generation mechanism of carbon cluster, fullerene, and ...maruyama/papers/99/seoul_paper.pdf ·...

Generation Mechanism of Carbon Cluster, Fullerene, and Metallofullerene

Shigeo Maruyama

Engineering Research Institute and Department of Mechanical Engineering,

The University of Tokyo 2-11-16 Yayoi, Bunkyo-ku, Tokyo 113-8656, Japan

e-mail: [email protected] URL: http://www.photon.t.u-tokyo.ac.jp/~maruyama

Abstract:

The formation mechanism of empty and metal-containing fullerene was studied through molecular dynamics simulations and Fourier Transform Ion Cyclotron Resonance (FT-ICR) mass spectroscopy of laser vaporized carbon cluster. With classical molecular dynamics simulations using modified Brenner potential, the clustering process starting from 500 isolated carbon atoms in gas phase was simulated under the controlled temperature condition. When the control temperature was at Tc = 3000 K, imperfect caged clusters like C60 and C70 were obtained. Additional annealing simulations to compensate the short time-scale of the simulation resulted the perfect Ih-C60 structure through Stone-Wales transformations. A fullerene formation model featuring the random caged structure and annealing at the size range of C40 to C60 was proposed through the detailed study of the precursor structures in simulations. In order to incorporate metal atoms in the simulation, multi-body classical potential functions for metal-carbon and metal-metal interactions were constructed based on DFT (density functional theory) calculations of various forms of small clusters MCn and Mn (M = La, Sc, Ni). The classical potential was expressed with the Morse term and the Coulomb term as function of coordinate number of a metal atom. The simulated clustering process with addition of 1 % of metal atoms was compared with the pure carbon simulation. When La atoms were applied, the stable open-cap structure surrounding the La atom resulted in the La-containing caged cluster. For Sc-C system, the host carbon clusters were not affected so much as the La-C case due to the weaker Coulomb interaction, and the Sc atom was encapsulated in the host cage at the final stage of the growth process. Ni-C system was also simulated to explore the possible role of metal atoms in the generation of SWNT. The precursor clusters were similar to those in Sc-C system, although the Ni atom finally stayed on a face of 7 or 8 member-ring of the caged structure.

Fourier Transform Ion Cyclotron Resonance (FT-ICR) mass spectrometer directly connected to the laser vaporization cluster beam source was implemented to study the clustering process. With increase of cluster nozzle pressure, three different types of positive mass spectra were obtained for pure carbon clusters: smaller than about C60 with odd numbered clusters up to C40; almost only C60 and a trace of C70; well-known even atom mass with intense peaks at C60 and C70. Qualitatively the lower pressure condition of the cluster source corresponded to the earlier stage of the MD simulation. Through these comparisons, we speculated that the even-numbered clusters

corresponded to the annealed random caged clusters. The FT-ICR mass spectra of metal-carbon binary clusters were studied for sample materials normally used for generation of metal-containing fullerene and SWNT; La: 0.8%, Y: 0.8%, Sc: 0.8%, Gd: 0.8%, Ce: 0.8%, Ca: 0.3%, and Ni:4.2% - Y: 1%. Positive La-C, Y-C, Sc-C, Gd-C, Ce-C binary clusters commonly showed strong MC2n

+ signal in the range of 36 < 2n < 76 with intense magic numbers at MC44

+, MC50+ and MC60

+. Characteristics of these small clusters were compared with results of molecular dynamics simulations.

In order to further study the information of clusters appearing in the mass spectra, reactivity of negative carbon clusters and metal-carbon binary clusters to NO were measured by the FT-ICR spectrometer. For empty clusters, even-odd alternation of reactivity was clearly shown; even clusters were less reactive. Furthermore, carbon clusters with La atom such as LaC44

- were very much unreactive to NO. The reactivity of clusters contaminated with a hydrogen atom was very curious. One hydrogen atom made odd-numbered clusters less reactive and even-numbered clusters more reactive. These experimental results were perfectly explained by a consideration of number of dangling bonds based on the random-raged geometric structure predicted by the molecular dynamics simulations.

