yasuhito

Ohta, Yoshiko Okamoto, Alister J . Page, Ying Wang, Stephan Irle, Keiji Morokuma1Fukui Institute for Fundamental Chemistry, Kyoto University2Institute for Advanced Chemistry and Department of Chemistry, Nagoya University3Cherry L. Emerson Center for Scientific Computation and Department of Chemistry, Emory University

3Emory University


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Outline

Motivation

Review: state of the art SWNT growth control and

theoretical modeling

Density-functional tight-binding (DFTB) method and its

application in molecular dynamics simulations

Continued growth simulations of armchair SWNTs,

temperature dependence; zigzag SWNTs

Surface diffusion, cap formation and cap growth on

transition metal cluster, acetylene decomposition

Summary and outlook



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Outline

MotivationMotivation









Summary and outlook



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Motivation A Nobelists Perspective

4

Sir Harry Kroto in D. J. Palmer, Where nano is going,

Nano Today 3, 46 (2008)

They [nanotubes andnanowires] have to havereproducible properties, andwe're not in that situation at the

present time; you can makevarious types of nanotubes andstudy the properties of them but

at the moment we don't havethe control to produce thenanotubes with accurately

specified diameter, structure,chirality, you name it.


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Outline

Motivation

Review: state of the art SWNT growth control andReview: state of the art SWNT growth control and

theoretical modelingtheoretical modeling







Summary and outlook



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Review SWNT Growth Control

Recent advancements in SWNT growth controlDiameter control:

C. Lu and J. Liu, Controlling the Diameterof Carbon Nanotubes in Chemical VaporDeposition Method by Carbon Feeding, J.

Phys. Chem. B 110, 20254 (2006)

H. Shinohara and coworkers: Synthesis ofsingle-wall carbon nanotubes grown fromsize-controlled Rh/Pd nanoparticles by

catalyst-supported chemical vapordeposition, Chem. Phys. Lett. 458, 346(2008)

Chirality control:D. E. Resasco, R. B. Weisman, andcoworkers, Narrow (n,m)-Distribution ofSingle-Walled Carbon Nanotubes GrownUsing a Solid Support Catalyst, J. Am. Chem.

Soc. 125, 11186 (2003)

Many others ...

T=800

C

C2

H6

feedstockRed: 4200 ppmGreen: 14,400 ppm

CoMoCAT:Co-Mocatalyst


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Other improvements

High yield:K. Hata, D. Futaba, et al. Water-AssistedHighly Efficient Synthesis of Impurity-FreeSingle-Walled Carbon Nanotubes, Science

306, 1362 (2004)

Defect control:S. Maruyama et al., Low-temperature

synthesis of

high-purity single-walled carbonnanotubes from alcohol, Chem. Phys. Lett.360, 229 (2002)

Length control:L. X. Zheng et al., Ultralong single-wallcarbon nanotubes, Nature Mater. 3, 673(2004)

Many other groups and improvements

so-called supergrowth

Low Raman D/Gratio = high puritywhen usingalcohols asfeedstock(ACCVD)


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But How to put the puzzle pieces together?

(5,5) SWNT

high yield, desired length, defect-free, eventually catalyst-free

ACCVD etc Selection of

appropriate

growth

conditions


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Review Experimental Growth Studies

Look here in situ environmental TEM studies of

SWNT nucleation and growth

H. Yoshida, et al. Atomic-Scale In-situ

Observation of Carbon NanotubeGrowth from Solid State CarbideNanoparticles, Nano Lett. 8, 2082 (2008)

Fe/SiO2

C2

H2

:H2

T=600

C

Fluctuating solid Fe3CS. Hofmann, et al. In-situ Observations of

Catalyst Dynamics during Surface-BoundCarbon Nanotube Nucleation, Nano Lett. 7,602 (2007)

Ni/SiO2

C2

H2

:NH3

T=480 to 700

C

Fluctuating solid pure nickel

F. Ding, et al.Appl. Phys. Lett.88, 133110

(2006)

Fe2000

, T=1007

C

REBO/MD

Lindemann

inde

x(a

.u.)


