nanoHUB-U Nanobiosensors L2.6: Settling Time – Beating the Limits — Droplet Evaporation

nanoHUB-U Nanobiosensors L2.6: Settling Time – Beating the Limits — Droplet Evaporation


>>[Slide 1] Thank you for
joining me again. This is week two and
we’re discussing how to beat the diffusion limit. In the first week and even for
the first lecture in this week, I said that diffusion is
a fundamental process, not only for biosensing but
for organism of all sort, that the molecules must
diffuse to the sensor’s surface and on the organism’s surface. And in that case, it is often
the geometry of the structure that determines how
efficient the capture is. But no matter what you do
with the geometry, at the end, there is a certain limit
beyond which you cannot go. And so, of course,
that’s the concern. And we are finding ways to go
around that “fundamental limit.” I have already discussed one
approach based on bio-barcode, essentially throwing a lot
of policemen, putting a lot of policemen in search
of suspects. And I explained to you how that dramatically reduces
the capture time. Here’s a second approach
that we’ll be talking about. [Slide 2] And the second approach
is based on the notion of droplet evaporation. I will explain the theory and
I will tell you a little bit about how this is actually
made, how the device that does this droplet-based
measurements or sensing how they are made because I think you’ll
find it very interesting. [Slide 3] Remember, where we are in terms
of this big “Mendeleev’s table,” we have understood the
diffusion limit associated with these types of–
various types of sensors and organize them according
to how they respond. And in fact, if you take
any modern sensors and don’t do anything special,
you can immediately analyze it in terms of, in terms
of their geometry. In fact, this is the first thing
we should do anytime we have a new sensor, understand
its fundamental limits, diffusion limits. Now, I haven’t explained to you
how the bio-barcodes sensor work and today, I want to explain to you how the droplet-based
sensor works is that as I said, very elegant and beautiful. [Slide 4] So, the three approaches
that we have discussed, the one that we focused
today, right now, is this approach
based on the droplet. The key idea is this. That we’ll be beating
the diffusion limit or making the tau,
diffusion limited tau smaller by making the L, the
length or the size of the box essentially
gradually progressively smaller. This is what happens when
you concentrate something. So the molecule might be
originally sitting anywhere within this box, which
is the blue molecule. And then, if you didn’t
do anything special, the molecule will walk around
and take a long time to get to the sensor’s surface. What can happen instead, if you
allow the water to evaporate, of course, the molecule
cannot evaporate, the molecule is sort of trapped. It’s a big molecule. So, water evaporates,
the molecule doesn’t. So, it is increasingly confined
to smaller and smaller boxes until it is sort of captured
by the sensor itself. And this time dependent L, increasingly smaller
L makes tau small. So, let’s discuss that. This would describe
that approach. [Slide 5] Now, before I get there, this is
a very nice example of how sort of ideas from biology or biomimetics essentially
inspires this type of droplet based sensing. In some way, you could say, even
the diffusion limited approach that I discussed previously
in the last week and also in the beginning of this week
also has the same biomimetic approach, the analogy to
biology, diffusion limit and all allow that to
understand the sensors. And this time, the
analogy to biology, this biomimetics will also
essentially also tell us how to beat the diffusion limit. So, nature teaches us both how
to analyze and how to overcome. So here, what I wanted
to tell you. So, the analogy that
one should– droplet and everyone can
think of is this lotus leaf. You can think– we all
know that a drop of water on this lotus leaf is very
spherical, essentially it sits on the surface and any particle
that you put in here, let’s say, you put a biomolecule or
a bacteria or something, it will always be
confined by the trap, by the cage of the droplet. Now, of course, one problem of
this droplet is it moves around. So, that’s the problem. But there’s another thing that
we also see, also sort of goes with this general idea about
trapping is the coffee ring. You know, in the morning, when
you pick the coffee, coffee cup, you will often see
that after a while, an unwashed coffee cup may
actually develop a ring like this. What happened? You see, what happened was
there is a fluid like this and essentially, because
the surface was not superhydrophobic, as
the fluid evaporated, this essentially
deposited the molecules of the coffee around the ring. So somehow, if we could
marry this concept of superhydrophobic surface
or hydrophobic surface which keeps the molecule
together and once it shrinks, it sort of drops the
biomolecule in the center. And this concept of