1

Congratulations to The 10th Anniversary of

the Institute of Advanced Machinery and DesignSeoul National University

Congratulations to The 10th Anniversary of

the Institute of Advanced Machinery and DesignSeoul National University

Generation Mechanism of Carbon Cluster, Fullerene,

and Metallofullerene

Generation Mechanism of Carbon Cluster, Fullerene,

and Metallofullerene

Shigeo Maruyama

Engineering Research Institute& Department of Mechanical Engineering

The University of Tokyoe-mail: [email protected]

URL: http://www.photon.t.u-tokyo.ac.jp/~maruyamaCo-Workers:Masamichi Kohno, Shuhei Inoue, Tetsuya Yoshida, Hideaki Hayashi, and Yasutaka Yamaguchi

Int. Symp. Micro/Nano Scale Mech. Eng.Dec. 1999, Seoul University

�Fullerene Formation Mechanism�Metal-Containing Fullerene �Hydrogen Storage by SWNT

�Laser-Vap. Cluster Source+ FT-ICR Mass Spectrometry+ Time of Flight

�Arc-Discharge Generator�Laser-Oven Generator (SWNT)

Fullerene & Carbon Nanotube

�Non-Adiabatic MD?�Laser Annealing of Clusters�Photo-Fragmentation

Light-Matter Interaction

�Liquid Droplet on Solid Surface�Vapor Bubble Nucleation�Droplet and Surface Tension�Thermal Boundary Resistance

Inter-Phase Phenomena

�Tight-Binding and Quantum MD�Dissociation Dynamics�Phase Change (Polycrystalline)

�Photo-Fragmentation in TOF�Chemical Reaction in FT-ICR�Quantum Dots?

Silicon Clusters, Surface & Bulk

Molecular Dynamics SimulationsExperimental

Current Research ProjectsCurrent Research Projects

2

Typical Structures of FullereneTypical Structures of Fullerene

(a) C60 (c) La@C82(b) C70

(e) SWNT (f) MWNT

C60

PVWin

(d) Sc2@C84

D S Ra c d

R R

e e= = = == = = == =

−6 325 129 15 13150 80469 0 011304 19 2 517 2 0

1

0 0 0

1 2

. eV . . � . �

. . .. � . �

βδ

A A

A A

Potential parameters

From D. W. Brenner: Phys. Rev. B, 42, 9458(1990)

1f

r0

R1 R2

Cut-off function

k

i j

θijk

Molecular Dynamics SimulationC-C Potential Function{ }��

<

−=i ij

ijAijijRb rVBrVE)(

* )()(

{ })(2exp1

)()( ee

R RrSSDrfrV −−−

= β��

�� −−

−= )(2exp

1)()( e

eA Rr

SSSDrfrV β

{ }δ

θ−

≠��

��

�+=

+= �

),(

* )()(1,2 jik

ikijkcijjiij

ij rfGBBB

B

��

��

�

++−+= 22

0

20

20

20

0 )cos1(1)(

θθ

dc

dcaGc

Total Energy Eb:

3

C10

C8

25001000 1500 2000500Time (ps)

C60C49

C28C26

C12 C15

C8

C330

20

40

60

C70C53

C8 Clu

ster

Siz

e

500 carbon atoms 342 Å cubic boxTc = 3000 K

Growth Process

PVWin

74

7

77

4 8

77

7

77

77 7

initial

215.81 ns 215.82 ns 216.35 ns 216.40 ns

216.45 ns 217.18 ns 218.39 ns 220.56 ns 221.70 ns (Ih C60)

A

215 ns

B

–6.72

–6.68

–6.64

–6.6

0

4

# of

dam

glin

gbo

nds

ND

B

Ep

NDB

pote

ntia

l ene

rgy　

E p(e

V)

time (ns)190 200 210 220 230

Ih C60

Annealing Process to perfect C60

PVWin

4

Chain Ring FlatC10 C20 C30

Tangledpoly-cyclic

Closed cage Stone-Walestransformations

C50

C70C60

Fullerene(stable)

