Welcome to the course of nano structured materials
synthesis properties, self assembly and applications.
We are going to start the first lecture of
module 3, we earlier had module one comprising
2 lectures and module 2 comprising 12 lectures.
So, totally we have completed 14 lectures
and today will be our 15 lecture or for the
whole course and is this, is the first lecture
of module 3. The first lecture we will start
with fullerene and carbon nano tubes and,
we will have three lectures on fullerenes
and carbon based nano tubes, today we have
the first lecture of this.
Now, fullerenes as some of you must have heard
was discovered in 1985, but previous to 1985
also there were reports about it. So, we will
discuss the historical development of this
structure nanostructure called fullerene,
you must have all known that normally carbon
has 3 allotropic forms. One is diamond, the
other is graphite and we have amorphous type
of or non crystalline carbon, today we know
of many other forms of carbon.
So, among them the first to be discovered
among these new forms of carbon is the C 60
molecule which is also called the buckyball
and is also called for fullerene. So, today
there are many other carbon based molecules
which are related to this buckyball with lot
number of carbon atoms per molecule. But,
there are more than 30 forms of such fullerenes,
now why this is called fullerene we will come
to that, it basically looks like a soccer
ball which has got a 6 membered carbon rings
and also 5 membered carbon rings. So, this
typical molecule has sixty carbon atoms which
is arranged like in a soccer ball or a football,
as we know in India, and if you replace the
vertices of each other those with carbon.
Then this becomes C 60 molecules and this
was discovered in 1985 and noble prize was
given for this discovery.
So, historically was this discovery of C 60
in 1985, the first time people thought of
this molecule no people have thought about
such molecules much earlier. So, for example
it was predicted by Osawain 1970 that there
can be a molecule like C 60 in 1970 there
was another proposal of a model of C 60. But,
the experimental evidence was not very strong
and hence this structure was not accepted
at that time these results have been later
acknowledged.
Now, for example in the journal carbon in
1999, much later that Henson propose this
structure in 1970, today we know that it is
correct and it is known experimentally apart
from that in 1973 in U S S R. But, earlier
U S S R, it was calculated using quantum chemical
calculations that a molecule like C 60 would
be stable and the electronic structure of
the molecule was calculated. So, the energy
level of the molecule, a molecular orbital
was calculated for a molecule like a C 60
theoretically and a paper was published in
proceedings of the U S S R academy of sciences.
So, there were several such studies which
were kind of indicating than there can be
a molecule like C 60, a very symmetrical molecule,
a molecule which looks like a football or
a soccer ball. So, this molecule was predicted
theoretically and some experiments were done,
but not flinching evidence was not there.
But, in 1985 a team of people from England
and USA contributed to the actual discovery
of C 60, the main players in the discovery
of C 60 were Harold, Kroto Robert curl and
Richard Smalley.
So, James heath was a student at that time
and these 4 people work in rice university
though Harold Kroto who was visiting a rice
university from U K. So, together they discovered
C 60 in 1985 and the idea behind their discovery
was they were looking for molecules on which
can be synthesized in the upper atmosphere
or in space where plasma exists. So, they
were trying to create a plasma are to an electric
discharge where such molecules which area
probably formed in outer space can be recreated
in the laboratory.
So, during that are discharged of using graphite
electrodes, they found a black colored material
getting deposited. Then it was analyzed using
several techniques including N M R or nuclear
magnetic resonance and they conform that it
is a C 60 molecule and molecule which has
60 atoms of carbon.
And the structure was just like the structure,
we showed like a soccer ball.
So, this was a the discovery of C 60 by Kroto
Curl Smalley and their coworkers at rice university
using electric discharge, and then analyzed
by several techniques give the structure which
was exactly.
So, which was kind like a soccer ball with
60 carbons having hexagonal rings and pentagonal
rings?
