Welcome back. We now change gears a little bit and start talking of something likely different. As you can see from the title of
the lecture itself, we are now going to talk about atomic force microscope. I do not know how many of you are aware with this name of atomic force microscope or the AFM as it is commonly known; it is very unique and a special type of a micro scope and is very widely use these days. Now, you might wonder in a course of instability and pattering, we have so far
primarily focused on the patterning aspect. And we have not talked about in much of instability as of now, but which we will do in the subsequent lectures. You might wonder why all of a sudden we pick up a special type of a micro scope. There
are many courses available both on line as well as class room courses, which talk about materials characterization, where you learn a whole lot of techniques; and whenever you talk of seeing something small, you tend to sort of relay on the fact that we go for a
micro scope. But if you remember the last couple of slides about soft lithography, we talk that features with 10 nanometer lateral resolution can be
made by soft lithography. So, critical question to ask is, how does one see this structures? I mean you might have made something, but how really does one see this, because a normal
micro scope even the highest end optical micro scope with a hundred x objective, which magnifies
your image by thousand times. You won’t be able to see anything below 400 500 nano
meter or may be a micron and that to pretty faintly.
The other thing is you have been routinely talking about topographic patterns like this,
and we talked about all sorts of things height this, that. Question to ask again is how do
you measure the feature height? Because a normal microscope what you see. Normal microscope
I also include a scanning electron micro scope in this regard, where the only difference
with an of course, it is very advanced equipment. But the major difference with an optical micro
scope lies in terms of the optical source. In an optical micro scope, you essentially
use white light to illuminative your sample. In scanning electron micro scope you use a
stream of electrons. So, that your wave lengths or small and therefore, you do you can resolve
to much higher extent. But do not forget I mean this course does
not permit me to going to the details of micro scopy. But do not forget that in a in a optical
micro scope or in scanning electron micro scope, ultimately what you see is more like
a projection, that is like a picture you take in your camera. It is a 2 D projection of
a 3 D system. So, with your digital camera or cell phone camera if you take a picture,
you are taking a picture of the 3 D world, but you are seeing it on a on a 2 D plane.
So, looking at a picture you really cannot say suppose, two people are standing at slight
differences one is closer to you, one is far away.
So, if you take a picture all you can see is the person who was standing closer to you
is appearing larger in the picture. And the person who is who was standing further away
from you is appearing smaller in the picture. But, you cannot looking at the picture say,
how what was the separation distance between them, how far the second person was standing
from the first person. So, what happens is that is since you are looking at a 2D projection,
the information about the depth sort of is lost. Exactly the same thing happens in optical
micro scope or scanning electron micro scope. You cannot get a clear idea about the feature
height, which is very, very important when you are talking about nano and meso scale
patterns. So, this atomic force micro scope which falls,
which is a special and the I would say the most popular instrument in the class of set
of instruments which again is relatively new early 80’s. The developments started what
is known now as the scanning probe micro scope group of techniques. So, this goes by the
name SPM why the name comes, how it works we will eventually discuss everything in very,
very simplistic fashion. So, you do not have to be earlier big time physicist to understand
this. We will have all the understanding considering that you are an engineering student of an
under graduate college or post graduate student in with a predominantly background in chemical
engineering. So, do not worry about that. So, SPM it is known as the scanning probe
micro scope. Typically, it has two major micro scopes; one is the STM which is known as the scanning tunneling microscope, what is tunneling effect? I will discuss very shortly, but you can just do a quick Wikipedia search what is tunneling and the atomic force micro scope. Why I talked about STM is STM was actually the predecessor of an AFM and based on the developments of STM only the AFM came up, but STM works only for a conducting surface. So, since you are talking mostly about a polymer surface STM does not work an AFM works perfectly well over there. So, you will talk about and AFM in much greater detail, but, just to give you an introduction.
