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3 Fullerenes Fullerenes, Large Carbon Molecules, and Hollow Cages of Other Materials

3 Fullerenes Fullerenes, Large Carbon Molecules, and Hollow Cages of Other Materials

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Carbon Nanostructures – Tubes, Graphene, Fullerenes, Wave-Particle Duality

Fig. 5.48 Mass spectra from an extract of the Allende meteorite containing C60 and larger carbon

clusters. (Reprinted with permission from [5.177]. © 1999 Nature Publishing Group)

occur naturally in minerals [5.176] or in the Allende meteorite (see Fig. 5.48 and

Sect. 3.8). Fullerenes have also been detected in the soot of candle lights (see

[5.178]). Thus, we now realize that humans have been synthesizing fullerenes for

thousands of years.

5.3.2 Fullerene Compounds

Endohedral metallofullerenes were synthesized where single or a few metal atoms

as La [5.179], Y [5.180], U [5.181], Fe [5.182], Co [5.183], and Gd [5.184] were

encapsulated in fullerene molecules and purified. A Sc dimer was encaged in C66

(Sc2 @C66 ; Fig. 5.49 a) and Sc2 @C84 in a carbon nanotube (Fig. 5.49b) forming a


Attachment of foreign atoms to the fullerene shell and integration of foreign

atoms into the shell have also been studied. When charge-donating K atoms are

attached to the C60 host, spectroscopic measurements show that each attached K

atom donates ∼0.6 electrons to the C60 molecule, thereby enabling its electronic


Fullerenes, Large Carbon Molecules, and Hollow Cages of Other Materials


Fig. 5.49 (a) Top view and side view of a Sc–Sc dimer in C66 derived from x-ray powder diffraction and 13 C nuclear magnetic resonance. The C66 molecule is stabilized by a charge transfer from

Sc–Sc (Sc–Sc distance 0.287 nm) resulting in a formal electronic state (Sc2 )2+ @C2−

66 of the endohedral metallofullerene [5.185]. (b) The atomic positions in Sc2 @C84 . Two divalent Sc atoms are

located at a 0.20 nm distance to the molecular center with the Sc–Sc distance 0.35 nm [5.186].

(c) Schematic presentation of the peapod with Sc2 @C84 molecules aligned in a SWNT [5.186].

(Reprinted with permission from [5.185] (a) and [5.186] (b) (c). © 2000 Nature Publishing Group

(a) and © 2003 American Physical Society (b) (c))

structure to be precisely and reversibly tuned (Fig. 5.50a). After incorporation of a

nitrogen atom into a C60 sphere by replacing a carbon atom, this C59 N molecule

(Fig. 5.50e) exhibits a rectifying effect. Further replacement of carbon atoms by

nitrogen yields the C48 N12 azafullerene (see Fig. 5.50f) with a high hardness of

7 GPa and a Young’s modulus of 37 GPa.

A cornucopia of organofullerenes can be created by, e.g., bonding organic

molecules to fullerenes or by polymerization of fullerenes (Fig. 5.51).

5.3.3 Superheating and Supercooling of Metals Encapsulated

in Fullerene-Like Shells

As discussed earlier (see Sect. 3.8), high pressures can be built up in the interior of fullerenes under electron irradiation. Nanometer-sized tin and lead crystals



Carbon Nanostructures – Tubes, Graphene, Fullerenes, Wave-Particle Duality

Fig. 5.50 (a–d) STM images showing the formation of K4 C60 (22.7 nm by 11.5 nm) [5.187]. (e)

STM image of C59 N molecule on an alkanethiol self-assembled monolayer (SAM). The height

profile along A–B is shown in the inset. The asymmetry induced by the N atom is visible [5.188].

(f) Structure of C48 N12 azafullerene; N is shown in gray. The solid line shows the (C6 ) symmetry

axis [5.189]. (Reprinted with permission from [5.188] (a–e) and [5.189] (f). © 2005 American

Physical Society (a–e) and © 2001 American Physical Society (f))

exhibit drastically altered melting and solidification behavior when encapsulated in

fullerene like graphitic shells. The melting transition of encapsulated Sn is shown

in an in situ electron microscopy study to occur at temperatures higher than 770 K

(Fig. 5.52), significantly higher than the melting point of bulk β-Sn (Tm = 505 K).

The liquid Sn droplets were found to solidify below 370 K, well below Tm . The driving force for superheating is a pressure buildup of up to 3 GPa that prevails inside

graphitic shells under electron irradiation [5.192].


Fullerenes, Large Carbon Molecules, and Hollow Cages of Other Materials


Fig. 5.51 (a) Organofullerene C60 HR (R=methyl, ethyl, etc.) [5.190]. (b) Polymers with C60 units

[5.191]. (Reprinted with permission from [5.190] (a) and [5.191] (b). © 1993 H. Eickenbusch (a)

and © 1993 Nature Publishing Group (b))

Fig. 5.52 Sn nanocrystals encapsulated by graphitic onion-like shells. (a) Sn nanocrystal superheated at 770 K. The spacing of the lattice fringes is 0.29 nm corresponding to the (200) lattice

planes of β-Sn. (b) Supercooled liquid Sn droplet (“liq”) at 370 K which was previously subject to

melting at high temperatures. Several adjacent particles overlap in the projection. (Reprinted with

permission from [5.192]. © 2003 American Physical Society)

5.3.4 Large Carbon Molecules

The basic unit of an armchair nanotube, referred to as “carbon nanohoop,”

(Fig. 5.53a) has been synthesized by solution-phase chemistry [5.193]. These

molecules (also called cycloparaphenylenes) consist of a circle of benzene rings,

where each ring is connected by a carbon–carbon single bond. This chemistry may

be used to prepare nanotubes with specific structures and hence specific properties.