Later, such C 60 are fullerene kind of materials
have been found naturally occurring in Russia
and it is also been discovered in cosmic Dustin,
a distant star several light years several
thousand light years away. So, 60, C 60 molecule
molecules are present in the, in space they
are also found in minerals and of course it
was made in the laboratory. So, for their
work Harold Kroto Robert and Richard Smalley
were awarded the 1996 Nobel prize in chemistry.
Though the discovery they made was in 1985,
they were ordered the Nobel prize in chemistry
in 1996, it was a great discovery a new allotropic
of carbon was discovered. So, it brought about
several new molecules related to C 60 like
C 70, C 80, C 82 and several large cage like
structures ring with cluster like structures
were discovered after these fullerene or C
60 was discovered.
So, the type of fullerenes that we know today
are like the common C 60 molecule, we just
discussed apart from that we have now made
several nano tubes which are made up of carbon.
So, these hollow tubes which have a very small
dimensions can have single walls or multiple
walls based on carbon these nano tubes are
very important for several applications as
we will discuss in the coming lectures. Then
you can have mega tubes much larger in diameter
than the nano tubes and can be prepared with
walls, which have varying thicknesses. Then
you can have full fullerene rings you can
also have fullerenes which are linked by carbon
chains.
So, those are called ball and chains, so those
are called ball and chain kind of dimmers,
so 2 buckyball or 260, C 60 molecules which
are linked by a carbon chain will then we
called a ball and chain dimmer. So, you can
have two buckyball which are connected to
each other to from fullerene rings then you
can have what are called nano onions spherical
particles based on multiple carbon layers
surrounding a buckyball core. So, you have
a C 60 core and there are layers of carbon
surrounding that C 60 molecule, so you may
have 5, 6, 7 layers of carbon which is surrounding
a C 60 molecules. So, if you take out one
layer another layer will be there, so that
is why the structure will be like an onion.
Hence, it is called nano onion, because the
dimension of the C 60 molecule is nanometer
in size less than 1 nanometer it is around
0.7 nanometers.
Now, the name fullerenes come from the name
of an architect Buckminster Fuller who first
made domes which are like the fuller in structure.
So, these geodesic domes as they are called
have been made in several places in Canada
and many other places which have domes which
are in the shape of this kind of the hexagonal
rings and pentagonal rings fuse together.
So, if you take half of it then it forms a
dome which is very similar 2 domes which Buckminster
Fuller, an architect made in the 1970s in
several countries and, so this molecule is
called fullerene after the name of Buckminster
Fuller.
So, fullerenes have 3 dimensional networks
of carbon atoms, they contain pentagonal and
hexagonal rings in which no 2 pentagons share
an edge. So, hexagons can share an edge one
hexagon can share an edge with one pentagon,
but 2 pentagons cannot share an edge. Then
each atom is connected to exactly 3 neighbors,
3 other carbon atoms and each atom is bonded
to 2 single bonds and 1 double bond example
in C 82.
So, again going through the main characteristics
of C 60 molecules there are 60 carbon atoms,
there a 5 membered rings and there are, so
this is a 5 membered ring as you see. Here,
there are 5 continents and there are 6 membered
rings here and this 6 membered ring can be
connected to another 6 membered ring in this
C 60 molecules. But, two 5 membered rings
cannot be connected to each other, the vendor
was diameter that means the distance between
the electron clouds from one end to another
end is about 1.1 nanometers. So, that is like
11 Angstrom, but if you take the nucleus of
the carbon here and the nucleus of the carbon
then that distance is around 0.7 nanometers
which is much less than 1 nanometer.
So, it is or averages, you can just say that
the fullerene molecule is of the order of
nanometer, but of course it depends on what
kind of diameter are you defining. So, if
you take the vendor walls diameter it is 1.1
nanometer and if you talk about the nucleus
to nucleus diameter then it is 0.71 nanometer,
which is equal to 7 Angstroms, 7.1 Angstroms.
