Zgryźliwość kojarzy mi się z radością, która źle skończyła.
MATERIALS
C
onsider the humble pencil. It may come
sheet. It is made up entirely of carbon atoms
bound together in a network of repeating hexa-
gons within a single plane just one atom thick.
For years, however, all attempts to make gra-
phene ended in failure. The most popular early
approach was to insert various molecules be-
tween the atomic planes of graphite to wedge
the planes apart
—
a technique called chemical
exfoliation. Although graphene layers almost
certainly detached from the graphite at some
transient stage of the process, they were never
identified as such. Instead the final product usu-
ally emerged as a slurry of graphitic particles
—
not much different from wet soot. The early in-
terest in chemical exfoliation faded away.
Soon thereafter experimenters attempted a
more direct approach. They split graphite crys-
tals into progressively thinner wafers by scrap-
ing or rubbing them against another surface. In
spite of its crudeness, the technique, known as
Graphene, a
newly isolated
form of carbon,
provides a rich
lode of novel
fundamental
physics and
practical
applications
BY ANDRE K. GEIM
AND PHILIP KIM
as a surprise to learn that the now com-
mon writing instrument at one time
topped the list of must-have, high-tech
gadgets. In fact, the simple pencil was once even
banned from export as a strategic military asset.
But what is probably more unexpected is the
news that every time someone scribes a line
with a pencil, the resulting mark includes bits of
the hottest new material in physics and nano-
technology: graphene.
Graphene comes from graphite, the “lead” in
a pencil: a kind of pure carbon formed from flat,
stacked layers of atoms. The tiered structure of
graphite was discerned centuries ago, and so it
was natural for physicists and materials scien-
tists to try splitting the mineral into its constit-
uent sheets
—
if only to study a substance whose
geometry might turn out to be so elegantly sim-
ple. Graphene is the name given to one such
90
SCIENTIFIC AMERICAN
© 2008 SCIENTIFIC AMERICAN, INC.
April 2008
EVERYDAY PENCIL MARKS
include minute quantities
of graphene, one of the hottest “new” materials in
science and engineering.
micromechanical cleavage, worked surprisingly
well. Investigators managed to peel off graphite
films made up of fewer than 100 atomic planes.
By 1990, for example, German physicists at
RWTH Aachen University had isolated graphite
films thin enough to be optically transparent.
A decade later one of us (Kim), working with
Yuanbo Zhang, then a graduate student at Co-
lumbia University, refined the micromechanical
cleavage method to create a high-tech version of
the pencil
—
a “nanopencil,” of course. “Writ-
ing” with the nanopencil yielded slices of graph-
ite just a few tens of atomic layers thick [
see box
on page 93
]. Still, the resulting material was thin
graphite, not graphene. No one really expected
that such a material could exist in nature.
That pessimistic assumption was put to rest
in 2004. One of us (Geim), in collaboration with
then postdoctoral associate Kostya S. Novoselov
and his co-workers at the University of Man-
chester in England, was studying a variety of ap-
proaches to making even thinner samples of
graphite. At that time, most laboratories began
such attempts with soot, but Geim and his col-
leagues serendipitously started with bits of de-
bris left over after splitting graphite by brute
force. They simply stuck a flake of graphite de-
bris onto plastic adhesive tape, folded the sticky
side of the tape over the flake and then pulled the
tape apart, cleaving the flake in two. As the ex-
perimenters repeated the process, the resulting
fragments grew thinner [
see box on page 95
].
Once the investigators had many thin fragments,
they meticulously examined the pieces
—
and
were astonished to find that some were only one
atom thick. Even more unexpectedly, the newly
identified bits of graphene turned out to have
high crystal quality and to be chemically stable
even at room temperature.
The experimental discovery of graphene led
to a deluge of international research interest.
Not only is it the thinnest of all possible materi-
als, it is also extremely strong and stiff. More-
over, in its pure form it conducts electrons fast-
er at room temperature than any other sub-
stance. Engineers at laboratories worldwide are
currently scrutinizing the stuff to determine
whether it can be fabricated into products such
as supertough composites, smart displays, ultra-
fast transistors and quantum-dot computers.
