[SLIDE 1] Hi we're back again trying to
finish up some of these topics related to
force versus displace measurements with an atomic force
microscope. In this particular lecture we're going to
discuss the ability for an atomic force microscope
to produce modulus and adhesion maps and I
like to run through some simple examples and
describe to you what's possible and give you
some sense of how this type of measurement
is actually made. [SLIDE 2] I think the
point to emphasize is that once the atomic
force microscope was shown to give these marvelous
images in three dimensions of samples with nanometer
resolution, it also became clear that you can
use the AFM to perform an entirely new
class of experiments. The idea is pretty simple
because since the AFM is a proximal probe
it just looks very locally or has the
capability of looking very locally at the properties
of a substrate, you imagine that if you're
doing an image scan and measuring the topography
of the substrate you see some nanoscale object
that's on the substrate. You want to learn
more about what that nanoscale object might be.
All of a sudden the AFM allows you
the possibility of asking the question, what could
be the structural properties of that particular object?
So you might might imagine being able to
position a tip above that object and executing
force versus displacement curve and then interpreting that
force versus displacement curve to infer interesting structural
properties about the nanoscale object of interest. So
this capability was very clear to a lot
of people in the very early days of
AFM and basically we're going to describe how
that whole process can be animated and then
show you some examples of that. [SLIDE 3]
So just as a way a reminder this
is the standard force versus displacement experiment, it's
summarized, it's condensed down into a full work
force snap shot of what's actually happening at
different points along the experiment. At the bottom
of the slide we're showing the final answer,
the final answer plots the loading force versus
the sample displacement, the dashed line indicates what
you would expect if the substrate were infinitely
hard. The experimental data always will lie to
the far side of that dashed line, indicating
that the tip is actually inventing or deforming.
You see the jump to contact feature that
we discussed in some detail and withdrawal you
see the feature in the force versus displacement
curve that allows you to map the adhesion
of the tip to the substrate. So this
is experimentally what your software will often display
to you. [SLIDE 4] In reality the experiment
is done in real time and so it's
useful to think about what the force the
tip experiences versus time might look like. I
illustrate that in the top region of the
panel of this view graph. This is actually
what goes on with time and of course
your software just folds everything back and gives
you a standard force versus displacement curve that's
shown in the bottom. Once you realize that
the signals that your instrument is actually acquiring,
those are time domain signals then you can
start to think about how to use that
information in a systematic way perhaps to extract
out more information than just a force versus
displacement curve performed at one point on the
sample. [SLIDE 5] So this is something that
a lot of people realized in the late
1900s, so maybe 10 years or so after
the atomic force microscope was established, various groups
around the world started to think in these
terms that I sort of sketched out on
this slide. So each feature in that force
versus displacement curve, each feature can be mapped
into a three-dimensional map which gives you information
about the sample. So for instance the loading
force, the preset loading force, that's indicated by
the solid black dot on the force versus
displacement curve. That point gives you the displacement
of the substrate that's required to achieve that
loading force, that then gives rise to a
topographic image and so for some position of
the tip on the substrate, let's say, position
i, j you can use the information that's
obtained from doing the force versus displacement curve
to give you the topographic image. Simultaneously there's
no reason why you couldn't measure, let's say,
the slope of force versus displacement curve, you
measure that slope, that slope is related to
the modulus of the sample at that particular
point. So you can imagine making a modulus
map simultaneously with the topographic map and then
also by measuring the liftoff force when the
tip is at a particular point on the
substrate. You could also imagine making an adhesion
map as the sample scan over the substrate.