So, that you do not feel like left out I did not know, I do not know S T M, but I talk
about AFM you do not realize that they fall in to the same group of methods. I just spend
a few minutes talking to about STM. So, remember that AFM is a special class of scanning probe
microscope probably the most popular class of these methods. And let us see what have
an AFM works. So, what we are going to do we are going to talk about the critical components and some operational aspect. As well as we talk about the basic physics,
which is extremely fascinating and we talk about here what is this atomic force? What
force exactly are we talking about? And it is actually a nice bridge between the two
parts of the course that is the pattering part on the instability part because the forces
we introduce here or talk about here are significantly, responsible for the instability in the first
or the second lecture of the course we talked about instability spontaneous instability.
So, those instability as we will see or caused by the same forces which are used to generate
an image in an atomic force microscope. You can guess it primarily we will be talking
about the Vander walls force (No audio from 08:26 to 08:30). And we will see how this
is used for imaging, as well as in subsequent lectures may be after five six lectures we
will start realizing how these forces are responsible for spontaneous instability or
different types of instability in thin films. So in early 80’s scanning probe microscopes
where first introduced and they are able to produced first real space images of a surface.
What is real space image? It is a essentially the three dimensionally images of a surface.
So, that you do not only see the lateral structures, you do not see only the lateral dimension
or only could measure the lateral dimension of the structures but you also get at true
information about the height of the feature height. So, in normal microscope so, if you
have a let us say feature like this, in a normal microscopy we will see something like
this. An AFM you will not only see like this, but you will also get an idea about height.
So, this is in very nut shell, this is one of the major advantages what an atomic force
microscope or an SPM group of method gives. So, now, SPMs are used in a wide variety of
disciplines including fundamental surface science, routine surface roughness analysis,
spectacular three dimensional imaging from atoms, to micron sized protrusions of surface
living cells. Also, the scanning probe microscope is an imaging tool with a vast dynamic range
spanning the realms of optical and electronic microscopes. It is also a profiler with unprecedented
3 D resolution. In some cases, scanning probe microscopes can measure physical properties
such as surface conductivity, static charge distribution, localize friction, magnetic
fields and etcetera. Which is another unique thing I will do not
be apply I mean really possible do with all what, where is written here you will understand all these things. So, AFM was discovered does I already pointed out it was early 80’s.
So, AFM was discovered in 1986 by Gerd binning and co workers at IBM Corporation, this particular paper if you have the access to P R L physical review letters, this 1986 paper contain the
details about A F M. So, it is essentially an extension cum derivation of the STM. And
binning and Rohrer were awarded Nobel Prize. The discovered was so unique that within four
years of discovery of STM they got the Nobel prize in 1986. If you are interested about
the short history of A F M, here is link you can sort of look into and you can get very
nice idea. So, this is the scanning probe microscope
or SPM group of family of techniques. On one side we have the scan scanning tunneling microscope there are so, STS, STP scanning electro thermal microscope. Scanning thermal microscope which gives a you an idea about the local temperature etcetera. For our purpose please do not be
over burdened with these parts. So, here we will just talk in a little bit about the scanning
tunneling micro scope. Because this side the left side of this view graph whatever you
have do not forget they require a conducting surface. (No audio from 11:56 to 12:03).
So, we will since, we are talking primarily about polymer so, we will not worry about
them. Next comes the SFM a again a generic names scanning force microscope of which the
of course, the most significant member the major platform is the atomic force micro scope.