In the meantime, the peculiar nature of gra-
phene at the atomic scale is enabling physicists to
delve into phenomena that must be described by
relativistic quantum physics. Investigating such
KEY CONCEPTS
■
Graphene is a one-atom-
thick sheet of carbon that
stacks with other such
sheets to form graphite
—
pencil “lead.” Physicists
have only recently isolat-
ed the material.
■
The pure, flawless crystal
conducts electricity faster
at room temperature than
any other substance.
■
Engineers envision a
range of products made
of graphene, such as
ultrahigh-speed transis-
tors. Physicists are finding
the material enables them
to test a theory of exotic
phenomena previously
thought to be observable
only in black holes and
high-energy particle
accelerators.
—
The Editors
SCIENTIFIC AMERICAN
91
www.SciAm.com
© 2008 SCIENTIFIC AMERICAN, INC.
[MOLECULAR FORMS]
THE MOTHER OF ALL GRAPHITES
Graphene (
below, top
), a plane of carbon atoms that resembles chicken
wire, is the basic building block of all the “graphitic” materials depicted
below. Graphite (
bottom row at left
), the main component of pencil “lead,”
is a crumbly substance that resembles a layer cake of weakly bonded
graphene sheets. When graphene is wrapped into rounded forms, fullerenes
result. They include honeycombed cylinders known as carbon nanotubes
(
bottom row at center
) and soccer ball–shaped molecules called buckyballs
(
bottom row at right
), as well as various shapes that combine the two forms.
Graphene
Graphite
Carbon nanotube
Buckyball
phenomena, some of the most exotic in nature,
has heretofore been the exclusive preserve of as-
trophysicists and high-energy particle physicists
working with multimillion-dollar telescopes or
multibillion-dollar particle accelerators. Gra-
phene makes it possible for experimenters to test
the predictions of relativistic quantum mechan-
ics with laboratory benchtop apparatus.
Meanwhile munitions makers had discovered
another use for the crumbly mineral: they found
it made an ideal lining in casting molds for can-
nonballs. That use became a tightly guarded mil-
itary secret. During the Napoleonic Wars, for in-
stance, the English Crown embargoed the sale to
France of both graphite and pencils.
In recent decades graphite has reclaimed some
of its once lofty technological status, as investi-
gators have explored the properties and potential
applications of several previously unrecognized
molecular forms of carbon that occur in ordinary
graphitic materials. The first of them, a soccer
ball–shaped molecule dubbed the buckyball, was
discovered in 1985 by American chemists Rob-
ert Curl and Richard E. Smalley, along with their
English colleague Harry Kroto. Six years later
Sumio Iijima, a Japanese physicist, identified the
honeycombed, cylindrical assemblies of carbon
atoms known as carbon nanotubes. Although
nanotubes had been reported by many investiga-
tors in earlier decades, their importance had not
been appreciated. Both the new molecular forms
were classified as fullerenes. (That name and the
term “buckyball” were coined in honor of the vi-
sionary U.S. architect and engineer Buckminster
Fuller, who investigated those shapes before the
carbon forms themselves were discovered.)
Meet the Graphene Family
Given how widespread the pencil is today, it
seems remarkable that what became known as
graphite did not play a role in ancient literate
civilizations such as those of China or Greece.
Not until the 16th century did the English dis-
cover a large deposit of pure graphite, then
called
plumbago
(Latin for “lead ore”). Its util-
ity as a marker was immediately apparent,
though, and the English wasted no time in mak-
ing it into an easy-to-use substitute for quill and
ink. The pencil soon became all the rage among
the European intelligentsia.
But it was not until 1779 that Swedish chem-
ist Carl Scheele showed that
plumbago
is carbon,
not lead. A decade later German geologist Abra-
ham Gottlob Werner suggested that the sub-
stance could more appropriately be called graph-
ite, from the Greek word meaning “to write.”
The discovery
of graphene
has led to
a deluge of
international
research
interest.
92
SCIENTIFIC AMERICAN
© 2008 SCIENTIFIC AMERICAN, INC.
April 2008
Molecular Chicken Wire
Graphite, the fullerenes and graphene share the
same basic structural arrangement of their con-
stituent atoms. Each structure begins with six
carbon atoms, tightly bound together chemically
in the shape of a regular hexagon
—
what chem-
ists call a benzene ring.