Opencage

Graphitic sheetToo low temperature

Chaotic 3-dimensionalstructure

Too hi

gh te

mperat

ure

Randomcage

Higherfullerene

Present Fullerene Formation Model

Studied Metal Atoms

Group 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18Period

1 21 H He

1.008 4.0033 4 5 6 7 8 9 10

2 Li Be B C N O F Ne6.941 9.012 10.81 12.01 14.01 16.00 19.00 20.18

11 12 13 14 15 16 17 183 Na Mg Al Si P S Cl Ar

22.99 24.31 26.98 28.09 30.97 32.07 35.45 39.9519 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36

4 K Ca Sc Ti V Cr Mn Fe Co Ni Cu Zn Ga Ge As Se Br Kr39.10 40.08 44.96 47.88 50.94 52.00 54.94 55.85 58.93 58.69 63.55 65.39 69.72 72.61 74.92 78.96 79.90 83.80

37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 545 Rb Sr Y Zr Nb Mo Tc Ru Rh Pd Ag Cd In Sn Sb Te I Xe

85.47 87.62 88.91 91.22 92.91 95.94 99.00 101.1 102.9 106.4 107.9 112.4 114.8 118.7 121.8 127.6 126.9 131.355 56 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86

6 Cs Ba * Hf Ta W Re Os Ir Pt Au Hg Tl Pb Bi Po At Rn132.9 137.3 178.5 180.9 183.8 186.2 190.2 192.2 195.1 197.0 200.6 204.4 207.2 209.0 210.0 210.0 222.0

87 88 104 105 106 107 108 109 110 111 1127 Fr Ra ** Unq Unp Unh Uns Uno Une Uun Uuu Uub

223 226 261 262 263 262 265 266 269 272 277－－－－

57 58 59 60 61 62 63 64 65 66 67 68 69 70 71La Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Lu

138.9 140.1 140.9 144.2 145 150.4 152 157.3 158.9 162.5 164.9 167.3 168.9 173.0 175.089 90 91 92 93 94 95 96 97 98 99 100 101 102 103Ac Th Pa U Np Pu Am Cm Bk Cf Es Fm Md No Lr227 232 231 238 237 239 243 247 247 252 252 257 258 259 262

* Lanthanides

** Actinides

5

M-C and M-M Potential Function Expression

CARij VVVE ++=

VR: Repulsive term VA: Attractive term

VC: Coulomb term

N C: carbon coordinate number

B*: normalized bond order

cM, cC : charge of M (+) and C(-)

f(rij) : cut-off function

{ })(2exp1

)( eije

ijR RrSSDrfV −−−

= β { })(/2exp1

)( *eij

eijA RrS

SSDBrfV −−

−⋅−= β

ijijC r

ccerfV MC

0

2

4)(

πε−=

�≠

+=)(carbon

C )(1jk

ikrfN

{ } δ)1(1 C* −+= NbB

)exp(3 2C

1M kNkc +−−= CMC / Ncc =

�≠

+=)( metal

M )(1jk

iki rfN2

MMji

ijNNN +=

{ })1(exp)( 21 −−+= ijDeeije NCDDND

{ })1(exp)( 21 −−−= ijReeije NCRRNR

M-C M-M

N Mi: metal coordinate number

ij

jiijC r

ccerfV MM

0

2

4)(

πε=

Metal-Carbon Potential functions

2 3 4

–2

–1

0

–3

pote

ntia

l ene

rgy

(eV)

distance r (Å)

VC (N C=15)

(a) La-C

La2

VC (N C=5)

Eb (N C=15)

Eb (N C=5)

–3

–2

–1

0

2 3 4

pote

ntia

l ene

rgy

( eV)

distance r (Å)