Nanoscale carbon molecular spoked wheels (Fig. 5.53b, c) can be synthesized with

various sizes and properties [5.194].



Carbon Nanostructures – Tubes, Graphene, Fullerenes, Wave-Particle Duality

Fig. 5.53 (a) Energy-minimized geometry of a carbon nanohoop with nine benzene rings as

calculated by density-functional theory [5.193]. (b) Scanning tunneling microscopy of a carbon

molecular spoked wheel. (c) Detailed structure of this wheel [5.194]. (Reprinted with permission from [5.193] (a) and [5.194] (b) (c). © 2008 American Chemical Society (a) and © 2007

Wiley-VCH (b) (c))

5.3.5 Hollow Cages of Other Materials

Forming football-shaped molecules is no longer the sole preserve of carbon atoms.

Clusters of 20 gold atoms or less can form clusters from pyramids to gold cages

(Fig. 5.54a) with diameters >0.55 nm. Larger hollow spheres have been prepared

from semiconductors such as GaN (Fig. 5.54b), ZnS [5.195], CdS [5.196] or

from uranium [5.197] and the existence of a stable boron buckyball B80 has been

predicted [5.198].

Fig. 5.54 (a) Nanocage of gold atoms [5.199, 5.200]. (b) TEM image of aligned hollow GaN

spheres [5.201]. (Reprinted with permission from [5.200] (a) and [5.201] (b). © 2006 Nature

Publishing Group (a) and © 2005 Wiley-VCH (b))


Fullerenes and the Wave-Particle Duality


5.4 Fullerenes and the Wave-Particle Duality

Since the early days of quantum theory it has been a fundamental question whether

the concepts of quantum physics do apply to every day “classical” objects as well

as to those in the atomic and sub-atomic regime. Can we meaningfully attribute

wave properties to an every day object such as a football or does quantum theory

break down at some level? More than 80 years ago Louis de Broglie suggested that

“atomic” particles such as electrons had wave as well as particle properties with the

wavelength λ = h/mv where h is Planck’s constant, m the mass of the particle, and

v its velocity. This suggestion received early confirmation from the Davisson and

Germer electron diffraction experiments [5.202].

An archetypal example demonstration of wave-particle duality is the two-slit

experiment with particles (Fig. 5.55a). A particle wave crosses a screen with two

slits. The wave splits into two parts, which are re-united on a screen, yielding an

interference pattern. It is the creation of an interference pattern that is an unambiguous signature of a wave. Interference – the addition or cancellation of overlapping

waves – is in this case a purely quantum effect and cannot be understood if the

molecules are viewed as discrete particles. It is possible only if the molecules are

in a superposition of states (see Sect. 7.2) – in several places at once (see [5.203].

On the other hand, when the object reaches the screen it is always detected as a

particle – hence the term “wave-particle duality.” The central question, if and how

quantum theory applies to macroscopic objects, has been extended to C60 molecules

[5.204, 5.205]. A C60 beam emerging from an oven at a temperature of 900 K is collimated, velocity selected, and passed through a grating whose slits are 50 nm wide

and 100 nm apart. The emerging beam is detected and found to form an interference pattern (Fig. 5.55b) that is completely explicable on the basis that the beam

has wave properties.

C60 is of course not a macroscopic object but it is an order of magnitude more

massive than anything else studied before. For studying even heavier particles,

Talbot–Lau interferometry [5.206–5.208] is employed which investigates near-field

effects where the curvature of the molecular wave fronts has to be taken into

account. By using this technique, the wave nature of the biomolecule tetraphenylporphyrin, serving as a color center, e.g., in chlorophyll and in hemoglobin, and

of the fluorofullerene C60 F48 more than twice as heavy as C60 (see Fig. 5.56),

or of perfluoroalkyl-functionalized azobenzenes (C30 H12 F30 N2 O4 [5.209]) could

be demonstrated. By a further development of this type of interferometry, tests of

the wave nature of particles thousand times heavier than C60 such as viruses, giant

proteins, or nanocrystals are envisioned [5.210].

For answering the question where the boundary between quantum behavior and

classical behavior of particles is located, not only the size but also the particles

interaction with its environment is of importance. When a hot particle cools in the

interferometer it loses its diffraction fringe-forming coherence by radiating to the

environment. The photons emitted from a hot C60 molecule carry information that

can localize its path. This information entangles the environment in a state that picks

out one path. This leads to decoherence and the particle becomes classical [5.213].



Carbon Nanostructures – Tubes, Graphene, Fullerenes, Wave-Particle Duality

Fig. 5.55 (a) Two-slit diffractometer setup for demonstrating the wave-particle duality. A beam

of particles passes through a double slit in the form of a wave and produces an interference pattern.

The experiments on C60 (b) demonstrate this effect. The molecule may absorb or emit radiation

when passing through the apparatus (dotted wave). Provided the wavelength of this radiation is

much larger than the distance of the slits, the interference pattern is unaffected, i.e., decoherence

is negligible [5.211]. (b) Far-field diffraction of C60 using velocity selection with a mean velocity

v¯ = 117 m/s and a width v/v ∼ 17%. The circles are the experimental data and the line represents

a Kirchhoff–Fresnel diffraction model. The van der Waals interaction between the molecule and

the grating is taken into account by a reduced slit width [5.205]. (Reprinted with permission from

[5.211] (a) and [5.205] (b). © 1999 Nature Publishing Group (a) and © 2003 American Association

of Physics Teachers (b))

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