Then you can have other than C 60, which has
60 carbon atoms, you can have C 70 which has
70 carbon atoms, you can have C 72, C 76,
C 84. So, you can have fullerenes with different
number of carbon atoms, but the shape will
change slightly. Now, you are number of hexagons
and number of pentagonal will change because
the number of hexagons and the pentagon’s
are related. So, always you will have 12 pentagons
the hexagons will change and that number will
be equal to V by 2 minus 10 where V is the
number of vertices.
So, this is given by Euler’s polyhedron
formula, so if you have C 82, if you have
82 vertices then you need to know how many
edges are there. So, how many faces and there
and you can use this formula V minus E plus
F equal to 2 where V, E, F are the vertices
edges and faces and you can find out that
there will be exactly 12 pentagons and V by
2 minus 10 hexagons. So, if you have C 84
if you have 12 pentagons, then you, if you,
the number of vertices is 84, so 84 by 2 is
42 and 42 minus 10 is 32 hexagons.
So, you can say that C 84that means the cluster
or the molecule C 84will have 32 hexagons
and 12 pentagons. So, in all these fullerenes
you will have variable number of hexagons
and you will have 12 pentagons and the number
of hexagons you can find out if you know the
number vertices.
But, the number of vertices you can get from
the number of carbon atoms you have on this
cluster, so you can have a large variety of
these fullerenes all related through hexagons
and pentagonal of carbon. Now, recently in
2007 instead of carbon, boron have at the
vertices has also been created to lead to
a buckyball kind of structure. However, the
formula which has been obtained is be 80 and
with each boron forming 5 or 6 bonds and it
is predicted that it will be more stable than
C 60.
So, this kind of boron buckyball has not been
isolated it has been predicted like periodically
and described and it is suggested that if
it is made. Then this V 80 molecule will be
more stable than C 60, so there are lots of
new things related to fullerenes which are
still under research.
So, how do you synthesize these fullerenes
the C 60, C 70 etcetera, so the technique
which is used is either you take graphite.
So, graphite is basically carbon one allotrope
of carbon where which has got sheet like structure
or layers of carbon forming hexagonal rings.
Now, each layer separated from another layer
by Van Der Waals distance of around 3.3 Angstrom
and this graphite with if you evaporate by
shining laser. Then you can get some soot
some carbon material deposited from where
you can extract fullerenes another method
is what is called the arc discharge method.
So, this is a method where you use 2 graphite
electrodes, so again graphite is being used,
but you have 2 graphite electrodes. So, you
know in the electrodes you apply a potential
and you generate a discharge between the 2
electrodes. So, there is a small gap between
the two electrodes and between that arc has
to be formed, so when you apply a very high
potential on the 2 electrodes then and an
arc is created then some soot is deposited
in the chamber around these electrodes.
So, this technique was developed in 1990 by
Kratschmer and Huffman and this also leads
to several fullerenes. So, you can use that
technique of shining laser on graphite and
collecting the soot or you can use a arc discharge
method to or using graphite electrodes by
which you can generates soot which collects
on the inner walls of the chamber. Now, which
you can collect and from that you will get
a variety of C 60, 70 type of fullerenes and
then you have to separate them.
Then you can use other techniques like where
electrons beam evaporation.
Now, where you can produce the higher fullerenes
to a larger amount or you can take some aromatic
compounds and then heat them, so you take
aromatic compounds like normally heat them.
So, you can get a shot from that soot also
you can get some fullerene type of compound
of course the proportion of which fullerene
you get depends on the method. Now, to get
pure fullerenes by one method is quite a tough
job normally you have to separate these fullerenes,
so once you get the soot through different
chemical processes.
Now, what would fit inside a buckyball or
a C 60 molecule, so you see this is a C 60
molecule and if can be put something inside
that has to be smaller in size. Then this
diameter of around 1 nanometer or 0.7 to 1
nanometer depending on how you define the
radius the distances, so either you take the
Van Der wails distances. But, you take the
distance between the nucleus to the nucleus
at the end of these diameter, so what would
fit inside a buckyball.