(b) Sc-C

VC (N C=15)

Sc2

VC (N C=5)

Eb (N C=15)Eb (N C=5)

–3

–2

–1

0

2 3 4

pote

ntia

l ene

rgy

( eV)

distance r (Å)

(c) Ni-C

Ni2

Eb (N C=15)

Eb (N C=5)

Table 1. Poten tial parameters for metal-carbon in teractions.De (eV) S β (1/Å) Re (Å) R 1 (Å) R 2 (Å) b δ k1 k2

La-C 4.53 1.3 1.5 2.08 3.2 3.5 0.0854 -0.8 0.0469 1.032Sc-C 3.82 1.3 1.7 1.80 2.7 3.0 0.0936 -0.8 0.0300 1.020Ni-C 3.02 1.3 1.8 1.70 2.7 3.0 0.0330 -0.8 －－

Table 2. Poten tial parameters for metal-metal interactions.S β (1/Å) De1 (eV) De2 (eV) CD Re1 (Å) R e2 (Å) CR R 1 (Å) R 2 (Å)

La-La 1.3 1.05 0.740 2.64 0.570 3.735 0.777 0.459 4.0 4.5Sc-Sc 1.3 1.4 0.645 1.77 0.534 3.251 0.919 0.620 3.5 4.0Ni-Ni 1.3 1.55 0.74 1.423 0.365 2.520 0.304 0.200 2.7 3.2

6

time (ps)20001000 30000

0

20

40

0

10LaC2 LaC5 LaC6LaC9

LaC3

LaC5

LaC35 LaC46

60

80

20LaC15 LaC17

C12

C13

LaC19

LaC48

C20

La@C73LaC51

(a) Growth process of a La@C73

(b) Growth process of a LaC17

cluster size

Growth Process of LaCn Clusters

Control temperature Tc = 3000 K500 C & 5 La in (342 Å)3 cubic box

PVWin

Collision Process of La Attached Clusters

cluster size

time (ps)4000 5000

0

20

40

60

LaC24 La2C38

LaC14

(La@C54) La

C16

7

Cluster Source Nozzle for FT-ICR

Pulsed Valve

Target Disk

Waiting Room

Focused Laser Beam

He 10 atm

Expansion Cone

Cluster Beam

Cluster Source for FT-ICR

Window

To ICR CellFast Pulsed Valve

ExpansionCone

“Waiting” RoomTarget Disc

Gears

Gears

Window

Feedthroughfor Up-down

Feedthroughfor Rotation

Vapo

rizat

ion

Lase

r

8

FT-ICR (Fourier Transform Ion Cyclotron Resonance)Mass Spectrometer

Turbopump

Gate Valve

Cluster Source

6 Tesla Superconducting Magnet

100 cm

DecelerationTube

Front Door

Screen Door

Rear Door

Excite & DetectionCylinder

ElectricalFeedthroughGas Addition

Ionization Laser

Probe Laser

rmvqvBF

2

==

mqB

rvf

ππ 22==

Mechanism of Fourier Transform Ion Cyclotron ResonanceMass Spectrometry (FT-ICR)

Mechanism of Fourier Transform Ion Cyclotron ResonanceMass Spectrometry (FT-ICR)

Magnetic FieldDigital

OscilloscopeDigital

Oscilloscope

PreAmplifier

Arbitrary WaveformGenerator

Excite

Detect Ion

Back Door

ICR Cell

9

Example of Excite and Detect WaveformExample of Excite and Detect Waveform

0 500 1000Frequency (kHz)

Inte

nsity

(arb

. uni

ts)

C60+

Excite

Detect

0 10 20 30 40 50Time (ms)

Volta

ge (a

rb.)