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Review Experimental Growth Studies

SWNT Growth N-dimensional Parameter Space

catalyst size [nm]

catalyst composition

T [ C]

Fe

CoNi

Co/Mo

Rh/Pd

600

1000

1 4 10

feedstock species

feeding rate/pressure

substrateetching agent

Fill all space with blocks/scan fullparameter spaceEvaluate interdependence relations perfect

(n,m)-specific synthesis

Systematic Investigation ofSWNT growth mechanism(s):

Can only construct ~1 machine/year

Let Theory Do It!! (computer time ischeap )

Experimentalist:


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J.-Y. Raty et al, Growth of Carbon Nanotubes on Metal Nanoparticles: A Microscopic

Mechanism fromAb Initio Molecular Dynamics Simulations, Phys. Rev, Lett. 95, 096103 (2005)

Nano-diamond: Inappropriate model!

Change from diamond structure (sp3) tofullerene cap (sp2) immediately!

simulation time~10 psToo short

to demonstrate

self-assembly

Review Previous CPMD

11

Previous Car-Parrinello Molecular Dynamics (CPMD)

J. Gavillet et al, Root-Growth Mechanism for SWNTs, Phys. Rev, Lett. 87, 275504 (2001)

Carbon precipitation on Co carbide

particle, 51 Co & 102 C atoms, 25ps 1 hexagon, 2 pentagons

C30

+44C on Co surface at 1500 K, 15

ps 5 carbon atoms diffused to cap

Heroic efforts on supercomputers, one-shot simulations!


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F. Ding et al., J. Phys. Chem. B 108, 17369 (2004)

Bond order potential allows bond breaking

via potential switching functions, but

does not include effects of -conjugation or charge transfer

Y. Shibuta & S.Maruyama, Chem. Phys.Lett. 382, 381 (2003)

Review Previous REBO MD

Reactive Empirical Bond Order (REBO) MD

Feedingcarbonatoms fromcenter of Feclusters:

Fe50 + nC,T=627

C

500 C atoms +nC,

Ni108

, T=2227 C(20 nm)

3

PBC

Classical potential, cheaper, many long simulations!

Y. Shibuta & S. Maruyama, Chem.Phys. Lett. 437, 218 (2003)

500 C atoms+nC, Ni256

on

LJ supportT=2227

C

(20 nm)3

PBC

F. Ding et al., J. Chem. Phys. 121, 2775(2004)

Fem

+ nC, T=527

C to 627

C

Many more studies


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Review Previous REBO MD

13

Review REBO/MD Simulations

Specific problems of REBO MD for SWNT growth

Problem 1: large number of non-hexagon rings!

REBO does not discriminate betweenaromatic or antiaromatic ringsUnrealistically many 4- and 8-membered rings (formally antiaromatic)

F. Ding et al., J. Phys. Chem.B, 108, 17369 (2004)

Amorphous structure formation

Problem 3: sp3 defects overestimated

N. A. MarksN. A. Marks et alet al.,., Phys. Rev. BPhys. Rev. B 6565, 075411 (2002), 075411 (2002)SI, G. Zheng, Z. Wang, K. Morokuma,SI, G. Zheng, Z. Wang, K. Morokuma, J. Phys. Chem.J. Phys. Chem.BB 110110, 14531 (2006), 14531 (2006)

Important for self-healing of graphitic sheetsVery slow transformation processesG.G. ZhengZheng, SI, M., SI, M. ElstnerElstner, K., K. MorokumaMorokuma,, J. Phys. Chem. AJ. Phys. Chem. A108108, 3182 (2004), 3182 (2004)

Problem 2: polyynes are underrepresented


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Dilemma of theoretical simulations for

scanning SWNT growth parameter space

Review MD Problems

-Conventional quantum chemical MD (like CPMD) is too expensive

-Classical REBO MD is qualitatively incorrect: too long time scale,

unrealistic events

Target MD

Quantum mechanics

??

