H.O. Pierson. Handbook of carbon, graphite, diamond and fullerenes. Properties, processing and applications. 1993

15

The Fullerene Molecules

1.0 GENERAL CONSIDERATIONS

1.l State of the Art

The

recent

discovery

of a family

of large,

solid carbon

molecules

with

great stability,

the

so-called

‘fullerenes”,

has

considerably

extended

the

scope

and variety

of carbon

molecules

known

to exist

and

is opening

an

entirely

new

chapter

on the

physics

and

chemistry

of

carbon,

with

many

potential

applications.

The fullerenes

can

be considered

as another

major

allotrope

of carbon

and its first stable,

finite, discrete

molecular

form.

They

are different,

in that

respect,

from

the

other two

allotropes,

graphite

and

diamond,

which

are

not

molecular

but

infinite-network

solids.

The

other

known

carbon

molecules,

C, to C,,,

are unstable

and found only

in thevapor

phase

at high

temperature

(see Ch. 2, Sec. 5.0).

The

fullerenes

are

generally

arranged

in

the

form

of

a

geodesic

spheroid

and thus

were named

after the inventor

of the geodesic

dome,

the

renowned

architect

Buckminster

Fuller.

They

were

originally

(and still

are

occasionally)

called

“buckminster-fullerenes”,

a name

fortunately

short-

ened to fullerenes.

They

are

also

known

as ‘buckyballs”.

1.2Historical Perspective

The fullerenes were discovered	in 1985	by Smalley	and	Kroto who,
while performing mass-spectroscopy	analysis	of carbon	vapor,	observed

356

		The Fullerene	Molecules	357
the presence		of even-numbered clusters of carbon atoms in the molecular
range	of C,	- C,,, as illustrated in Fig. 15.1 .tlj-M The	experiment	was
canied	out in the apparatus shown schematically in Fig. 15.2, consisting of

a pulsed laser beam directed onto the surface of a rotating-translating

graphite disk. Clusters of fullerenes				were generated spontaneously			in the
condensing		carbon vapor when the hot plasma was quenched by a stream
of helium.	This research		provided the clue that led to the elucidation				of the
fullerene	structure.
The practical synthesis of fullerenes					as solid aggregates was demon-
strated by Kratschmer and Huffman				in 1990, by the simple evaporation of
a graphite electrode as will be described					in Sec. 5.0.t4]	Fullerenes are now
readily available in increasing quantities					for study and evaluation.
These		discoveries	generated	considerable interest in the scientific
community		and in the general public, as demonstrated				by the number of
publications		on the subject, estimated to total nearly one thousand in 1993,
only eight years after the fullerenes				were first observed.

	'00	'11 I	'	I	'				I
						60'	'	'	'

1

80

20

0’	’	’	’	’	’	’	’	’	’	’	h A
0		20		40		60		80		100	120

Cluster Size

Figure 15.1. Time-of-flight mass spectrum of carbon clusters produced by laser vaporization of graphite.[*]

358 Carbon, Graphite, Diamond, and Fullerenes

ton Detector

		Pulsed	Cluster
		Vaporization
	High Pressure		Growth
		Laser
	Helium (10 atm)		Zone
	\	I	/

			t
			Time-of-Flight
Lias	Beam		Mass
	Rotating		Spectrometer
JPPet
	Translating
‘alve
	disk
I
Seal
Figure 15.2. Carbon-cluster beam source with		pulsed	laser.121[3]
2.0 STRUCTURE	OF THE FULLERENE	MOLECULES

2.1Molecular Structure of the Fuiierenes

Geodesic	Structure.	Unlike graphite or diamond,	the fuiierenes are
not a single material, but a family of molecular, geodesic			structures	in the
form of cage-like	spheroids,	consisting of a network of five-membered		rings
(pentagons) and six-membered rings (hexagons). In order to close				into a

spheroid, these geodesic structures must have exactly twelve pentagons,

but can have a variable number of hexagons (m), with the general composition: C20+2m. Such an even-numbered distribution is unique to the

element carbon.

Atomic Bonding. in order to account for the bonding of the carbon

atoms of a fuiierene	molecule, the hybridization must be a modification of
the sp3 hybridization	of diamond and sp2 hybridization of graphite (see Ch.
2, Sets. 3.0 and 4.0).	It is such that the sigma (a) orbitais no longer contain

ail of the s-orbital character and the pi (z) orbitals are no longer of the purely p-orbital character, as they are in graphite.

The Fullerene

Molecules

359

Unlike

the

sp3 or sp2 hybridizations,

the

fullerene

hybridization

is not

fixed

but has

variable

characteristics

depending

on the

number

of carbon

atoms

in the

molecule.

This number varies from twenty

for

the

smallest

geometrically

(but

not

thermodynamically)

feasible

fullerene,

the

C20. to

infinity

for graphite

(which

could

be considered

as the

extreme

case of all

the

possible

fullerene

structures).

It determines

the

size

of the molecule

as

well

as the angle

0

of the basic pyramid

of the structure

(the common

angle

to the

three

u-bonds).

The number

of

carbon

atoms,

the pyramidization

angle

(0 -

903,

and

the

nature

of

the

hybridization

are

related

and

this

relationship

(in

this

case

the s

character

in

the n-orbital)

is

given

in

Fig.