At the next level of organization is graphene
itself, a large assembly of benzene rings linked
in a sheet of hexagons that resembles chicken
wire [
see box on opposite page
]. The other gra-
phitic forms are built up out of graphene. Bucky-
balls and the many other nontubular fullerenes
can be thought of as graphene sheets wrapped up
into atomic-scale spheres, elongated spheroids,
and the like. Carbon nanotubes are essentially
graphene sheets rolled into minute cylinders. And
as we mentioned earlier, graphite is a thick, three-
dimensional stack of graphene sheets; the sheets
are held together by weak, attractive intermolec-
ular forces called van der Waals forces. The feeble
coupling between neighboring graphene sheets
is what enables graphite to be broken so easily
into minuscule wafers that make up the mark left
on paper when someone writes with a pencil.
With the benefit of hindsight, it is clear that
fullerenes, despite going unnoticed until recent-
ly, have been close at hand all along. They occur,
for instance, in the soot that coats every barbe-
cue grill, albeit in minute quantities. Just so, bits
of graphene are undoubtedly present in every
pencil mark
—
even though they, too, long went
undetected. But since their discovery, the scien-
tific community has paid all these molecules a
great deal of attention.
Buckyballs are notable mainly as an example
[THE AUTHORS]
of a fundamentally new kind of molecule, al-
though they may also have important applica-
tions, notably in drug delivery. Carbon nano-
tubes combine a suite of unusual properties
—
chemical, electronic, mechanical, optical and
thermal
—
that have inspired a wide variety of in-
novative potential applications. Those innova-
tions include materials that might replace silicon
in microchips and fibers that might be woven
into lightweight, ultrastrong cables. Although
graphene itself
—
the mother of all graphitic
forms
—
became part of such visions just a few
years ago, it seems likely that the material will
offer even more insights into basic physics and
more intriguing technological applications than
its carbonaceous cousins.
Andre K. Geim
(
left
) and
Philip
Kim
(
right
) are condensed matter
physicists who in recent years have
investigated the nanoscale proper-
ties of one-atom-thick, “two-
dimensional” crystalline materials.
Geim is a fellow of the Royal Soci-
ety and Langworthy Professor of
Physics at the University of Man-
chester in England. He also directs
the Manchester Center for Meso-
science and Nanotechnology. Geim
received his Ph.D. from the Insti-
tute of Solid State Physics in Cher-
nogolovka, Russia. Kim, a fellow of
the American Physical Society who
received his doctoral degree from
Harvard University, is associate
professor of physics at Columbia
University. His research focuses on
quantum thermal and electrical
transport processes in nanoscale
materials.
Exceptional Exception
Two features of graphene make it an exceptional
material. First, despite the relatively crude ways
it is still being made, graphene exhibits remark-
ably high quality
—
resulting from a combination
of the purity of its carbon content and the order-
liness of the lattice into which its carbon atoms
are arranged. Investigators have so far failed to
find a single atomic defect in graphene
—
say, a
vacancy at some atomic position in the lattice or
an atom out of place. That perfect crystalline
order seems to stem from the strong yet highly
flexible interatomic bonds, which create a sub-
stance harder than diamond yet allow the planes
to bend when mechanical force is applied. The
flexibility enables the structure to accommodate
a good deal of deformation before its atoms must
reshuffle to adjust to the strain.
The quality of its crystal lattice is also respon-
[GRAPHENE IN THE MAKING]
MARK OF THE NANOPENCIL
Making graphitic samples that approach the thickness of single-layer
graphene has taken considerable effort. One way is to attach a graphite
microcrystal to the cantilever arm of an atomic-force microscope and
scratch the tip of the microcrystal across a silicon wafer (
left
). This
“nanopencil” deposits thin graphene “pancakes” onto the wafer (
right
).
The samples in the electron micrograph are magnified 6,000
.
Atomic-force microscope cantilever
Graphite microcrystals
Silicon wafer
Graphene
“pancakes”
SCIENTIFIC AMERICAN
93
© 2008 SCIENTIFIC AMERICAN, INC.
Interpreting
quantum
electrodynamics
never comes
without
a good deal
of wrestling
with ordinary
intuition.
sible for the remarkably high electrical conduc-
tivity of graphene. Its electrons can travel with-
out being scattered off course by lattice imper-
fections and foreign atoms. Even the jostling
from the surrounding carbon atoms, which elec-
trons in graphene must endure at room temper-
ature, is relatively small because of the high
strength of the interatomic bonds.