It has several additional features lateral force microscopy, phase contrast microscopy,
magnetic force microscopy, electrostatic force microscope. And also an AFM platform can be
used itself as one of the direct write pattering techniques which is which goes by the name
DPN or dip pen nano lithography. We have talked about some of the direct write
methods, in while talking about pattering. So, here is another method and I will talk
about it in somewhere details. There can be so, AFM platform can also be augmented with
an optical microscope platform and you can have something like scanning near filed optical
micro scope. Or, which is known as the s normal n some which actually produced an optical
image and since you are imaging at the near filed so, this sort of over comes the diffraction
limitation. But we will not go into the details of that, we will talk only a little bit about
the same very little, very fundamental basics of a STM we will talk about and then we will
move on to an A F M. So, I will as I have already pointed out I
will try to give you a sort of a perspective so that you understand the operational aspects
of an AFM along with the physics and the key components. Now, AFM sort of started to hit
the market or commercially they stared to get available in early 90’s. And now very
many companies in the world make their own atomic force microscopes. Various institutes
in India now have A F Ms all the major IITs and many other research institutes. So, AFM
is pretty routine now, but still the physics is extremely fascinating and if you understand
how the images are generated. I am sure you will you really like it and also it is important
from the standpoint of using an AFM that you understand the basic physics. Because that
will really help you to enhance the resolution or quality of your image to a large extent. So, this is how we will proceed. So, this
is what is a scanning tunneling microscope is all about. It uses of a very sharp metallic
tip to scan a metallic surface or a conducting surface. Now, this is based on the concept
of quantum tunneling, which very simply put when a conducting surface is brought or conducting
sharp tip is. So, you have a sharp metallic tip let us say
very sharp metallic tip is brought in contact proximity in very close proximity to another
metallic surface. And you apply a voltage or bias between the two, what happens is the
do their might not be direct contact between the two, you still can have a flow of electrons between this two surfaces like this. So, this is what is known as the tunneling current.
And the tunneling current once you start having so, once you apply a specific voltage and
you have a tunneling current. The magnitude of this current is a function of the separation
distance between the tip and the sample or between the tip and the surface.
So, in other words, if you decide to move your tip along with the voltage over the surface
at a constant height and the surface is something like this. So, as the tip moves there is a
now a variation in the separation distance between the tip and the surface. So, as a
consequence of this variation in the heights so, let us say it is d 1 over here and d 2
over here what is going to happen as the tip moves? So, the location one the tunneling
current the magnitude tunneling current will be different from the magnitude of the current
tunneling current at the second location. So, this the principle based on which an STM
works. So, idea is that you take a surface so, this is we are seeing from the top, you
have the tip like this and the tip sort of rusters so, what is ruster scan? It is more
like a do loops. So, the tip starts from the one edge goes all the way up to here comes
back, starts from here goes all the way up to here, comes back goes to the next line
again goes comes back again goes comes back like this. So, what are the essential features?
You have sharp metallic tip. you have a conducting surface, you apply a bias or a voltage and
then the tip scans or rusters. Now, since the magnitude of the tunneling current is
a function of the separation distance. So, the undulations on the surface during the
undulations on the surface, the tip encounters during undergoing this Ruster scan gets reflected
in a change get reflected as change in the magnitude of tunneling current. And then you
can map this there are two different modes I am going to talk about it very quickly and
very shortly. But this can itself the variation in the tunneling current itself can sort of
act as a measure of the surface topography. So, here it is, when a conducting tip is brought
very near to the surface to be examined which has to be a conducting surface also. And bias
which is a voltage difference is apply between the two then electrons tunnel through the
vacuum or air between them. Of course, this typically works in vacuum so that the electrons
the tunneling electrons do not collide with the molecules of air and sort of ionize get
distracted. The resulting tunneling current is a function
of the tip position applied voltage. So, tip position essentially here means the distance
between the tip from the surface. And the applied voltage and the local density of state
of the sample you can ignore this, if you are interested you can look into. Now, what
local density of state means, but forget about that for specific sample at a given condition,
what is more important is that the tip position and the applied voltage they sort of determine the magnitude of the tunneling current. So, information is acquired by monitoring the
current as the tips position scans across the surface. So, this particular sentence
if you paragraph, if you now look at we have already talked that the tip sort of under
takes a ruster scan and one can acquire the, one can monitor the information is acquired
by monitoring the current how it is done we will see. Practically STM can be a challenging technique
as it require extremely clean and stable surfaces sharp tips, excellent vibration control and
sophisticated electronics, but let us not talk about that. STM can be designed to scan
a sample in two possible modes. So, this is important it you can have two different modes;
one is the constant height mode and other one is the constant current mode. The one
we briefly described to over here is actually the constant height mode. So, you maintain
a constant height and go on scanning the surface or Ruster the surface. And this undulations
as the tip at a fixed height encounters the undulations you keep track of the change in
the magnitude of the tunneling current and from that you try to reconstruct the surface.