Then: scan ofparameter space


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Outline

Motivation



DensityDensity--functional tightfunctional tight--binding (DFTB) method and itsbinding (DFTB) method and its

application in molecular dynamics simulationsapplication in molecular dynamics simulations





Summary and outlook



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Self-consistent-charge density-functional tight-

binding (SCC-DFTB)

12

2

tot i i rep

i

E f E q q

D. Porezag, Th. Frauenheim, T. Khler, G. Seifert, R. Kaschner, Phys. Rev. B 51, 12947 (1995)M. Elstner et al., Phys. Rev. B 58, 7260 (1998)

0vi iv

c H S Second order-expansion of DFT total energy with respect to charge fluctuation

TB-eigenvalue equation~100 atoms~100s ps

DFTB Energy, Mermin, gradient

Single-zetaSTO basis set

Conjugation explici tFinite temperature approach (Mermin

free energy EMermin)

1

exp / 1i

i 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

rep

i i i i

i

EH H SF f c c q q

SR R R R

0 1if

Atomic force

E

2fi0 1 2

M. Weinert, J. W. Davenport, Phys. Rev. B 45, 13709 (1992)

EMermin = Etot - TeSe

Openshellnessexplicit

DFTB P f


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Fullerene Isomer Geometries and Energies vs B3LYP/6-31G(d)

G. Zheng, SI, M.Elstner, K. Morokuma,Chem. Phys. Lett. 412,210 (2005)

DFTB Performance

Vibrational IR and Raman Spectra

H. A. Witek, SI, G.Zheng, W. A. de Jong,K. Morokuma, J. Chem.Phys. 125, 214706

(2005)

RMS [ ] NCC-DFTB SCC-DFTB AM1 PM3C20-C36 0.025 0.019 0.035 0.030

C60-C86 0.014 0.014 0.016 0.015

R (lin. reg.) NCC-DFTB SCC-DFTB AM1 PM3C20-C36 0.88 0.93 0.77 0.73C60-C86 0.97 0.98 0.86 0.84

Geometries

Energetics

102 Fullerene Isomers small cage non-IPR C20

-C36

(35), large cage IPR C70

-C86

(67)

R2: linear regression coefficient between E(Method) and E(B3LYP)

Ih-C60 D5h-C70D2-C28

DFTB P f


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A B C

DFT:PW91[1]

-6.24 -5.63 -1.82

SCC-DFTB[2] -5.17 -4.68 -1.86

Adhesion energies (eV/atom)

A B C

PW91: An ultrasoft pseudopotential with a plane-wave cutoff of 290 eV for the single metal and theprojector augmented wave method with a plane-wave cutoff of 400 eV for the metal cluster

Fe-Fe and Fe-C DFTB parameters from: G. Zheng et al., J. Chem. Theor. Comput. 3, 1349 (2007)

[1] Phys. Rev. B 75, 115419 (2007) [2] Fermi broadening=0.13 eV

H10

C60

Fe H10

C60

FeH10

C60

Fe55

Fe55

icosahedron

(5,5) armchair SWNT (H10C60) + Fe / Fe55

DFTB Performance

Y. Ohta, Y. Okamoto, SI, K. Morokuma, Phys. Rev. B, in press

DFTB DFTB/MD A li ti


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DFTB/MD simulations of carbon nanostructure formation

SI,G.Zheng,Z.Wang,K.Morokuma,J.Phys.Chem.B110,14531(2006)andothers

Fullereneformation

ShrinkingHotGiant

Road

2000K

+108ps

+SiC

Si

SI,Z.Wang,G.Zheng,K.Morokuma,M.

Kusunoki,J.Chem.Phys.125,044702(2006)

Z.Wang,

SI,

G.

Zheng,

M.

Kusunok,

K.

Morokuma,J.Phys.Chem.C111,12960(2007)NoncatalyticCNTgrowth

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DFTB DFTB/MD Applications

Ar/O2Fullerenes

in

benzene

combustion

C>~170Giantfullerenes

Metallofullerene

formation

Fe/Co/Ni

catalyzedCNT

nucleation

3000K 3000K

0.1ps 25.0ps 64.2ps

NDto

Spiroid

to

Onion

Transformationupon

Heating

B.Saha,S.Shindo,SI,K.Morokuma,submitted

F u l l e r e n e

f o r m e d o n l y a f t e r a l l H atoms are gone.