15.3.[51

The bond lengths

of the fullerenes

are reported

as 0.145

+/-0.0015

nm

for the bonds

between

fiveand six-membered

rings, and

0.140

+/- 0.0015

nm for the

bond

between

the six-membered

rings.f6)

5

10

15

Pyramidalization Angle (8,,-90)”

Figure 15.3. Hybridization of fullerene molecules as a function of pyramidization angle (&XT - 907. @an is the common angle of the three CTbonds.[5]

360 Carbon, Graphite, Diamond, and Fullerenes

2.2 Characteristics of the Fuilerene Molecules

General Characteristics. The fullerene structure is unique in the sense that the molecules are edgeless, chargeless, and have no boundaries, no dangling bonds, and no unpaired electron. These characteristics

set the fullerenes apart from other crystalline structures such as graphite or diamond which have edges with dangling bonds and electrical charges.p)

Such features allow these molecules, and particularly the C, which is the most symmetrical, to spin with essentially no restraint at a very high rate.R

The Fullerene Family. Many fullerene structures are theoretically possible, some with hundreds of atoms. Five have been unambiguously identified and structurally characterized so far: the C,, &, &, C,s, and c,.m

. At one end of the fullerene family is the CZO,the simplest structure, which is composed of twelve pentagons with no hexagon and with a pyramidization angle of 18”. All its atoms would have the sp3 configuration but it is thermodynamically unstable.fe)

•The first stable fullerene and the first to be discovered is the C,. It is the dominant molecule with sixty carbon atoms arranged so that they form twenty hexagons, in addition to the necessary twelve pentagons, giving it the appearance of a soccer ball (known as a football outside the U.S.A. and U.K.). Each hexagon is connected to alternating pentagon and hexagon, and each carbon atom is shared by one pentagon and two hexagons. Its hybridization is partially sp3 and partially sp2, with a

pyramidization angle of 11.6”. It is shown schematically

in Fig. 15.4.	The C,	has a calculated diameter		of 0.710
t/- 0.007 nm. It is intensely			purple in apolar solvents.fr)f6)
. The higher	fullerenes	are	shown schematically	in Fig.

15.5.p) The Cr, is the second most prominent fullerene. It has a rugby-ball appearance and is has a deep orange-

red color in solution. The CT6 is chid with a structure

consisting of a spiraling arrangement of pentagons and hexagons.t9) It has a bright yellow-green color in solution

The Fullerene Molecules 361

and in the crystal. The Cr, is chestnut brown or goldenyellow and the C,, is olive-green. The electronic absorption spectra for these fullerenes is shown in Fig. I 5.6.t61

. As the number ofcarbon atoms increases, the s-character in the x-orbital becomes less and less pronounced to become zero in the case of the ideal graphite crystal, when the pyramidization angle is zero and the number of atoms is infinite.

Figure 15.4. Schematic of a C,, fullerene molecule.

362 Carbon, Graphite, Diamond, and Fullerenes

c70

c76

c78

Figure 15.5. Schematic of GO, C,,, and C,, fullerene rnolecules.~]

The Fullerene Molecules 363

x20

tL c70

C78

200 300 400 500 600 700 800 900

Wavelength (nm)

Figure 15.6. Electronic-absorption spectra of fullerenes in solution (C,, and GO in hexane, G, and C,, in dichloromethane).v]

364 Carbon, Graphite, Diamond, and Fuiierenes

Related Structures.

it appears

that

the spheroid

fuiierenes

such

as

C,

are not the

only type of large curved

carbon

molecules.

Geometrically,

many

such

structures

are feasible.tlOl

iijima and

coworkers

have actually

detected

carbon molecular

structures

by transmission

electron

microscopy

that

are

in

the

form

of

cylindrical

tubes,

closed

by

polyhedral

caps

and

known

as “buckytubes”.

These structures

have

the

hexagons

arranged

in

a helix

around

the tube axis and some

have a negative

curvature.[ll]

The

defect

in

the

hexagonal

network

that

triggers

the

formation

of

such

structures

is believed

to be a single

heptagonal

ring.

Some

of these tubes

are

whisker-like

and

may

reach micron

size.

2.3Mechanism of Formation

As described

by

Smalley,

the

formation

of a

fuiierene

follows

an

“efficient mechanism

of self-assembly

of an architecturally

useful

structure

on a nanometer

scale.“f2t

The isolated Pentagon Rule. A model

of the

growth

mechanism

of

thefullerenes

is based

on the isolated

Pentagon

Rulewhichstates

that such

geometrical

structure

must

meet

the

following

three

criteria: (a) it must

be

made

only

of hexagons

and pentagons,

(b) it must

have

twelve

pentagons,

and (c) it must

not include

adjacent

pentagons.[2tmt12j

This

last criterion

is also requiredfrom

the thermodynamicsstandpoint

since

the

fusion

of

two

pentagons

is

not

favorable

energetically

due

to

increased

ring

strain,

and

carbon

structures

with

adjacent

pentagons

are

unstabie.p]

The C,

is the

first fullerene

that

avoids abutting

pentagons.

it

is the

most

stable

and

symmetrical

of

all

the

stable

fullerene

molecules.

Smallergeodesicstructures,

such

asthe

C,,

mentioned

above,

cannot form

or be stable

since

they

would

incorporate

abutting

pentagons.

Formation. It had been

originally

suggested

that the molecule

begins

as a graphitic

network

that

adds carbon

atoms

as pentagons

(in addition

to

the graphitic

hexagons)

causing

the

sheet

to

curl

and

eventually

close

to

form

a

geodesic

sphere.

A

more

likely

mechanism

is formation

by

the

aggregation

of

small

carbon

radicals.f21

This occurs

when

graphite

is

vaporized

at very

high

temperature.

The condensing

free-flowing

graphitic

sheets

in the vapor

have

no atoms

to form

dangling

bonds and the

physical

tendency

to reach

the

lowest

energy

level

induces

them

to curl

and

anneal

into the

fullerene

structure.t3tf13]

A hypothetical

growth

sequence

is shown

in Fig.

15.7.R

The Fullerene Molecules 365

Figure 15.7. Hypothetical growth sequence of a C,, molecule.[31