The second exceptional feature of graphene
is that its conduction electrons, besides traveling
largely unimpeded through the lattice, move
much faster and as if they had far less mass than
do the electrons that wander about through or-
dinary metals and semiconductors. Indeed, the
electrons in graphene
—
perhaps “electric charge
carriers” is a more appropriate term
—
are curi-
ous creatures that live in the weird world where
rules analogous to those of relativistic quantum
mechanics play an important role. That kind of
interaction inside a solid, so far as anyone knows,
is unique to graphene. Thanks to this novel mate-
rial from a pencil, relativistic quantum mechan-
ics is no longer confined to cosmology or high-en-
ergy physics; it has now entered the laboratory.
el in an ordinary conductor. The “free” elec-
trons that make up an electric current in, say, a
metal are not really free; they do not act exactly
like electrons moving in a vacuum. Electrons, of
course, carry a negative charge, and so when they
move through a metal they leave a charge deficit
in the metal atoms from which they originate.
Thus, when electrons move through the lattice,
they interact with the electrostatic fields it creates,
which push and pull them to and fro in a complex
way. The end result is that the moving electrons
act as if they had a different mass than ordinary
electrons do
—
their so-called effective mass. Phys-
icists call such charge carriers quasiparticles.
These charged, electronlike particles move
much slower than the speed of light through the
conducting metal. There is no need, therefore, to
apply the corrections of Einstein’s theory of rela-
tivity to their motions; that theory becomes im-
portant only at speeds approaching that of light.
Instead the interactions of quasiparticles in a
conductor can be described either by the familiar
classical physics of Newton or by “ordinary”
(that is, nonrelativistic) quantum mechanics.
As electrons travel through the chicken-wire
web of carbon atoms in graphene, they, too, act
as if they were a kind of quasiparticle. Astonish-
ingly, however, the charge-carrying quasiparti-
cle in graphene does not act much like an elec-
Big Bang in Carbon Flatland
To appreciate the weird behavior of the electric
charge carriers in graphene, it may be useful to
compare it with the way ordinary electrons trav-
Quantum Electrodynamics Enters the Lab
1
Electrons move virtually unimpeded through the highly regular atomic
structure of graphene, reaching such great speeds that their behavior cannot
be described by “ordinary” quantum mechanics. The theory that applies
instead is known as relativistic quantum mechanics, or quantum
electrodynamics (QED), a theory whose distinctive (and weird) predictions
were thought, until now, to be observable only in black holes or high-energy
particle accelerators. With graphene, though, physicists can test one of the
weirdest predictions of QED in the laboratory: “perfect quantum tunneling.”
In classical, or Newtonian, physics, a low-energy electron (
green ball in
1a
) acts like an ordinary particle. If its energy is not enough to carry it over
the top of a potential-energy barrier
,
it remains trapped on one side of the
barrier (
1b
) as surely as a truck out of gas in a valley remains stranded on
one side of a hill.
In the ordinary quantum-mechanical picture, an electron acts in some
contexts like a wave that spreads out in space. The wave represents, roughly,
the probability of finding the electron at a particular point in space and time.
When this “slow-moving” wave approaches a potential-energy barrier (
blue
wave in 2a
), it penetrates the barrier in such a way that there is some
probability, neither 0 nor 100 percent, that the electron will be found on the
far side of the barrier (
2b
). In effect, the electron tunnels through the barrier.
When a high-speed electron wave in graphene (
orange wave in 3a
)
comes to a potential-energy barrier, QED makes an even more startling
prediction: the electron wave will subsequently be found on the far side of
an energy barrier with 100 percent probability (
3b
). The observation that
graphene conducts electricity so well seems to confirm that prediction.
CLASSICAL PHYSICS
Electron as
low-energy
particle
No chance of
penetrating
barrier
Barrier
a
b
No tunneling
2
QUANTUM MECHANICS
Electron as
“slow-
moving”
wave
Some
chance of
penetrating
barrier
a
b
Partial tunneling
QUANTUM ELECTRODYNAMICS
3
Electron as
high-speed
wave
100%
chance of
penetrating
barrier
a
b
Perfect tunneling
94
SCIENTIFIC AMERICAN
© 2008 SCIENTIFIC AMERICAN, INC.