Now, of course it has to be much smaller than
7 Angstrom or much smaller than 0.7 nanometers
and such materials where there is something
inside the cage are called car and endohedral
compounds. So, these are also called cage
compounds or endohedral compounds so nitrogen
can you put in an atom of nitrogen sure you
can put an atom of nitrogen.
But, because what is the diameter of the nitrogen
atom it is of the order of 1.2 Angstrom or
0.12 nanometers which is much smaller than
0.7 nanometers is the diameter of the fullerene.
So, definitely you can put nitrogen can you
put hydrogen, also we can put because it is
of the order of 0.5 Angstroms or 0.15 nanometers.
So, we can put a molecular of hydrogen in
this cage, now can we put a larger molecule
say a molecule of sulfuric acid.
So, molecule of sulfuric acid has a diameter
of approximately 7 Angstroms which is like
0.7 nanometers and you know this whole thing
is of the order of 0.71 nanometers. So, this
will be very difficult or more or less impossible
to put a molecule of sulfuric acid inside
a C 60 cage, so not likely, so this is not
likely to be the case. Now, such molecules
like if you put nitrogen inside this C 60
molecule then these are called endohedral
compounds and these endohedral compounds are
given by this formula where M is whatever
you have put inside the cage.
So, if it is nitrogen then you write N at
C 60 that means N is inside C 60, if you put
lanthanum a rare earth element and it is known
that it goes in inside this cage. But, lanthanum
goes into larger fullerenes C 82 which has
a larger diameter than C 60 and lanthanum
is a bigger atom than nitrogen. So, lanthanum
goes in a C 82 kind of a fullerene, but not
a C 60 fullerene whereas a small atom like
nitrogen can go inside C 60. So, both of them
are endohedral fullerenes because they are
in lying inside the cage and the formal is
m at C 60 where M is inside the cage.
Now, can we have exohedral, this one was endohedral
means inside can we have exohedral, yes we
can have, so this is the C 60 molecule and
you have got molecule on top of it outside,
so this is called an exohedral compound. So,
we can have endohedral compound and we can
have exohedral compound in the exohedral compound
you can have either inorganic groups. So,
you may have a metal with some legants, so
you can have say platinum or some nickel our
gold some metal with some accompanying legants
on the surface of the C 60 or 70 molecule
and this is another protection.
So, the C 60 or C 70 molecule is inside and
you have got these atoms outside so this kind
of exohedral compounds have also been made
in the laboratory and these gives you lot
of applications. So, because you can modify
the properties of C 60, C 70 using these molecules
which are attached outside on the periphery
of the surface of C 60 or C 70 or other fullerene
type of compounds.
Now, you can also have atoms bond to fullerenes
as salts, for example you can have a salt
where you have a positive metal and a negative
an ionic 60, so when you have a an ionic C
60 then it is called a fuller ride. So, if
it is neutral say C 60 molecule then we call
it a fullerene when you have a ionic C 60
then we call it a fuller ride. So, this metal
cation is like a typical cation that you studying
chemistry cations are form from elements which
donate electrons easily.
So, you have these alkali metals alkaline
earth metals like lithium sodium potassium
are alkaline metals and you have elements
like calcium barium strontium which are alkaline
earth materials they like to donate electrons
these elements. So, when they donate electrons
the electrons go to the C 60 and C 60 can
accept those electrons because there are lots
of orbitals in C 60 pi orbitals and, you can
transfer electrons and then C 60 becomes negatively
charged.
So, depending on how many electrons you donate
this charge will change from 1 minus 2 minus
2 N minus, so you have a cation which is outside
and you have x, the number to balance the
charge over here. Now, what happens when you
add these electrons when you add these electrons
then the electrical conductivity or the resistivity
changes because you are now adding electrons
to this fullerene moiety. So, which becomes
a fuller ride and the electrical resistivity
decreases by several orders of magnitude,
in the case when you are adding alkali metal
ions.