concentration of the analyte, if we could combine them,
then we would be able to beat the diffusion limit. So, let me explain. [Slide 6] So, this is how it works. This is cartoon, let’s say, if
it were a teaspoonful full of seawater, there’d be
millions of biomolecules, millions of bacteria in here. But even if it’s a
small quantity of blood, you may have a– within this
system, you may have at a– femtomolar concentration, quite
a few copies of the biomolecule. Now, if you waited for them
to diffuse down and get to the bottom of the
sensor’s surface as you know, you’d have to wait a long time. We have discussed that already. Instead, you could
do the following. For example, if you put
this droplet on a surface and these dots are
special, I’ll come back to that in a little bit. After 10 minutes, let’s say
the diameter is something like 500 micron or the
radius is about 500 micron, now the water evaporates. It becomes little smaller,
smaller and by 35 minutes, which is half an hour,
essentially it has, the size has reduced to
five micron, let’s say. How many force have the
concentration increased do you think? Well, if this was 500 micron
and if this is 5 micron, then 4 by 3 pi r cube. So, 500 micron divided by
q divided by 5 micron q, almost as I say, million fold. So, any concentration that
you had that was let’s say, an at attomolar concentration
here, at this point, the concentration
has become picomolar. Now, classical sensors can
subtly detect a picomolar. That’s not a problem and although the original
concentration was an attomolar. So, this ability to
concentrate has given us a way to beat the diffusion limit. And in fact, once the
molecule is deposited, and this picture is taken
from this particular paper, you can image it and detect
where the molecule itself was. [Slide 7] So, how does it work? How long should I wait? You know, we want to be– I know the droplet
will evaporate quickly. But, you know, droplet of
all sizes will not work. If you make a humongous droplet, that will also take a long time
before it evaporates, right? If you have a swimming pool, it doesn’t simply evaporate
overnight and gives you the– all that residues on the bottom
of the pool the next day. So, we have to sort of have
a theory of how long it– how long it takes to evaporate– given size of droplet to see whether we’ll have
any advantage or not. So, the idea is this. Consider this droplet
of radius R, and assume that the
concentration on the surface is Cs,
concentration of the vapor. And at infinity, the
concentration is zero. As the droplet is
evaporating, the diffusion of the water molecules is
going away and it’s going away through the diffusion equation because the particles
are living. They are sort of
randomly walking around and getting lost to infinity. So, inverse problem of the
captured by a nanosphere. Here, the particles are going
away because the source is here and sink is at the infinity. Now, you could immediately get
the solution of this problem. The amount of– the amount
of water lost is dm, dt, and that must be given by the
difference in the analyte– the difference of waters
vapor concentration on the surface and at infinity. And the CD,ss, because we are
solving the diffusion equation, here comes the CD,ss again
but in a different context. And the capacitance,
equivalent– diffusion equivalent
capacitance is 2 pi Dr because it’s a sphere. So therefore, if you go back to
the formula of the capacitance for a sphere, you
will see this formula. Now the m, the amount of
mass lost is essentially lost a shell of a shell of the droplet
at a given time, delta t. So, you will write it as 4 pi r
squared Dr and that’s the amount of mass lost multiplied by
the density of water, right? That’s how much you lost and
the only unknown variable in this particular case is r
and t. And so, we can connect r with t and be done with it. And once you have done it, it
tells you how long the droplet– it will take for the droplet
to go from the initial radius of Ri, let’s say 500
micron to the final radius, which would be five
micron or even smaller. And if you will sort of neglect
this quantity with respect to this, assume the
concentration of vapor at infinite distance, infinite, meaning let’s say
100 micron, is zero. So, then it immediately
tells you that your– in order to make
it go very fast, then your initial radius
has to be relatively small. It helps if you have
a lower density because it will go faster. It helps if the water molecules, the vapor can diffuse
fast in the environment. And it helps to have a
higher– lower vaporization. But the bottom line
is this r squared. Is the reason why a pool
doesn’t evaporate overnight but a little droplet
on the order of micron squared or 100 micron
q essentially will evaporate very, very fast. And this is where
the nanotechnology of biosensing helps you to
beat the diffusion limit. Now, the cS, the called
surface concentration depends on the pressure, the temperature
and the universal gas constant and so on and so forth. But for the time being,