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Outline

Motivation





Continued growth simulations of armchair SWNTs,Continued growth simulations of armchair SWNTs,

temperature dependence; zigzag SWNTstemperature dependence; zigzag SWNTs



Summary and outlook


A h i SWNT G th E i t & M d l S t


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Model system and carbon supply

R.E. Smalley et al. JACS 128, 15824 (2006)

fcc Fe38

(5,5) armchair SWNT

length = 6.2

diameter = 7.5

Silicon-oxide

Diameter: ~1nm

Fe particle

Total: 108 atomsY. Ohta, Y. Okamoto, SI, K. Morokuma,

ACS Nano 2, 1437 (2008)

Armchair SWNT Growth Experiment & Model System

21

A h i SWNT G th M th d l


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Simulation Flow Chart

Tn

= 1500 K = 1227

C

t=1 fs

Nose-Hoover chain

Equilibrated for 10 ps

10 geometries arerandomly sampledbetween 5 and 10 ps

One C atom is supplied aroundthe C-Fe interface every 0.5 ps,incident velocity correspondingto Tn

velocity Verlet

45 ps, 90 Cs are added

Y. Ohta, Y. Okamoto, SI, K. Morokuma,ACS Nano 2, 1437 (2008) &

J. Phys. Chem. C, 113, 159-169, (2009).

Armchair SWNT Growth Methodology

22

catalyst composition

T [

C]

FeCo

Ni

feedstockC C2 C2

H4

750

1227

Smalleys experiment

DFTB/MDsimulation

List of theoretical crutches :

Targeted C atom shooting to Fe/C regionSmall Fe nanoparticle (~0.7 nm)Very fast C atom supply

Armchair SWNT Gro th DFTB/MD


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Armchair SWNT Growth DFTB/MD

10 Trajectories after 45 ps C supply

Tubelengt

h[]

Time [ps]23

Schematic depiction of C atom insertion events Trajectory F

new 5-, 6-, 7-membered rings

ACS Nano 2, 1437 (2008)

Growth rate: ~10 pm/ps

Armchair SWNT Growth Sidewall Annealing


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Self-healing process of sidewall (annealing)

Fe-Carbon mobili ty at interface important!Trajectory 6: Tn

= 1500 K, Te

= 10k K, Cint

=1500 K

24.5 ps -

27.5 ps

Armchair SWNT Growth Sidewall Annealing

Movie

F. Ding, et al. Appl. Phys.Lett. 88, 133110 (2006)

Fe2000

, T=1007

CREBO/MD

Lindema

nn

index

(a.u.)

Armchair SWNT Growth SCC DFTB Charges


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SCC-DFTB Mulliken atomic partial charges

Carbon

Iron

C2

and C3

on the surface of Fe

cluster are negatively charged

Negatively charged

C atoms penetrateinto the Fe cluster

Charge transfer nearmetal-carbon boundary

Armchair SWNT Growth SCC-DFTB Charges

Slowcarbideformation

Armchair SWNT Growth Behavior of Fe Particle


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Armchair SWNT Growth Behavior of Fe Particle

2 4 6 8 100

1

2

3

4

5

6

r []

gFe-Fe

5 ps20 ps30 ps45 ps

Fe-Fe radial distribution functiondata sampling in 5 ps intervals

Snapshot at 45 psTrajectory 2: Tn=1500K, Te=10kK, Cint

=

500K

Slow Fe-carbide formation

Short polyyne chains such as C2

,C3, C

form on the surface of Fe cluster

C atoms penetrate intothe Fe cluster

Armchair SWNT Growth Length and Ring Statistics


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0 10 20 30 400

5

10

15

2025

30

0 10 20 30 400

5

10

15

20

25

30

0 10 20 30 40

7

8

9

10

11

Time [ps]

Tub

elength[]

Numberofrin

gs

0 10 20 30 40

7

8

9

10

11

Time [ps]

F H

Tub

elength[]

Numberofrings

27


Relationship between ring type and length



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10 trajectories, Tn = 1500 K

28


For comparison: Fullerene formation from C2 w/o Fe catalyst

S30

5

10

15

20

25

30

35

40

45

50

0 5 10 15 20 25 30 35 40 45

Time [ps]

Pentagon# in MD geom.