Excite Detect

40 50 60 70 80

720 740Ion Mass [amu]

C60+

Number of Carbon Atoms

Inte

nsity

(arb

. uni

ts)

LaC44+ LaC50

+

LaC60+

Lanthanum-carbon binary clusters

10

Growth Process of a Sc Containing Cluster

ScC3

60

4000

ScC18 ScC37 ScC39

C11

C12

ScC43 ScC49 Sc@C54 Sc@C550

20

40

20000time (ps)

cluster size

1000 3000

Graphite-like Open cage

Metal outside Metal inside

Fan-type Closed cage

Sc: 5, C: 500 in 34.2nm box

PVWin

40 50 60 70 80

720 760 800Ion Mass [amu]

ScC60+

C64+

Sc2C56+

Number of Carbon Atoms

Inte

nsity

(arb

. uni

ts)

ScC60+

C60+

ScC50+

ScC44+

Scandium-carbon binary clusters

11

For Production of Single Wall Nanotube (SWNT)For Production of Single Wall Nanotube (SWNT)

Combination of Metals: Ni-Co or Ni-Y is necessaryfor Production of Single Wall Nanotube

TEM Pictures of SWNT RopesTEM Pictures of SWNT Ropes

Individual tube diameter: 1.3 nmSpacing: 0.34 nmMisalignments and Terminations

12

Molecular Simulation of Hydrogen Storage in SWNT

Hydrogen 5376 molecules

Bundle of SWNT560x8-140

=4340 C Atoms

Growth Process of Ni Attached Clusters

Graphite-like Open cageChain or Ring

Metal inside & outside

time (ps)20001000 3000 4000

0

20

40

NiC2

NiC18 NiC35 NiC49 NiC50NiC44

C16

cluster size

400 800 1200 1600

0

10NiC6 NiC10 NiC12 NiC14NiC9

Ni: 5, C: 500 in 34.2nm boxPVWin

13

Tc = 2500 KAnnealing of NiC78 and Ni2C54 Cluster

# of

pos

itive

inne

r pro

duct

s

time (ps)400 8000

10

20

30

insideoutside

400 800

NiC78 Ni2C54

500 700 900 1100 1300Ion Mass [amu]

Inte

nsity

(arb

. uni

ts)

Ni:4.2% Y:1.0%

YC50+

YC60+

YC44+

C60+

f1 time = 370µs

f1 time = 380µs (x5)

Y2C82+YC82

+YC70+

Nickel-Yttrium-carbon clustersNickel-Yttrium-carbon clusters

14

Yttrium-carbon binary clustersYttrium-carbon binary clusters

500 700 900 1100 1300Ion Mass [amu]

Inte

nsity

(arb

. uni

ts)

f1 time = 365µs

f1 time = 375µs (x2)

YC60+

Y:0.8%

YC50+

YC44+

C60+

YC70+ YC82

+

Y2C82+

As injected Negative Clusters

As injected Negative Clusters

400 600 800

20 40 60 80Number of Carbon Atoms

Inte

nsity

(arb

itrar

y)

(a) pure carbon

(b) La–C

(c) La–C

(1:130)

(1:130)

Cluster ion mass (amu)

15

Reaction with NO 10-5 Torr

Reaction with NO 10-5 Torr

440 460 480 500


Inte

nsity

(arb

itrar

y)(a) as injected

(b) SWIFTed

(c) NO 1s

(d)NO 3s

(e) NO 10s


C37–+C37H

–C40

–

C37H– C37NO–

C40NO–

Even-odd Difference of Reactivity for

Negative Pure Carbon Cluster



400 500

30 33 36 39 42


Inte

nsity

(arb

itrar

y)

(a) as injected

(b) SWIFTed

(c) NO 1s

Number of Carbon atoms

C30– C33

– C36–

C39–

C33NO– C39NO–

16





450 500 550 600

38 40 42 44 46 48 50Number of Carbon Atoms

Inte

nsity

(arb

itrar

y)

(a) as injected

(b) SWIFTed

(c) NO 1s


C38– C41

– C44–

C47–

C41NO– C47NO–

LaC44- was not

Reactive to NO.LaC44

- was not Reactive to NO.