So, as X increases you reach a minimum in
the metallic resistivity for x equal to 3,
so the typical formula that you can generate
in these fuller rides or something like M
3 C 60. So, that means three moles of potassium
or rubidium or cesium per 1 mole of C 60 as
the maximum it goes, so in that case you will
have 3 electrons transfer to C 60. So, the
charge here will become 3 minus and actually
several of these materials like K 3 C 60 or
rubidium 3 C 60 becomes superconducting at
low temperature.
So, a 30 Kelvin which is minus 243 degree
Celsius for the metal being rubidium which
is a alkali metal down the group this compound
rubidium 3 C 60 becomes a superconductor at
low temperatures of 30 Kelvin. So, that is
minus 243 degree centigrade and we have the
superconducting properties which mean 0 resistance
perfect diamagnetism. But, will show levitation
and other properties that any superconductor
shows, so in C 60 and fullerene kind of materials
also you can see super conductivity.
Now, you can also recently it has been shown
that an organic compound like c h b r three
it is like bromo form it is called bromo form
like you have chloroform for C S C L 3 you
have bromo form. So, this can be added to
C 60 to increase the conductivity or lower
the resistivity, so if you have a metal ions
like potassium rubidium etcetera. Also, you
can lower the resistivity transferring electrons,
similarly it has been recently shown that
organic compounds can also be added to C 60
to show increase in conductivity or decrease
in resistivity.
Now, both combination of endo and exiheat
exohedral compounds that means you have gadolinium
G d it is a lanthanide; that means it belongs
to the lanthanide series and gadolinium is
inside the C 82 moiety. So, this is the formula
for an endohedral compound, so gadolinium
is inside the cage of C 82 and outside C 82
you have got hydroxyl groups. So, this is
the exohedral part and this is the endohedral
part, so you can have a combination of endo
and exohedral compounds and this is a classic
case.
So, this is what I just mentioned that gadolinium
is inside the cage and outside is covered
with hydroxyl groups and it is possible material
very good material for magnetic resonance
amazing that is what their research has shown.
So, there is lot of a potential in this material
it is a also been shown that this material
can be used for anti cancer therapy which
is very important. So, this kind of material
based on gadolinium can be made as a endo
hedral compound and can also be made as a
endo and exo hedral compound.
Now, there are several other properties fullerenes,
now fullerenes if you apply pressure so you
apply pressure from outside external pressure
very high pressure like three thousand atmospheres.
So, you we are at one atmosphere, now imagine
3000 times that pressure is falling on an
object, so the high pressure the fullerenes
get the deform. but as soon as you remove
the pressure the fullerenes get back to their
original shape.
So, this is a very interesting property of
fullerene that after being subjected to very
high pressure like 3000 atmospheres, if you
release the pressure the fullerene molecule
again comes back to its normal or original
shape. So, then the fullerenes do not born
to each other through chemical bonding, so
there if you take fullerenes they bond to
each other through week Van Der Waal forces.
Now, like in graphite where have got layers
of rings of carbon atoms which do not born
to each other through covalence bonds, but
through Van Der Waal bonds.
Hence, graphite is a good lubricant similarly
fullerenes also do not born through covalence
bounds to each other and, hence they are also
used as good lubricants. But, there are catalytic
properties of fullerenes which has been shown.
So, for example a very important reaction
industrial process which is one of the 10
most important industrial processes in the
world is to convert ethyl benzene to styrene.
So, C 60 has been shown the fullerenes have
been shown to be good catalyst in this conversion
of ethyl benzene into styrene there are other
properties like electrical conductivity data
which can be used in data storage devices
in solar cells. Now, in fuel cells these fullerenes
also shows large non linear optical response,
so non linear optical response means that
if you have a frequency omega. Then you can
generate a frequency 2 omega three omega that
is non linear kind of behavior is observed
when you use fullerene type of materials and
this is important for telecommunications.
Now, there have been many applications as
drugs and also as vesicles for drug delivery,
so C 60 or other fullerenes have are their
derivatives is have been used as drugs. Now,
their C 60 has been used to make vesicles;
that means channels through which drugs can
be delivered inside the body, so there are
lots of properties are fullerenes.