April 2008
zanotowane.pl doc.pisz.pl pdf.pisz.pl hannaeva.xlx.pl
C
onsider the humble pencil. It may come
sheet. It is made up entirely of carbon atoms
bound together in a network of repeating hexa-
gons within a single plane just one atom thick.
For years, however, all attempts to make gra-
phene ended in failure. The most popular early
approach was to insert various molecules be-
tween the atomic planes of graphite to wedge
the planes apart
—
a technique called chemical
exfoliation. Although graphene layers almost
certainly detached from the graphite at some
transient stage of the process, they were never
identified as such. Instead the final product usu-
ally emerged as a slurry of graphitic particles
—
not much different from wet soot. The early in-
terest in chemical exfoliation faded away.
Soon thereafter experimenters attempted a
more direct approach. They split graphite crys-
tals into progressively thinner wafers by scrap-
ing or rubbing them against another surface. In
spite of its crudeness, the technique, known as
Graphene, a
newly isolated
form of carbon,
provides a rich
lode of novel
fundamental
physics and
practical
applications
BY ANDRE K. GEIM
AND PHILIP KIM
as a surprise to learn that the now com-
mon writing instrument at one time
topped the list of must-have, high-tech
gadgets. In fact, the simple pencil was once even
banned from export as a strategic military asset.
But what is probably more unexpected is the
news that every time someone scribes a line
with a pencil, the resulting mark includes bits of
the hottest new material in physics and nano-
technology: graphene.
Graphene comes from graphite, the “lead” in
a pencil: a kind of pure carbon formed from flat,
stacked layers of atoms. The tiered structure of
graphite was discerned centuries ago, and so it
was natural for physicists and materials scien-
tists to try splitting the mineral into its constit-
uent sheets
—
if only to study a substance whose
geometry might turn out to be so elegantly sim-
ple. Graphene is the name given to one such
90
SCIENTIFIC AMERICAN
© 2008 SCIENTIFIC AMERICAN, INC.
April 2008
EVERYDAY PENCIL MARKS
include minute quantities
of graphene, one of the hottest “new” materials in
science and engineering.
micromechanical cleavage, worked surprisingly
well. Investigators managed to peel off graphite
films made up of fewer than 100 atomic planes.
By 1990, for example, German physicists at
RWTH Aachen University had isolated graphite
films thin enough to be optically transparent.
A decade later one of us (Kim), working with
Yuanbo Zhang, then a graduate student at Co-
lumbia University, refined the micromechanical
cleavage method to create a high-tech version of
the pencil
—
a “nanopencil,” of course. “Writ-
ing” with the nanopencil yielded slices of graph-
ite just a few tens of atomic layers thick [
see box
on page 93
]. Still, the resulting material was thin
graphite, not graphene. No one really expected
that such a material could exist in nature.
That pessimistic assumption was put to rest
in 2004. One of us (Geim), in collaboration with
then postdoctoral associate Kostya S. Novoselov
and his co-workers at the University of Man-
chester in England, was studying a variety of ap-
proaches to making even thinner samples of
graphite. At that time, most laboratories began
such attempts with soot, but Geim and his col-
leagues serendipitously started with bits of de-
bris left over after splitting graphite by brute
force. They simply stuck a flake of graphite de-
bris onto plastic adhesive tape, folded the sticky
side of the tape over the flake and then pulled the
tape apart, cleaving the flake in two. As the ex-
perimenters repeated the process, the resulting
fragments grew thinner [
see box on page 95
].
Once the investigators had many thin fragments,
they meticulously examined the pieces
—
and
were astonished to find that some were only one
atom thick. Even more unexpectedly, the newly
identified bits of graphene turned out to have
high crystal quality and to be chemically stable
even at room temperature.
The experimental discovery of graphene led
to a deluge of international research interest.
Not only is it the thinnest of all possible materi-
als, it is also extremely strong and stiff. More-
over, in its pure form it conducts electrons fast-
er at room temperature than any other sub-
stance. Engineers at laboratories worldwide are
currently scrutinizing the stuff to determine
whether it can be fabricated into products such
as supertough composites, smart displays, ultra-
fast transistors and quantum-dot computers.