Understanding the fact that if your tunneling current, if the magnitude of the tunneling
current is higher, then the surface was closer to the tip. If it is lower than the surface
was further away from the tip and so you can reconstruct the surface. So, this is constant
height mode the tip travels in a horizontal plane above the sample. And the tunneling
current varies depending on topography and the local surface electronic properties of
the sample. The tunneling currents measured at each location on the sample surface constitute
the data set which is the topographic image. So, essentially the variation in the tunneling
current itself is a measure of the topography of the surface. The other mode, in the constant current mode
the STM now uses a feedback loop. So, in addition to the hardware we have already talked about.
So, you have a tip you have a conducting surface. You apply a bias and you also have a feedback
loop, this is important you are all chemical engineering students you are all understand
what is the feedback. So, what it does that you have a set point specify a set point
in terms of the tunneling current. (No audio from 21:52 to 22:01). Now, the tip starts
to Ruster, starts to scan so, let us say this was the set point the c 1 it goes to the second
location where the current is now c 2 because of the surface topography. This c 1 minus
c 2 is now the deviation from the set point or the error. (No audio from 22:22 to 22:34).
This error is now fed to the feedback loop which then allows the tip to move up or down.
How it is moved? We will discuss when we talk about an atomic force microscope. But this
error is now fed to the feedback loop so that it adjusts the position of the tip. So, let
us say the tip was here it was corresponding to a. (No audio from 23:00 to 23:06). So,
this is let us say the set point configuration, the current was c 1 it has now gone to the
second point, the distance has increased. So, the current has reduced actually so, this
c 1 minus c 2 is now the error and based on this the error is fed to the feedback loop.
So, that it allows the tip again to comeback so that this distance matches this distance
here and the current again becomes c 1. So, in this case, the location of the tip it is
self reflects the contour of the surface and you can generate the image like this.
Now, it is important to understand the existence of the feedback, we will going to we are going
to talk about it in greater detail because all the commercial or the current AFMs what
with this feedback loop mechanism. So, this is in a very brief nut shell the operation
of an STM. Important thing to need is that the principle of a STM requires tunneling
current. And which is possible only with a very sharp (No audio from 24:16 to 24:23)
metallic tip and a metallic or again a conducting surface. And therefore, though it is extremely
useful, scientifically extremely fascinating. It has unfortunately limited application in
terms of polymer structures, imaging in polymer structures. I was still I think this much
amount of fundamental knowledge in STM will help you, both to understand how the AFM evolved.