So, these are some commercial and biology
applications like sunscreens which is due
to the photo physical properties of fullerenes
where used as a antibacterial due to their
chemical reactivity and red ox properties.
Now, superconducting properties like in the
alkaline, alkali metal doped fuller rides
like K 3 C 60 or rubidium 3 C 60, which shows
superconducting properties. So, you can have
photo physical properties anti bacterial and
supper conducting properties in these fullerenes
or the derivatives of fullerenes and fuller
rides.
Now, in fullerenes or are 3 a larger congeners
like C 82, etcetera, you had a kind of a spherical
molecule like a spherical cluster. But if
we go towards a cylindrical object then we
get what are called carbon nano tubes, so
a cylindrical fullerene was discovered in
1991 or was exactly understood in 1991 by
Lijima in electron microscopic studies. So,
this nanostructure has diameter in the nanometer
range like 1 nanometer or so but the lengths
can be very large they can be hundred nanometers
or they can even be much longer.
So, the internal diameter can be varied from
1 to 15 nanometers and length can be much
larger up till several microns, so several
thousand of nanometers you can extend and
these carbon nano tubes also called C N Ts
have tremendous applications. So, they can
be made of a single layer of graphene sheet
that means only 1 layer of carbon is present
and roll together to form to a tube or there
are multiple layers. So, if it is made up
of only one layer then it is call single wall
nano tube if it is made up of multiple layers.
Then it is called multi walled nano tube as
you see here there are 1, 2, 3 and 4 layers,
so this is a 4 layer multi wall nano tube
of course all made up of carbon.
But, you can also make single wall nano tubes
double wall nano tubes etcetera, they have
not lots and lots of properties very interesting
properties many of these are semiconducting
in nature, but you can also make conducting
nano tubes. So, a typical room temperature
resistivity is given here it is around 108
ohms, it should be ohm centimeter which is
the resistivity of simple carbon nano tubes
at room temperature.
Now, these carbon nano tubes are made of 1
atom thick sheet F F carbon, so if you take
graphite which has got layers of carbon hexagonal
orientated carbons. So, you have got rings
of carbon and, if you have one layer of carbon
only then it is called graphene. But, if you
have several years of carbon one below the
other which is connected through week Van
Der Waal forces then that is graphite. So,
graphene is only one layer of graphite, now
if you take that one layer of graphite which
is called graphene and you roll it up in a
cylinder.
Then you get the carbon nano tube and if you
have only one layer then you get single wall
carbon nano tube and if you have several years
you will have multi wall carbon nano tube.
Now, these sheets if you are rolling the graphene
sheet this how are you rolling the graphene
sheet will change the nature of the tube,
which you will get ultimately.
So, the sheets which are rolled at specific
and discrete angles will give rise to different
types of nano tubes some of them will become
chiral the others will be called zigzag or
arm chair as we will discuss. So, you can
get single wall nano tube multi wall nano
tubes chiral nano tubes and several other
kind of nano tubes and individual nano tubes
align themselves sand are weekly held by Van
Der Waal forces.
So, if you have a several nano tubes then
you get a bundle of nano tubes and these nano
tubes interact with each other through random
wall forces and they have kind of form ropes
in one direction. Now, the chemical bonding
of nano tubes inside the carbons are all S
P 2 hybridized carbons, so that is true for
all these carbons in these nano tubes.
So, to have a look at these nano tubes this
is a single wall nano tubes and this diameter
is of the order of 1 nanometer and this is
a multi wall nano tubes. So, you have one
nano tube here and then this is the second
nano tube and then you have a third nano tube,
so this is the multi wall nano tube it was
observer first by endo in 1975. But, was really
highlighted by Lijima in 1991 and the world
came to know about carbon nano tubes through
Lijima work in 1991.