just let’s focus on t and r that the r has to be small in
order for the diffusion time, the concentration time to be
faster than the diffusion limit. All right. [Slide 8] So, how do you do this? How do you make such a device? You can make it relatively
easily. You can have an array
of electrodes that will create a
sensor’s surface. You see, we don’t have
lotus leaf and how would– even if you had a lotus leaf, how would you actually put
contact within the lotus leaf. So, we have to make
our own lotus leaf to beat the diffusion limit. And this is a way of making
the lotus leaf, I will– as I will explain
in a little bit. So, what is done is that you
make a series of pillars, certain electrodes and you can
electrically connect them in order to measure the
analyte concentration. And from a top view,
it looks like a coffin. So, you can see as if
somebody is lying around there but essentially, this is a
droplet, elongated droplet because the pillars are along in a particular direction,
so that elongates it. In a lotus leaf, it would be– the structure would be
symmetric making it spherical. But essentially, the
physics will essentially, generally be the same. So then therefore, if you start
with such structure like this, within a few minutes
essentially, you can evaporate the sensor’s
surface, evaporate the droplet. And while you’re evaporating
the droplet, you can measure for the analyte concentration. And that will give you the– allow you to beat
the diffusion limit. And it’s very similar
to the picture that you had seen before. Now, let me tell you
a little bit about how to create this superhydrophobic
or hydrophobic surface because that is sort of essential element
to this strategy. [Slide 9] So, if you think about a water
droplet sitting on a surface, most of the time or often, depending on the
standard surface, it may look slightly elongated. It’s not hydrophobic enough
to sort of roll up or ball up. Why not? Think about
these three systems. So you have a vapor, you
have liquid and a solid, and for the time being,
forget about this evaporation. So, we have a time independent
droplet sitting somewhere. So, how– what determines
its shape? Well, what determines its shape
is essentially at this point, at the corner, you can
essentially look what the forces are. If the forces are very
strong, then it will sort of get elongated, forces between
the solid and the liquid. If they like each other very
much, it will get elongated. If they repel each other,
then it will be sort of pushed in and it does– the droplet
will become spherical. And so therefore, you
should be looking at– we should be looking
at three surfaces. One is the top half is the
air, bottom half is the liquid, that sort of gives you the force
on this side of the interphase. In here, bottom side is
solid, top side is liquid. So in this corner, you will
have essentially balance of these two forces and on
this side, when going away, you have solid on the bottom,
vapor on the top and the balance of these two forces will
determine the net force in this particular case. So, balance of these three
forces will determine what type of shape do you actually
have for such a system. [Slide 10] Now, this is something Young
has developed a long time ago. Again, the sphere,
the hemisphere is– a sort of cut sphere is
representing the droplet. The radius r is the radius of
curvature and the angle theta, you can convince yourself that this angle theta also
defines the angle theta of the droplet with respect
to the sensor’s surface. And as you can see, bigger the
theta, more spherical the shape. The volume of a truncated sphere
is given by, in terms of theta and r, by this formula. The surface area is
given by R sin theta which gives you the radius and
pi r squared gives you the area. And the top surface area is
given by the following formula. And so, you can see the
total energy of the system. LV stands for liquid to vapor. So on the top surface, we have
liquid on the bottom and vapor on the top, so you
multiply with S, that gives you the
total surface energy. This is surface tension. And then on the bottom,
we have solid and liquid, that’s the interphase and their
spread over A. And finally, solid to vapor is
everything that is not A. So, all these areas outside,
A infinity minus A, is essentially the
energy associated with the solid to,
solid to the vapor. And therefore, if you calculate,
you know, this S depends on R and theta and you can
replace everything therefore, after you do the substitutions,
you can replace R and express G, the energy G, in
terms of theta alone. Once you know theta and once
you know the volume, right, once you know these two things, you know the total
energy of the system. Now, of course, you may say that
the theta could be variable. For a given V, I can
have all sorts oftheta. Yes, but this energy
must be minimized for the shape to be stable. And once you minimize this
energy with respect to theta, you try out different
theta in order to see where the energy is minimized, you correspondingly
get Young’s equation which relates the theta