[SLIDE 6] So all you have to do
to achieve this goal is to write some
software that's sufficiently flexible that allows you to
pull off of the standard force versus displacement
curve which here I plot as a function
of time. You just have to pull relevant
information off that curve in a periodic and
systematic fashion. So typically when you do an
adhesion map or a modulus map, you do
not perform it at the same resolution as
the topographic map simply because of the time
required to do this. So typically, you know
if you had to make an estimate typically
of adhesion map or a modulus map contains
something on the order of 128 x 128
pixels and to acquire an image with 128
x 128 pixel resolution that typically requires 5
to 10 minutes to complete. So that tells
you immediately that during the course of the
experiment you have to have a very stable
situation, you can't have lot of thermal drift
and requires you to warm your system up
and let everything stabilizer up if you're going
to get reliable data. [SLIDE 7] So this
is just a real simple example of something
that we were able to achieve here at
Purdue in the very early days of this
adhesion mapping and modulus mapping business. We did
some experiments on very simple samples that we
had available on the lab. Simple samples consisted
of a gold bridge that were connected by
two much larger gold contact pads. The gold
brined the gold pads were evaporated onto a
hard glass substrate and we wrote some simple
software that allowed us to measure for instance
topography and adhesion simultaneously as we scanned over
a small region of the substrate. So the
type of information we were able to obtain
are indicated in the two slides in the
far right-hand corner. The results aren't of great
interest scientifically but they demonstrate, they illustrate a
very nice capability. So we were able to
immediately identify the topographic features just from the
height histogram's of the different regions of the
sample. So we were then able to map
out average heights and we were able to
estimate from this topographic analysis the roughness of
each of the three regions of the substrate
that we were imaging simultaneously and then in
addition to that we focused on the adhesion,
the pull off force, of the tip of
the substrate. We were able to do histograms
of the pull off force in different regions
of the substrate and these histogram show very
nicely that on average the tip stuck or
adhere much more strongly to the glass than
it did to the gold. It also show
there was a slight difference between the adhesion
to a thick gold contact pad and the
adhesion to a thinner gold bridge that also
came through very nicely. [SLIDE 8] This whole
area has progressed quite a bit in the
last 12-15 years. I just like to run
through an example of sort of what I
consider state-of-the-art adhesion and modulus mapping. This is
a study that was performed at Purdue by
Ryan Wagner, a student of Arvind Raman, and
he investigated the mechanical properties of something called
cellulose nanocrystal so in this slide it's referred
to as CNC. Cellulose nanocrystal is an object
that's obtained from the pulp of a tree.
So if you decompose the wood from a
tree, you find that ultimately that wood is
comprised of these very small nano crystals. They
have diameters roughly between 5 and 50 nm,
they have different lengths and the question is,
what's the modulus of elasticity of one of
the cellulose nano crystals and how do you
go about making that measurement in a systematic
way. [SLIDE 9] So in this particular study
all the i's were dotted and all the
t's were cross that's what I'm referring to
in the course of this talk. Now just
by way of a very quick summary point
out they checked accurately the z the calibration
of their instrument by scanning a reference sample
and measuring very accurately the height difference between
the base and the top plateau of a
well-defined feature. They calibrated the spring constant of
the cantilever, using this thermal tuning method that
will be discussed more in part two of
this course. They also calibrated their spring constants,
they performed force versus displacement curves on very
stiff samples, that's also indicated and then they
also went through and made an effort to
show that the tip that they used in
the experiments was not appreciably altered by showing
very nice scanning electron microscope images of the
tip before and the tip after the modulus
maps were made. [SLIDE 10] The basic ideas
they were able to image these CNC nano
crystals that's indicated by this bright bridge on
this topographic image at different points on that,
in fact the different points over the entire
image they executed the typical sample versus force
displacement curve. The types just a representative of
the displacement curve versus voltage from the position
sensitive detector that's representative set of data shown
in the slide. Software is sophisticated enough now
that you can go in and you can
analyze each of those curves and in this
particular case I think they converted the sample
displacement in z to I think a distance,
a gap separation distance d. The data shown
here is the indentation part of the curve.
So this is showing how the tip indents
into the CNC. The CNC were infinitely hard,
of course, all this data would be a
vertical line centered at the distance equal to
zero in this plot. You can see they
were able to estimate the uncertainties in each
data point. These uncertainties are just related to
the experimental noise that contained in the individual
data points in that force versus displacement curve
shown in the upper right. [SLIDE 11] Then
at the end of the day, if you
perform this measurement you'll have an ensemble of
data points along the CNC and these ensemble
of data points can then be plotted and
you can start to get systematic, statistically significant
information about such things as, for instance, the
Young modulus. So they found that the Young's
modulus, the average value of Young's modulus for
this CNC was on the order 8 GPa.
You can see the range of variability in
their experimental data which is very nice because
now you can add an uncertainty estimate to
the average elastic modulus. By focusing on the
liftoff forces that require to remove the tip
from the CNC nano crystal, they were able
to estimate an average liftoff force, that lift
off force can then be interpreted with using
various models to get to the work that's
required to surface energy basically between the tip
and the CNC nano crystal. So they found
a number and again you can see the
spread in the data so you can actually
associated an air bar with the numbers that
they achieved. So this ability to automate this
whole process and obtain these modulus maps and
to also to obtain adhesion maps as a
function of x and y over a sample
with nanometer resolution, that's a unique feature of
the atomic force microscope and it's been widely
exploited in labs throughout the world. I just
wanted to give you an example of what
I consider a very nice study, very systematic
careful study, that's been performed. Hopefully you may
find a use for this type of measurement
in the research that you're performing. [SLIDE 12]
So the next lecture which will end of
week four of the first part of this
course, I like to just discuss lateral force
microscopy in a general way and try to
show you some of the experiments that a
lateral force microscope can perform. Give you a
little bit of background about how lateral force
microscope works. So come on back for the
next lecture, we'll have a short overview of
this type of microscopy in that lecture. So
thank you very much and see you at
the next lecture.