Now, these are some of the real pictures the
transmission electron micrographs of multi
walled nano tubes and you can see it some
of them are broad and wide and this scale
is of 100 nanometers. So, this diameter is
this is a very thick nano tube these are thin
nano tube, so this may be of the order of
may be 5 or 10 carbon layers are there in
this nano tubes. So, this maybe a 10 nanometer
or 5 nanometer tube this is may be a 15 nanometer
tube and none of them are single walled nano
tube because single walled nano tube, the
diameter will be of the order of 1 nanometer
in general.
Now, so nano tubes can be straight, they can
be spiral and this, they can be of the type
of springs they depend how you grow these
nano tubes. Then you can control then you
need to know how to control the shapes of
these nano tube, how to get them straight,
how to get there in the spring fashion for
certain applications.
So, that depends on the growth conditions
how you are doing the discharge or if you
are doing using a laser how you are creating
these nano tubes. Now, are you using a metal
catalyst many times metal catalysts, are use
to grow carbon nano tube, so all these things
matter to ultimately control the shape of
these nano tubes.
Now, here you can see a transmission electron
micro graph of bundles of single walled carbon
nano tubes, so these are a single walled nano
tubes. But, there are many such nano tubes,
so this is one nano tubes, second nano tubes,
is the third nano tube like that there are
several nano tubes which are forming a bundle.
So, this ability of these nano tubes to come
together is through Van Der Waal forces and
these are again a picture of nano tubes this
is curd nano tubes and you can see this scale
is of five nanometers. So, this diameter is
of the order of 1 to 1.5 nanometers typically
for single walled nano tubes, so these are
all single walled carbon nano tubes.
Now, how to roll the nano tube as we were
discussing if you have one layer of graphite
which is called graphene, so this is a graphene
sheet. So, you have all six membered carbons
forming the sheet and how do you roll this
sheet because if you roll the sheet in one
way you get one kind of nano tube. But, if
you roll it in another, you get another type
of nano tube and other type of nano to you
so there are certain definitions, so in this
hexagonal lattice you define what is called
a chiral vector. So, in this 2 dimensional
lattice you define a chiral vector C 8 which
is dependent on to vectors a 1 and a 2, so
these are the two vectors a 1 and a 2. So,
in any hexagonal lattice you can define these
two vectors and what are the numbers or the
coefficients of these 2 vectors.
So, if you take a very large a 1 and a very
small a 2, that means n is very large and
m is very small you will get one type of ruling.
But, if you take n and m both same then it
will not result in a chiral it will result
in something else if you take n some number
and m you make it 0 then you get another kind
of nano tube again it will not be chiral.
So, the chirality of the tube is dependent
on this formula and from this formula you
can define the chiral angle theta.
So, these vectors and their coefficients are
important the efficient are very important
and also what is how do you end the nano tube
toward, if you want to close the nano tube
at the end and not leave it open then what
how do you cap it. So, these are certain things
which give flexibility to the various kinds
of nano tubes that you can generate using
a simple graphene sheet. But, just based on
the angle the chiral angle at which you are
rotating this plainer structure or rolling
the plainer structure into a cylindrical structure.
So, that is what I said if you take a vector
a one and a two such that the coefficient
of a 1 is n and a 2 is 0 that means the vector
that you are taking is in this direction because
a 2 is 0 and only a 1 exists. So, you are
looking at this victor and that means this
is the n 0 vector, so this is called the zigzag
nano tube the nano tube that you will get
if n has a value and m is 0. Then if you roll
all the graphene sheet in that manner then
you ultimately end up in a nano tube who is
a direction.
So, this is, this will be the direction of
the nano tube and it is called as zigzag nano
tube, so the coefficient m is 0. However,
you can choose any other coefficient n and
m if you choose n equal to m that means n
and m both are same. Then your direction will
be in this manner because you have the same
magnitude the coefficient of this vector and
coefficient of this vector both are same.
So, you will have a resultant like this and
that is what it is being shown this is parallel
to that the resultant which you get here and
you will get the n, n carbon nano tube which
is called commonly as the armchair nano tube.