And also STM has a technique itself is extremely power full and there are many application
areas where the STM finds rather significant application. With that we now move on to atomic force microscope,
which as I have already pointed out is to large extent based on the developments related
to STM or in every true sense the STM was the predecessor of the A F M. So, let us see
what are the advantages? Firstly, the first thing without going into any details you need
to understand, that AMF does not suffer from the one major limitation which is their in
an STM. AMF does not require a conducting sample or conducting surface and can work
for any type of sample. Therefore, since it does not require a conducting surface, it
cannot work on the principle of tunneling, but it works on the principle of something
that is more fundamental. And that is the interaction forces between molecules or particles
or surfaces. So, AFM relies between the inter atomic interaction forces. Now, one of our
previous lectures we have actually talked about these interaction forces and I am I
think I have already introduced you to the concept of Vander Waal’s force, we will
revisit it today. So, this is what we can be an atomic microscope,
do not going to the details of the definitions and all these things, these are things that
everything we will understand what, how it works and all that. In an atomic force microscope,
the imaging or more accurately the information about the topography of a surface is done
based on the modulation of interaction forces between two atoms. So, interaction forces
this is important, we talk about the interaction forces between atoms or molecules. In reality
we cannot go down to the atomic level and we work based on the interaction forces between
two surfaces. The in reality the instrument operates based on the interaction between
two surfaces the sample and a sharp tip. So, here also you have a sharp tip and you have
a sample, but unlike STM, there is no tunneling effect arising out of the tip, but we will
see how exactly it differs. So, this is in a nut shell the heart of an
AFM operating heart. So, here you have a tip so, here you have molecules and here you have
the surface molecules. So, the instrument essentially works based on interaction (No
audio from 28:07 to 28:14) between the tip and the surface. This is a picture which you
will see again and again and again. This is this particular technique which is now the
standard industry standard of a cantilever mounted tip and a laser and a photo detector this is known as the beam bounce method. We will understand so, get used to this figure,
but I can sure you that after two see lectures when you completed atomic force microscope,
you will understand every single component of how it works and what it means. So, with an open mind let us start understanding an AFM, what how it works? So, first thing we need to understand, what is this intermolecular
interaction forces we are talking about. Now, these forces are the so call Vander Waal’s
forces and I am sure that you understand that will large extend what they are? They are
the most fundamental form of force, somebody who has slight confusion. So, this is a nucleus
and then you have the electrons which are in a atom for example, you have the electrons
which are encircling the nucleus. This is picture I am sure you have got use to from
your school days, let us school days may be seventh or eighth standard.
In this picture we use to draw, but reality it is that it is not so simple the it is either
electrons or not like this isolate discrete entities rotating like the planets. I am sure
in your school days you also learnt at some point or the other what is the similarity
and the difference between the electronic structure and the solar system. In reality,
it is very high frequency oscillation of the electrons around the nucleus. And at any given
instance t 0 let us say what happens is there is a charge localization. (No audio from 30:25
to 30:32). The moment there is charge localization this leads to a delta minus charge which is
localized over this area. Now, this delta minus charge what it does? It sort of induces
a delta plus positive charge on the neighboring atom.
And therefore, since this is this has opposite polarity the nature of interaction is sort
of always attractive. But what happens is this delta minus is a temporary localization.
So, we are talking about molecules which are charge neutral
and there is no permanent dipole. So, even in a charge neutral, non dipolar molecule
you have this phenomena occurring at all instances of time so, this is the type of interaction
which is known as the induced dipole (No audio from the 31:31 to 31:36) induced dipole type
of interaction. This is what is known as the lifshiftz Vander Waal’s forces and this
the most fundamental form of force. Now, what happens is the subsequent instants
what happens is this localization the position of this localization now changes. So, this
is now let us say localized here and it induces a charge over here. So, this force or this
attraction though the overall nature of the interaction is attractive. There is no physical
attraction present or any bond formation text place because of the fact that the charge
localization sort of the position of the charge localization changes with every instance of
time. And therefore, this attraction sort of is dispersed over the entire material or
entire bulk of the material. So, this is also often referred to as the dispersion forces.
So, this is available or these results in all materials and some of you might be knowing
the this is the most fundamental form of any force. What is important to realize the though
this is the most fundamental form of force, in reality or in our macroscopic world we
hardly see the signature of Vander Waal’s force. And everything we see is sort of a
function or dominated by gravity. The reason for this is the, this interaction sort of
scales with so, v d w the Vander Waal’s the interaction scales with one by r to power of 6 between two particles, next they let us say atoms or molecules. So, r is the separation distance between the two. In contrast, your gravitational force scales
with m g h, h is the separation distance. So, you can understand immediately that in
the microscopic world where a h r whatever so this can be r there equivalent here. If
r is large, this term will be much much larger then Vander Waal’s force. And therefore,
in our macroscopic world we do not see any signature of Vander Waal’s interaction.