In the meantime, the peculiar nature of gra-
phene at the atomic scale is enabling physicists to
delve into phenomena that must be described by
relativistic quantum physics. Investigating such
KEY CONCEPTS
■
Graphene is a one-atom-
thick sheet of carbon that
stacks with other such
sheets to form graphite
—
pencil “lead.” Physicists
have only recently isolat-
ed the material.
■
The pure, flawless crystal
conducts electricity faster
at room temperature than
any other substance.
■
Engineers envision a
range of products made
of graphene, such as
ultrahigh-speed transis-
tors. Physicists are finding
the material enables them
to test a theory of exotic
phenomena previously
thought to be observable
only in black holes and
high-energy particle
accelerators.
—
The Editors
SCIENTIFIC AMERICAN
91
www.SciAm.com
© 2008 SCIENTIFIC AMERICAN, INC.
[MOLECULAR FORMS]
THE MOTHER OF ALL GRAPHITES
Graphene (
below, top
), a plane of carbon atoms that resembles chicken
wire, is the basic building block of all the “graphitic” materials depicted
below. Graphite (
bottom row at left
), the main component of pencil “lead,”
is a crumbly substance that resembles a layer cake of weakly bonded
graphene sheets. When graphene is wrapped into rounded forms, fullerenes
result. They include honeycombed cylinders known as carbon nanotubes
(
bottom row at center
) and soccer ball–shaped molecules called buckyballs
(
bottom row at right
), as well as various shapes that combine the two forms.
Graphene
Graphite
Carbon nanotube
Buckyball
phenomena, some of the most exotic in nature,
has heretofore been the exclusive preserve of as-
trophysicists and high-energy particle physicists
working with multimillion-dollar telescopes or
multibillion-dollar particle accelerators. Gra-
phene makes it possible for experimenters to test
the predictions of relativistic quantum mechan-
ics with laboratory benchtop apparatus.
Meanwhile munitions makers had discovered
another use for the crumbly mineral: they found
it made an ideal lining in casting molds for can-
nonballs. That use became a tightly guarded mil-
itary secret. During the Napoleonic Wars, for in-
stance, the English Crown embargoed the sale to
France of both graphite and pencils.
In recent decades graphite has reclaimed some
of its once lofty technological status, as investi-
gators have explored the properties and potential
applications of several previously unrecognized
molecular forms of carbon that occur in ordinary
graphitic materials. The first of them, a soccer
ball–shaped molecule dubbed the buckyball, was
discovered in 1985 by American chemists Rob-
ert Curl and Richard E. Smalley, along with their
English colleague Harry Kroto. Six years later
Sumio Iijima, a Japanese physicist, identified the
honeycombed, cylindrical assemblies of carbon
atoms known as carbon nanotubes. Although
nanotubes had been reported by many investiga-
tors in earlier decades, their importance had not
been appreciated. Both the new molecular forms
were classified as fullerenes. (That name and the
term “buckyball” were coined in honor of the vi-
sionary U.S. architect and engineer Buckminster
Fuller, who investigated those shapes before the
carbon forms themselves were discovered.)
Meet the Graphene Family
Given how widespread the pencil is today, it
seems remarkable that what became known as
graphite did not play a role in ancient literate
civilizations such as those of China or Greece.
Not until the 16th century did the English dis-
cover a large deposit of pure graphite, then
called
plumbago
(Latin for “lead ore”). Its util-
ity as a marker was immediately apparent,
though, and the English wasted no time in mak-
ing it into an easy-to-use substitute for quill and
ink. The pencil soon became all the rage among
the European intelligentsia.
But it was not until 1779 that Swedish chem-
ist Carl Scheele showed that
plumbago
is carbon,
not lead. A decade later German geologist Abra-
ham Gottlob Werner suggested that the sub-
stance could more appropriately be called graph-
ite, from the Greek word meaning “to write.”
The discovery
of graphene
has led to
a deluge of
international
research
interest.
92
SCIENTIFIC AMERICAN
© 2008 SCIENTIFIC AMERICAN, INC.
April 2008
Molecular Chicken Wire
Graphite, the fullerenes and graphene share the
same basic structural arrangement of their con-
stituent atoms. Each structure begins with six
carbon atoms, tightly bound together chemically
in the shape of a regular hexagon
—
what chem-
ists call a benzene ring.