So, the zigzag nano tube and the armchair
nano tube are two special cases all other
nano tube what if you take any other value
of n and m you will get chiral nano tubes.
But, n 0 and n, n that means the same value
for n and m will give you zigzag and arm chair
nano tubes.
So, this is the n, n is a naming scheme it
tells you about the vector which you have
chosen these coefficients, tell you about
that and it will tell you about the chirality
of the nano tube which will result. So, if
you roll the tube in such a manner that the
coefficients which you have chosen are n and
m, and this is very important in finding out
the property because the properties of the
nano tube will depend on this factor.
So, the integers n and m as I discussed tell
you about the unit vectors along 2 directions
in the plainer graphene layer or the carbon
layer and if m equal to 0 the nano tubes are
zigzag. But, if n and m are same then they
are called armchair any other value of n and
m they are called chiral nano tubes. So, the
diameter of an ideal nano tube can be calculated
using n m and a, where a is this value 0.246
nanometer and actually it comes from this
distances.
So, it is the distance between this carbon
and this carbon the carbon which are 1 and
3 positions, if you measure this distance
that is equal to 2.46 Angstrom or 0.246 nanometers.
So, that is the value of a, if you use that
value and you know what is n and what is m
you can calculate the diameter of any nano
tube.
Now, when you look at these nano tubes, which
result as you roll them in a particular fashion,
for example when m is equal to n then you
get the armchair type of nano tube and the
angle which you have is 30 degrees. So, the
chiral angle of course this here 5, 5 means
m is 5 and n is 5 and it gives you a nano
tube like that and at the end if you want
to close it this part we look exactly as half
of the C 60 molecule. So, if you have a arm
chair nano tube the cap being part will be
C 60 molecule say exactly like the C 60 molecule.
However, if you have a zigzag nano tube a
zigzag nano tube has a theta value of 0 and
if you come to the end of the nano tube you
cannot close it with the C 60 molecule you
have to close it with the C 70 molecule and
that is what is shown here. So, you take half
of the C 70 that will exactly fit at this
part, so what how to cap the end of a nano
tube is also dependent on what kind of nano
tube it is nano tube. But, it is if it is
armchair nano tube only half of C 60 can cap
it if it is a zigzag nano tube then half of
a C 70 molecule can cap it if it is any other
kind.
So, for example this is chiral molecule, it
is not zigzag it is not armchair and the angle
theta is neither 0 nor 30, it is in between
0 and 30 then that chiral nano tube will have
an end which is neither C 60 nor C 70. But,
is a half of C 8 molecule, so a half of C
8 molecule will cap it that means for different
types of a nano tubes you need different types
of caps.
So, the properties of nano tubes change significantly
with the n and m values and one like electrical
conductivity is a very important property.
So, it shows drastic difference you can have
metallic nano tubes, semiconducting nano tubes
and these properties have been used for applications.
Now, one of the first applications was a molecular
field effect transistor and this was made
in 2001 by I B M who showed that using these
carbon nano tubes you can make a molecular
field effect transistors. So, which is a great
invention, because you are lowering the size
of the transistor from a normal transistor
of one molecule is being used as a transistor
and this was done in 2001.
So, there are several other applications of
these nano tubes, look at the mechanical properties
of these nano tubes. So, carbon nano tube
compared to stainless steel, carbon fiber
glass and keylar, keylar you know is a polymer
and it is used in bullet proof vests if you
compare even with keylar. So, most of these
numbers you see for carbon nano tube are much
higher than these numbers, so look at the
strength the strength is 10 to 60 for carbon
nano tube where are none of these are of the
order of 10.
But they are all less than 5, whether it is
steel, whether it is carbon fiber or whether
it is this polymer which is used for bulletproof
vests. So, today we have discussed several
of the features of carbon nano tubes and fullerenes
and we will continue our study of carbon based
nano structures in the subsequent lectures.
Thank you very much.