However, you can now imagineif r is small, what happens? What happens is that since r
is in the denominator therefore, with progressive reduction of r this term becomes dominating
or becomes much much larger. And for very small r at the molecular level or at the meso
scale, the Vander Waal’s force sort of dominates much at much higher rate as compared to the
gravitational force. Now, one of the thing that is interest to
note is that we talk so much about nanotechnology. So, everything everyone is talking about nanotechnology.
Now, there are quite a few factors which make nanotechnology at this particular length scales.
So, unique and even in the introduction of this particular course we did talk about some
of these methods or some of these reasons. But one of the reasons of course, is the fact
that at these length scales very small length scales. Length scales corresponding to few
molecular diameter or let us say up to 10 or 100 nanometer what happens is you also
have a very strong signature of these Vander Waal’s forces and gravity is almost absent. So, many of the spectacular phenomena so call
spectacular phenomena, one sees at these length scale is attributed to the fact that the interaction
forces or the intermolecular interaction forces have or have a significant role in some of
those phenomena. So, for all understanding what is important to note that Vander Waal’s
force between two particles have a scaling of one by r to the power of 6. And for the
time being you belief me that this sort of stretches, this interaction stretchers to
roughly around ten nanometer definitely not beyond ten nanometer where this becomes large
and eventually so for r greater than ten nanometer tends to zero.
The other thing you need to understand at the this moment and it will I will we will
take of the derivation in after couple of classes is that this same force scales as
one by r square between two surfaces. How it comes? r square from r to the power minus
six we will show. So, what happens is the decay, the nature of the decay of the force
becomes much weaker now. So, that it tapers of at much slower pace and consequently the
interaction sort of structures up to 100 nanometer beyond or greater than 100 nanometer. So,
v w surface I would say again tends to 0. Now, in one of the slides we have already
mentioned that atomic force micro scope primarily operates based on the interaction between
two surfaces. So, this is more of an important number for us and we will see how this becomes
important. So, the signature of non retarded Vander Waal’s force, the type of Vander
Waal’s force we talked about is an induce dipole type interaction the what has been
assumed implicitly is that this induction of the charge is instantaneous. (No audio
from 38:08 to 38:15). And this is what is known as the non retarded Vander Waal’s
force, but you in you also have something called retarded Vander Waal’s force to which
about I suggest that you look into the internet and get an idea what it is, it is not essentially
very important for this particular course to have a very clear idea about it. So, between two fundamental particles the
scaling is one by r to the power of 6 and stretches roughly up to 10 nanometer. Between
two surfaces the scaling changes to one by r square and stretches are around 80 to 100
nanometer. The forces in the range of inter atomic forces is in the range of 10 to power
of minus 13 to 10 to the power of minus 6 newton. There can be host of other types of
interaction forces between the tip and the sample like mechanical contact, Vander Waal’s,
capillary force, chemical bonding, electrostatic forces, magnetic forces, cassimere forces,
solvent salvation forces etcetera. Some of which we will take up in little be
detail, but the most important thing to realize that an AFM sort of works for mostly based
on the Vander Waal’s forces. And like to sort of draw your attention at this point
towards this particular potential curve. This some of you might be very well conversant
with this. This is a typically potential curve, it can be the famous Lennard Jones potential,
it can be any other type of potential. So, what it gives you is an idea of how the force
between let us say two particles or two surfaces change as function of separation distance.
So, let us say you have two surfaces which are at infinite separation distance. So, then
there is no interaction between them. So, the force is 0. Now, think of the fact that
you are progressively bringing in one of the surface in close proximity to the other.
If you are talking about the Vander Waal’s potential or the forces arising because of
van Vander Waal’s interaction. We already understand that this stretches maximum up
to 100 nanometer. The other thing we understand that the nature of this interaction is attractive.