Hexagon# in MD geom.

Heptagon# in MD geom.Pentagon# in Opt. geom.

Hextagon# in Opt. geom.

Heptagon# in Opt. geom.

2000K

SI, G. Zheng, Z. Wang, K. Morokuma, J.Phys. Chem. B 110, 14531 (2006)

Note: No 4- or 8-membered ringsas in REBO/MD

Growth T dependence DFTB/MD Growth Rates


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T=1500K T=2000KT=1000K

Continued SWNT growth as function of

temperature10 Trajectories for 3 temperatures

727 C 1227 C 1727 C

T[

C] 727 1227 1727

Growth rate

[pm/ps]a 3.48 5.07 4.13

Chain carbonsa 3.9 0.3 0.2

SWNT C atomsa 112.9 110.1 102.7

( (5,5) armchair SWNT)

Y. Ohta, Y. Okamoto, SI, K. Morokuma, J.Phys. Chem. C, 113, 159-169, (2009).

Growth T-dependence DFTB/MD Growth Rates

aaveraged over 10 trajectories/T

Growth T dependence DFTB/MD Growth Rates


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Growth T-dependence DFTB/MD Growth Rates

T=727

C

10 Trajectories after 45 ps

Encapsulation of Fe by polyyne

Trajectory C

A B C D E

F G H I J

(a)

8.60 ps7.40 ps 8.32 ps

(b) Dissociation of C2

from Fe/C

T=1727

C

10 Trajectories after 45 ps

Trajectory G

Zigzag SWNT Growth DFTB/MD


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H10

C62

Fe38

(8,0) zigzag

length = 7.1

diameter = 6.3

Equilibrated at 1500 K

Zigzag SWNT Growth DFTB/MD

1C

0.0 ps 0.5 ps

59C

30.0 ps 50.0 ps

40C 52C

76.0 ps

Using (8,0) seed SWNT

fcc Fe38


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Outline

Motivation







Surface diffusion, cap formation and cap growth onSurface diffusion, cap formation and cap growth on

transition metal cluster, acetylene decompositiontransition metal cluster, acetylene decomposition

Summary and outlook


Cap Growth DFTB/MD


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Cap Growth DFTB/MD

C20 cluster

H10

C20

Fe38

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

1 C 32 Cs 33 Cs

20 ps 40 pst = 0 0.5 ps

Nanotube 10 longwas formed.

Y. Ohta, Y. Okamoto, S. Irle, and K. Morokuma, Phys. Rev. B, in press(2009)

Side Top

Experimental snaphots

0 10 20 30 400

2

4

6

8

10

12

3- ring4- ring5- ring6- ring7- ring

During growth, non-hexagonal rings and polyyne chains frequently formedand then rearrangement of sp2 network occurs to construct carbon sidewall.

Surface Diffusion DFTB/MD Annealing


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Surface Diffusion DFTB/MD Annealing

t = 0 20 ps 180 ps

40 Cs

0 20 40 60 80 100 120 140 1608.0

8.5

9.0

9.5

10.0

10.5

0 20 40 60 80 100 120 140 16002

4

6

8

10

1214

16pentagon

hexagon

0 20 40 60 80 100 120 140 1605

6

7

10

11

12pentagonhexagon

Time variation of theaveraged number of rings

Lift-off of cap clusterwas observed

C40 cluster

H10

C40

Fe38

Annealed at1500 K

Only pentagons

and hexagonswere formed

Y. Ohta, Y. Okamoto, S. Irle, and K. MorokumaCarbon 47, 1270-1275 (2009).

Annealed at1500 K

Cap Fragment Formation DFTB/MD Annealing


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Annealed at1500 K


35

Y. Ohta, Y. Okamoto, A. J. Page, S. Irle, and K. Morokuma, submitted

1 3 4 5

86 7 9 10

2

1 3 4 5

86 7 9 10

2

10 geometries arerandomly sampledbetween 5 and 10 psfor ten trajectories.