At the next level of organization is graphene
itself, a large assembly of benzene rings linked
in a sheet of hexagons that resembles chicken
wire [
see box on opposite page
]. The other gra-
phitic forms are built up out of graphene. Bucky-
balls and the many other nontubular fullerenes
can be thought of as graphene sheets wrapped up
into atomic-scale spheres, elongated spheroids,
and the like. Carbon nanotubes are essentially
graphene sheets rolled into minute cylinders. And
as we mentioned earlier, graphite is a thick, three-
dimensional stack of graphene sheets; the sheets
are held together by weak, attractive intermolec-
ular forces called van der Waals forces. The feeble
coupling between neighboring graphene sheets
is what enables graphite to be broken so easily
into minuscule wafers that make up the mark left
on paper when someone writes with a pencil.
With the benefit of hindsight, it is clear that
fullerenes, despite going unnoticed until recent-
ly, have been close at hand all along. They occur,
for instance, in the soot that coats every barbe-
cue grill, albeit in minute quantities. Just so, bits
of graphene are undoubtedly present in every
pencil mark
—
even though they, too, long went
undetected. But since their discovery, the scien-
tific community has paid all these molecules a
great deal of attention.
Buckyballs are notable mainly as an example
[THE AUTHORS]
of a fundamentally new kind of molecule, al-
though they may also have important applica-
tions, notably in drug delivery. Carbon nano-
tubes combine a suite of unusual properties
—
chemical, electronic, mechanical, optical and
thermal
—
that have inspired a wide variety of in-
novative potential applications. Those innova-
tions include materials that might replace silicon
in microchips and fibers that might be woven
into lightweight, ultrastrong cables. Although
graphene itself
—
the mother of all graphitic
forms
—
became part of such visions just a few
years ago, it seems likely that the material will
offer even more insights into basic physics and
more intriguing technological applications than
its carbonaceous cousins.
Andre K. Geim
(
left
) and
Philip
Kim
(
right
) are condensed matter
physicists who in recent years have
investigated the nanoscale proper-
ties of one-atom-thick, “two-
dimensional” crystalline materials.
Geim is a fellow of the Royal Soci-
ety and Langworthy Professor of
Physics at the University of Man-
chester in England. He also directs
the Manchester Center for Meso-
science and Nanotechnology. Geim
received his Ph.D. from the Insti-
tute of Solid State Physics in Cher-
nogolovka, Russia. Kim, a fellow of
the American Physical Society who
received his doctoral degree from
Harvard University, is associate
professor of physics at Columbia
University. His research focuses on
quantum thermal and electrical
transport processes in nanoscale
materials.
Exceptional Exception
Two features of graphene make it an exceptional
material. First, despite the relatively crude ways
it is still being made, graphene exhibits remark-
ably high quality
—
resulting from a combination
of the purity of its carbon content and the order-
liness of the lattice into which its carbon atoms
are arranged. Investigators have so far failed to
find a single atomic defect in graphene
—
say, a
vacancy at some atomic position in the lattice or
an atom out of place. That perfect crystalline
order seems to stem from the strong yet highly
flexible interatomic bonds, which create a sub-
stance harder than diamond yet allow the planes
to bend when mechanical force is applied. The
flexibility enables the structure to accommodate
a good deal of deformation before its atoms must
reshuffle to adjust to the strain.
The quality of its crystal lattice is also respon-
[GRAPHENE IN THE MAKING]
MARK OF THE NANOPENCIL
Making graphitic samples that approach the thickness of single-layer
graphene has taken considerable effort. One way is to attach a graphite
microcrystal to the cantilever arm of an atomic-force microscope and
scratch the tip of the microcrystal across a silicon wafer (
left
). This
“nanopencil” deposits thin graphene “pancakes” onto the wafer (
right
).
The samples in the electron micrograph are magnified 6,000
.
Atomic-force microscope cantilever
Graphite microcrystals
Silicon wafer
Graphene
“pancakes”
SCIENTIFIC AMERICAN
93
© 2008 SCIENTIFIC AMERICAN, INC.
Interpreting
quantum
electrodynamics
never comes
without
a good deal
of wrestling
with ordinary
intuition.
sible for the remarkably high electrical conduc-
tivity of graphene. Its electrons can travel with-
out being scattered off course by lattice imper-
fections and foreign atoms. Even the jostling
from the surrounding carbon atoms, which elec-
trons in graphene must endure at room temper-
ature, is relatively small because of the high
strength of the interatomic bonds.