So, here we follow a convention that an attractive force
is negative and repulsive force positive. So, this potential curve can be generated
for two atoms, or two particles, or two surfaces whatever you want it is roughly the generic
nature will be the same. Only thing is the curvatures and the distances will change.
So, if you are talking about let us say between two particles which is easier to understand
infinite separation distance apart there is no interaction. You bring the particles closer
to each other and then you understand that once you cross this number 10 nanometer so,
let us say it is over here, then the interaction starts or the interaction is no longer zero,
the interaction starts and the interaction is attractive. So, the force is somewhere
over here, you also have a scaling of one by r to the power of six and so, r progressively
reducing the interaction force sort of increases so, you get a curve like this. Till you with
this point where if you look at the potential curve you see a short increase.
So, all the way down to the repulsive regime so, I and I hope you have understood this
part of curve. So, this is the point up to which this particular interaction sort of
stretches. Now, what is this point? This point is the point where the two atoms of the molecules
sort of physically come in contact. So, you have this nucleus you have this electron and
then the physically come in contact. What is assumed here or it is easy to understand
actually we assume this the validity of the hard sphere model, but even other ways if
these two know or in contact and then you still try to force them closer to each other.
What is going to happen? There is going to be an overlap of the electron clouds and there
is going to be an electrostatic repulsion so that is what is captured here.
So, you force them even closer once they have come in direct contact with each other and
you try to bring them even closer so there is going to be a strong sharp electrostatic
repulsion. So, this is the repulsive regime, this is the attractive regime and beyond this
point there is no interaction so, this is we have drawn it for let us say two particles.
If you now consider this for two surfaces (No audio from 44:09 to 44:20) if you consider
it for two surfaces for example, the nature of the curve will be roughly the same, only
difference is this interaction will now stretch longer the decay will be slower we understand
that it is stretches upto 100 nanometer. So, the decay will be little sluggish and
rest of the rest the remaining part of the curves remains pretty much the same. So, here
it is sort of which is a maxima in terms of the attraction beyond which repulsion starts
so, which means that at this point the two surfaces comes in direct contact. And so,
this distance if you can measure, this is the minimum separation distance between two
surfaces or two molecules. That is present that will be so; we will discuss this in one
of our subsequent lectures. When they are in contact, they cannot be this is not equal
to d 0, d 0 is not equal to 0 because of the fact that if you try to bring them in absolute
contact our make d 0 equal to 0, you have to overcome the physical repulsion of the
electrons. So, which is not possible and beyond d 0 this Vander Waal’s force is dominated
by the electrostatic repulsion are which is known as the short range electro static repulsion
forces. So, many times we follow a potential curve like (No audio from 46:07 to 46:14)
this is the rather famous Lennard-Jones potential. This I guess this a by r to the power of 6
to minus sign now you understand this part of the potential curve represents the attractive
interaction due to the Vander Waal’s forces. A is constant forget about this number, we
do not worry about it. And then you have this B divided by r to power of 12 which is the
short range electrostatic repulsion force, here also you can see that if r is very large
let us say it is beyond 10 nanometer then both the terms into 0. So, I will probably
rewrite it. So, here is the potential curve. This is that
let us say it is the limit 10 nanometer or whatever. So, this is the phi of the potential,
this is r the separation distance. And if you have a potential like this
there can be three situations; where r is greater than r zero both terms tend to zero
and phi tend to 0. So, for a large separation distance
there is no interaction. For an intermediate r, that is in this zone
the second term dominates over the all we assume that order
of A order of B order of B the same. So, what happens is you have the this terms the second
terms of the dominates of the first term so, your phi it is sort of a net negative and
you have an attraction. For very small r, again since r is the denominator
so, smaller is the value of r, r to the power of 12 will start dominating the first term
dominates (No audio from 48:55 to 49:02) and you have phi equal to positive. Two important
points are this point, this is the point of contact where the separation distance is d
0 between two surfaces let us say and this point is also important here again phi is