Initial model: Fe38

Annealed at1500 K

10 ps

410 ps

t = 0 ps

30 C2s30 ps

t = 410 ps


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Cap Fragment Formation DFTB/MD AnnealingY. Ohta, Y. Okamoto, A. J. Page, S. Irle, and K. Morokuma, submitted

A

100 ps 410 ps

0 5 0 1 0 0 1 5 0 2 0 0 2 5 0 3 0 0 3 5 0 4 0 00

1

23

4

5

6

7

8

Numbero

fpolygonalrings

T i m e [p s ]

f iv e - m e m b e r e d r in gs ix - m e m b e r e d r in gs e v e n - m e m b e r e d r in g

200 ps 300 ps

5

Movie, 5t(frames)=2ps

Typical sp2 carbon network nucleation and annealing


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Typical sp2-carbon network nucleation and annealing(A)polyyne chains formed on the metal surface attached to eachother creating a Y-shaped structure which preferentially formeda pentagon;(B) polyyne chains on a pentagon formed a pentagon orhexagon fused to the pentagon;

(C) pentagon-to-hexagon self-healing rearrangement took placewith the help of short-lived polyyne chains stabilized by themetal.

The nucleation process resembles fullerene cage formation.The metal particle (catalyst) differentiates the two processes.In particular, the metal particle:

1. holds carbon fragments on the surface (Saturation ofdangling bonds); 2. slows down diffusion; 3. makes the Fe-C bond the most reactive;

4. slows down bond rearrangement processes; 5. prevents closure of the curved open-ended carbon structure.

Acetylene Decomposition DFTB/MD


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Polyacetylene formation, largest carbon cluster: C6Hx

Acetylene Decomposition DFTB/MD

Initial model: Fe38

Annealed at1500 K10 ps

10 geometries arerandomly sampledbetween 5 and 10 psfor ten trajectories.

t = 0 ps

30 C2H2s

30 ps

1 2 3 4 5

6 7 8 9 10

Annealed at

1500 K15 ps

1 2 3 4 5

6 7 8 9 10


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Outline

Motivation

Review: state of the art SWNT growth control

(experiment and theory)







Summary and outlookSummary and outlook


SummarySummary & Outlook


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DFTB/MD method very useful to probe SWNT growth parameter

space by more realistic simulations of SWNT growth on metal particle.

Carbon atom supply in Fe/C interface region leads to developmentof short polyyne chains that grow into 5/6/7 rings, some temperature

dependence of growth.

Summary

SWNT (n,m) chirality NOT preserved! Chirality should be

preserved if carbon addition is slower than defect annealing (10sof picoseconds)

Summary & Outlook

Pentagon-hexagon-only growth achieved by slower surface

diffusion.

First-ever cap nucleation from C

2

molecules observed by slow

surface diffusion.

Cap nucleation very similar to fullerene cage nucleation,

slowed down by presence of Fe cluster (immobility of C2

andpolyynes)

Summary & Outlook Outlook


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Extension of DFTB/MD time scale is needed:

Faster alternatives to BOMD but with similar time step

Different type of MD?

Faster computer?

y

Future Studies:

What is the role of carbide formation for nucleation?Different carbon feedstock and different metals

Finally: scan of

parameter space

Acknowledgements


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Research Center for Computational Science(RCCS), Okazaki Research Facilities, National

Institutes for Natural Sciences.

Computer resources :

CREST grant in the Area of High PerformanceComputing for Multi-scale and Multi-physicsPhenomena from JST

Academic Center for Computing and MediaStudies (ACCMS), Kyoto University

Funding :

JST Tenure Track Funding by MEXT MSCF (to SI)

g

Center for Nanophase Materials Sciences(CNMS) Oak Ridge National Laboratory

005 keiji morokuma

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