520 570 620 670 720

45 48 51 54 57 60Number of Carbon Atoms

Inte

nsity

(arb

itrar

y)

(a) as injected

(b) SWIFTed

(c) NO 1s


C44–

C47– LaC44

–

C44NO– C47NO–

17

55 60Number of Carbon Atoms

Inte

nsity

(arb

itrar

y)(a) as injected

(b) NO 2s

LaC44–

LaCoddIs More

Reactive

LaCoddIs More

Reactive

Reaction with H During formation

(Dirty Source)

Reaction with H During formation

(Dirty Source)


Inte

nsity

(arb

itrar

y)

3.6%6.4%43.0%47.0%n: odd1.6%7.2%19.6%71.6%n: evenCnH3CnH2CnH Cn

Average of n = 42-51

18


Inte

nsity

(arb

itrar

y)LaC36

- has no Hydrogen Atom by Dirty Source.

LaC36- has no

Hydrogen Atom by Dirty Source.

LaC36-

Even Clusters with H

Reacts with NO.

Even Clusters with H

Reacts with NO.

52 54 56Number of Carbon Atoms

Inte

nsity

(arb

itrar

y)

(a) as injected

(b) NO 2s

19

Summary for Bare ClustersSummary for Bare Clusters

Ceven: Less Reactive

Codd: More Reactive

Effect of H: Unreactive

Effect of H: More Reactive

Reaction with NO

Reaction with H (Dirty Source)

Ceven: Less Reactive

Codd: More Reactive 3.6%6.4%43.0%47.0%n: odd1.6%7.2%19.6%71.6%n: evenCnH3CnH2CnH Cn

Average of n = 42-51

��

→+ −

−−

NOCHNOC

NOHCeven

eveneven

−− →+ NOCNOC oddodd

Possible Reaction SitesPossible Reaction Sites

Even Numbered Clusters# of Dangling Bond = 0, 2, 4, …

Odd Numbered Clusters# of Dangling Bond = 1, 3, 5, …

H or NO

Euler’s Theorem:223

323 42,2

2,

23,2 vfvvvvfvveevf +−=+=+=+=+=+

20

Revisit the Use of Euler’s TheoremRevisit the Use of Euler’s Theorem

Euler’s Theorem: 2+=+ evff: faces, v: vertices, e: edges

Usual Explanation of Even Numbered Positive Spectra

��

+=+=

+=

65

65

65

653652

ffvffe

fff

��

+==

6

5

22012

fvf

5f6f

23

2323

vvv

vve

+=

+=

More General TreatmentMore General Treatment

3vEuler’s Theorem: 2+=+ evf

When All Carbon has 3 Bonds

ve23=

2v

42223 −=→+=+ fvvvf

When Some of Carbon has Dangling Bond

23 422

2vfvvf +−=→+=

v must be even

v2 is even/odd when v is even/odd

21

Summary for La-C Binary ClustersSummary for La-C Binary Clusters

Ceven: Unreactive

Codd: Reactive

Effect of H: Unreactive

Reaction with NO

Reaction with H (Dirty Source)

Ceven: Less Reactive (less than 10% react)

Codd: More Reactive (about 40% react)

)36( ≥n

MD SimulationLa25+C2500, 3000K

MD SimulationLa25+C2500, 3000K

1

7

6

2

3

4

5

8

910

11

22

La@’’’C47

La@Cn Structures (n = Odd) Observed in Molecular Dynamics Simulation

La@Cn Structures (n = Odd) Observed in Molecular Dynamics Simulation

La@’C47

La@C54 La@’’C54

La@Cn Structures (n = Even) Observed in Molecular Dynamics Simulation

La@Cn Structures (n = Even) Observed in Molecular Dynamics Simulation

23

ConclusionsConclusions

La@Ceven La@’’Ceven

La@’’’CoddLa@’Codd

FT-ICR Reaction Results SuggetAnnealed Random Cage Model

@Ceven @’’Ceven

@’Codd @’’’Codd

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