equal to 0. But there is a difference between the phi equal to 0 over here and phi equal
to 0 over here. Here, phi is equal to 0 because in this particular area attraction and repulsion
both equal to 0, over here it is different and the attractive forces and the repulsive
forces match each other. So, (No audio from the 49:55 to 50:04) and
beyond this so, this is the repulsive regime, this is the attractive regime. So, beyond
this you have a purely repulsive regime. So, this potential curve is going to very very
important in understanding the operation of an AFM that is way I decide to spend some
time into it. For the contacts of an AFM so, that is why we understood it is the interaction
between two particles or two surfaces this also represents for an AFM interaction between the tip and the surface to be scanned. Because of the fact that you if you know look carefully, this is the configuration of an AFM so, this is the tip; this is the surface
to be scanned. One additional information I am giving you right know the tip is sharp,
radius of curvature is between 10 to 20 nanometer. Assume in organic molecular as size roughly
of the order of an Angstrom. So, we are not talking about roughly hundreds of molecules
of the order of that. So, this is also a surface the tip is not single molecule at the n like
a STM tip. But so, essentially you are talking about the interaction between two surfaces
and the two surfaces here of the surface of the AFM of tip and the surface of the sample
you want to scan. So, the interaction between these two at close contact proximity is governed by this potential curve. So, that is why this curve is very very important
for the atomic force microscope. So, I guess we do a quick recap on this potential curve,
we just introduced the concept of induce dipole induce dipole type interaction which is known
as the Vander Waal’s forces which is also known as the inter molecular interaction.
And we understand that this type of interaction is the most fundamental form and is available
or is present even in molecules which do not have any permanent dipole including in charge
neutral molecules. So, we understand that this interaction has it is origin in quantum
mechanical has quantum mechanical origin. It is attributed in simple words to the localization
of the electron cloud at any given instance of time, which induces a charge of opposite
polarity on the neighboring molecule. Since, the polarities are opposite therefore, the
interaction is always attractive, but no physical movement of molecules takes place because
of the attraction. Because the localization changes the position at every instance of
time and it goes on changing, that is one of the reason why it also known as the dispersion
forces. Now, this type of induce dipole induce dipole interaction is known as the lifshiftz
Vander Waal’s force. Or the Vander Waal’s force there can be
other types of interaction as well which can be the permanent dipole permanent dipole type
interaction or, the permanent dipole induce dipole type interaction, we are not going
into the details. What we agreed that this attraction between two fundamental particles
scales as one by r to the power 6 and in comparison to gravity which is m g h and therefore, at
the nano scale these forces dominated, dominate a lot. Between two surfaces so, one by r to
the power of 6 and it is sort of stretches up to roughly 10 nanometer between two surfaces
the scaling changes to one by r square which we will see how it is change.
And therefore, the decay becomes a little sluggish and the interaction sort of stretching
up to roughly 100 nanometer. We then try to understand how these potential curves looks
like, we also found out that in addition to the Vander Waal’s force. Where is very short
range electrostatic repulsion which originates because of the overlap of the electron charge
cloud. And then we introduce the concept of the Lennard-Jones potential a typically potential
which is also call the six twelve potential sometimes. This part of the this particular
term represents the representing the attraction, this term representing the repulsion and we
understand that depending on the value of r, there can three distinct regimes for very
large both the terms are 0 and that is no interaction.
For intermediate the second term may dominate over the first term and you might haven overall
you haven overall attraction. And for very small r, the first term again dominates over
the second time and we can have an effective repulsion. We also understand that this is
the point at the two surfaces of the particles coming contact and there are electron clouds
sort of starts overlapping and therefore, the repulsion starts. We have already we also
discussed that this interaction between the two surfaces is going to be very important
in understanding the interaction between the tip and the sample in an atomic force microscope. We start discussing the operation and other critical issues about an AFM from this point. Thank you. Keywords: Scanning probe Microscope, Scanning
Tunneling Microscope, Atomic Force Microscope, van der waals force.