The second exceptional feature of graphene
is that its conduction electrons, besides traveling
largely unimpeded through the lattice, move
much faster and as if they had far less mass than
do the electrons that wander about through or-
dinary metals and semiconductors. Indeed, the
electrons in graphene
—
perhaps “electric charge
carriers” is a more appropriate term
—
are curi-
ous creatures that live in the weird world where
rules analogous to those of relativistic quantum
mechanics play an important role. That kind of
interaction inside a solid, so far as anyone knows,
is unique to graphene. Thanks to this novel mate-
rial from a pencil, relativistic quantum mechan-
ics is no longer confined to cosmology or high-en-
ergy physics; it has now entered the laboratory.
el in an ordinary conductor. The “free” elec-
trons that make up an electric current in, say, a
metal are not really free; they do not act exactly
like electrons moving in a vacuum. Electrons, of
course, carry a negative charge, and so when they
move through a metal they leave a charge deficit
in the metal atoms from which they originate.
Thus, when electrons move through the lattice,
they interact with the electrostatic fields it creates,
which push and pull them to and fro in a complex
way. The end result is that the moving electrons
act as if they had a different mass than ordinary
electrons do
—
their so-called effective mass. Phys-
icists call such charge carriers quasiparticles.
These charged, electronlike particles move
much slower than the speed of light through the
conducting metal. There is no need, therefore, to
apply the corrections of Einstein’s theory of rela-
tivity to their motions; that theory becomes im-
portant only at speeds approaching that of light.
Instead the interactions of quasiparticles in a
conductor can be described either by the familiar
classical physics of Newton or by “ordinary”
(that is, nonrelativistic) quantum mechanics.
As electrons travel through the chicken-wire
web of carbon atoms in graphene, they, too, act
as if they were a kind of quasiparticle. Astonish-
ingly, however, the charge-carrying quasiparti-
cle in graphene does not act much like an elec-
Big Bang in Carbon Flatland
To appreciate the weird behavior of the electric
charge carriers in graphene, it may be useful to
compare it with the way ordinary electrons trav-
Quantum Electrodynamics Enters the Lab
1
Electrons move virtually unimpeded through the highly regular atomic
structure of graphene, reaching such great speeds that their behavior cannot
be described by “ordinary” quantum mechanics. The theory that applies
instead is known as relativistic quantum mechanics, or quantum
electrodynamics (QED), a theory whose distinctive (and weird) predictions
were thought, until now, to be observable only in black holes or high-energy
particle accelerators. With graphene, though, physicists can test one of the
weirdest predictions of QED in the laboratory: “perfect quantum tunneling.”
In classical, or Newtonian, physics, a low-energy electron (
green ball in
1a
) acts like an ordinary particle. If its energy is not enough to carry it over
the top of a potential-energy barrier
,
it remains trapped on one side of the
barrier (
1b
) as surely as a truck out of gas in a valley remains stranded on
one side of a hill.
In the ordinary quantum-mechanical picture, an electron acts in some
contexts like a wave that spreads out in space. The wave represents, roughly,
the probability of finding the electron at a particular point in space and time.
When this “slow-moving” wave approaches a potential-energy barrier (
blue
wave in 2a
), it penetrates the barrier in such a way that there is some
probability, neither 0 nor 100 percent, that the electron will be found on the
far side of the barrier (
2b
). In effect, the electron tunnels through the barrier.
When a high-speed electron wave in graphene (
orange wave in 3a
)
comes to a potential-energy barrier, QED makes an even more startling
prediction: the electron wave will subsequently be found on the far side of
an energy barrier with 100 percent probability (
3b
). The observation that
graphene conducts electricity so well seems to confirm that prediction.
CLASSICAL PHYSICS
Electron as
low-energy
particle
No chance of
penetrating
barrier
Barrier
a
b
No tunneling
2
QUANTUM MECHANICS
Electron as
“slow-
moving”
wave
Some
chance of
penetrating
barrier
a
b
Partial tunneling
QUANTUM ELECTRODYNAMICS
3
Electron as
high-speed
wave
100%
chance of
penetrating
barrier
a
b
Perfect tunneling
94
SCIENTIFIC AMERICAN
© 2008 SCIENTIFIC AMERICAN, INC.
April 2008