associated with the fluid equate to the surface tension between
solid to liquid, solid to, you know, liquid
to vapor and solid to vapor using this
simple relationship. Now, in most surfaces, it
will not be superhydrophobic or hydrophobic. So therefore, our
original strategy of beating the diffusion
limit will not work. So, we need to work
a little bit harder as I’ll show you
in the next slide. [Slide 11] So, what we need to do
is that in many cases, the angle may be small
because this solid to liquid tension may be very,
very large and therefore, it can elongate,
elongate the droplet. So, this strategy is–
in the following. You can cross multiply. And then you realized
on the bottom surface, essentially there’s a
competition between solid to vapor and solid to liquid. Somehow, we have to make the
solid to vapor quantity larger in order to make
the theta larger. How do you do that? Well, what you can do is
that essentially cut holes, drill holes in the surface
and therefore, all the points that previously had solid to liquid will now
have vapor to liquid. So phi is the sort of the periodicity
associated with this. So, the solid to vapor
and solid to liquid, the original surface has been
reduced to phi, only the top wire it’s touching it, and
one minus phi has been replaced with liquid to vapor
because this is liquid and this hole has vapor in it. And so there correspondingly, the theta will rise
dramatically. And that is how you make a
superhydrophobic surface. That is the purpose of the
pillars that we talked about. [Slide 12] So very quickly then,
what you do, you put down, you create the pillars with
the right configuration so that it creates a droplet. Once you have the droplet, you have the anode
and then the cathode. So, they not only create
the superhydrophobic surface but also the sensor in between. So, you can measure
the impedance between one set anode– one
set of electrode to the next and the impedance
is plotted here. And as the droplet, as the
droplet, and you have initially, we have one droplet that
gives you a certain impedance and as the droplet
is evaporating, your impedance continues
to decrease. And from this value of the
impedance and these values as the function of
time, you can detect the analyte concentration. And in fact, if your analyte
concentration is lower then, of course, your impedance
would be a little bit lower. And– But the point is,
our impedance would be, if your analyte concentration is
higher then your impedance would be lower. But the bottom line is, using
this approach, you may be able to detect tens of attomolar
approach because this has sort of allowed you to
concentrate on a single point, thereby beating the
diffusion limit. And this actually
gives fantastic, fantastic sensitivity. [Slide 13] So, let me summarize then,
bringing us back to the old plot that the way the droplets with evaporation allows
enhancement of sensitivity is that it starts at a very
low concentration. Evaporation essentially
pushes it– pushes the concentration
at much higher value so then you can use the planar
sensor or a nanowire sensor. It doesn’t matter. In that case, you’ll have very
high sensitivity beating the diffusion limit. [Slide 14] So again, this is a summary
which sort of tells us that these approaches
essentially allows you to approach very low
concentration levels that classical diffusion
limit prevents these classical sensors, standard
nanobiosensors from reaching. [Slide 15] So let me conclude. I told you about
superhydrophobic surface. Superhydrophobic surface
simply means something is so hydrophobic that the
ball is almost rolled up so that when the biomolecule is
brought closer to the surface, they’re all drop
at a single point. Unlike the coffee
ring which sort of spreads it around. Because then, you have to
put sensors all around. Here is much better because
it will bring everything down to the point where you
really want to sense it. Now, I told you about how
droplet allows pre-concentration to beat the diffusion limit. And these type of superhydrophobic surfaces
are relatively easy to design and therefore, this type of sensors can be pretty
interesting in terms of being able to beat
the diffusion limit. So, that’s it. In this lecture, I told
you about one strategy, the second strategy of
beating the diffusion limit. In the next lecture, I
will tell you a little bit about that how there
are other approaches that beats the diffusion limit. But you may have notice that
I have not really told you how if you have a fluid
flow, flow the fluid, bring the analyte faster to
the sensor’s surface whether that can give you a significant
enhancement in sensitivity. The surprise is that it doesn’t. And I’ll explain to
you in the next slide that while it beats the
diffusion limit to some extent, there’s not dramatic
enhancement. And from that then
onward, we’ll be able to understand how the
different techniques of beating the diffusion
limit compare. So until next time. Take care.

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