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Slide 1
Motion of a Single Colloidal Particle
Levitated above an Electrode in an A/C Field
Jeffrey A. Fagan, Paul J. Sides and Dennis C. Prieve
Center for Complex Fluids Engineering and
Department of Chemical Engineering
Carnegie Mellon University
Pittsburgh, Pennsylvania 15213
Carnegie Mellon
1
ELKIN 2004
During the last tens years, a number of groups around the world have been trying to understand
the self-assembly of 2D colloidal crystals on the surface of electrodes. Thanks to John Anderson’s
group, I think we do now understand the mechanism in dc electric fields: electroomotic flow
around the particle. But particles have been observed by many groups to aggregate in a/c fields. In
a/c fields the mechanism is more subtle.
Today I am going to show you experiments on the normal motion of single particles near a/c
electrodes. I think normal motion is relevant to self-assembly because the same electroosmotic
flows cause both normal and lateral motion of particles on the electrode surface.
20-minute talk presented in the session on “Electrokinetic Self-Assembly” at the International
Electrokinetics Conference, Pittsburgh, PA, June 14, 2004.
1
Slide 2
Instantaneous Elevation h(t) Monitored by
Scattering of Evanescent Waves
Prieve & Walz, Applied Optics 32, 1629 (1993)
schematic of side view
I (h) = I 0 e −βh
top view through microscope
where β =
4π
λ
bns sin θg2 − n 2f
typical β-1 = 100 nm (∆h = 1 nm produces ∆I = 1 %)
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ELKIN 2004
To monitor the normal motion of the particles we use TIRM which looks at the scattering of a
single microscopic particle when it is illuminated by an evanescent wave. Owing to the
exponential decay in intensity of evanescent wave itself as we move away from the interface, the
scattering also decays exponentially with elevation. Because of this exponential sensitivity, a very
small change in h produces a measureable change in intensity. We can detect changes in h of the
order of 1 nm.
20-minute talk presented in the session on “Electrokinetic Self-Assembly” at the International
Electrokinetics Conference, Pittsburgh, PA, June 14, 2004.
7
Slide 3
The Experiment
Glass
Indium-Tin Oxide
NaHCO3 or KOH sol'n
< 12 Vac
~
PS latex bead
6 µm
1.34 mm
Indium-Tin Oxide
Glass
3
ELKIN 2004
Like those of many other groups, we employ a flow cell constructed of two parallel-plate
electrodes sandwiching about 1 mm of fluid containing the particle to be studied. We look down
through the upper electrode and observe the response of the particle located near the bottom
electrode.
20-minute talk presented in the session on “Electrokinetic Self-Assembly” at the International
Electrokinetics Conference, Pittsburgh, PA, June 14, 2004.
Slide 4
Movie of TIRM Experiment
Two 6 µm PS beads in 0.13 mM KOH over ITO Electrode
4
ELKIN 2004
Here you see two 6-micron PS particles levitated above a transparent electrode. The bright spot
at the top of each particle is the light scattered from the evanescent wave. Those are interferences
fringes running perpendicular to the line connecting the centers of the two spheres.
Once this video clip starts, you will see about 15 seconds of Brownian motion of these particles
with no voltage applied to the electrode. Then you will see what happens when a 10 Hz a/c voltage
is applied. The bright spots will blink about 10 times per second as the particles rise and fall above
the electrode under the action of the electric field. You will also see the particles slowly drift
apart. This demonstrates that an a/c electric field applied normal to the electrode also causes
adjacent particles to drift laterally. It is the mechanism of this lateral motion which motivates this
study.
All the remaining results I will show are obtained for a single sphere.
20-minute talk presented in the session on “Electrokinetic Self-Assembly” at the International
Electrokinetics Conference, Pittsburgh, PA, June 14, 2004.
Slide 5
Brownian Fluctuations (no Field)
6 µm PS bead in 0.13 mM KOH over ITO Electrode
400
Elevation (nm)
350
300
250
200
150
100
0
1000
2000
3000
Time (ms)
5
ELKIN 2004
Here are some sample observations of elevation fluctuations caused purely by random Brownian
motion normal to the electrode. We can record the elevation at 1 millisecond intervals.
20-minute talk presented in the session on “Electrokinetic Self-Assembly” at the International
Electrokinetics Conference, Pittsburgh, PA, June 14, 2004.
Slide 6
Brownian Fluctuations After A/C Field Starts
6 µm PS bead in 0.13 mM KOH over ITO Electrode (3 V, 100 Hz)
300
250
200
300
150
100
250
Elevation (nm)
50
0
200
0
10
20
30
40
50
60
70
80
90 100
150
Average (no field)
Average with a/c field
100
50
0
0
1000
2000
8000
Time (ms)
6
ELKIN 2004
Here are results under very similar conditions immediately after the start of applying 3 volts
peak-to-peak at 100 Hz. The insert shows that the particle oscillates up and down in elevation at
the same 100 Hz frequency in response to the oscillating electric field.
During the first second the particles drifts downward to reach a new stationary position closer to
the electrode.
20-minute talk presented in the session on “Electrokinetic Self-Assembly” at the International
Electrokinetics Conference, Pittsburgh, PA, June 14, 2004.
Slide 7
Effect of Amplitude on Mean Elevation
6 µm PS bead in 0.13 mM KOH over ITO Electrode (100 Hz)
Mean Elevation (normalized)
1.4
1.2
1.0
0.8
0.6
KOH
0.4
0.2
0.0
0
2
4
6
8
10
12
Applied Voltage (peak to peak)
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ELKIN 2004
This slide summarizes a number of experiments like this in which the amplitude of the voltage
was systematically varied. These elevations have been normalized by the no-field average. Notice
that the mean elevation goes through a minimum with the amplitude of the a/c voltage.
20-minute talk presented in the session on “Electrokinetic Self-Assembly” at the International
Electrokinetics Conference, Pittsburgh, PA, June 14, 2004.
Slide 8
Response Depends on Electrolyte
4.6 or 6.2 µm PS beads in 0.13 mM over ITO Electrode (100 Hz)
Mean Elevation (normalized)
1.4
1.2
1.0
0.8
0.6
0.4
KOH (6.2 µm)
NaHCO3 (6.2 µm)
0.2
HNO3 (4.6 µm)
simulation
0.0
0
2
4
6
8
10
12
14
Applied Voltage (peak to peak)
8
ELKIN 2004
This slide summarizes two more series of similar experiments in which the electrolyte KOH was
replaced by sodium bicarbonate or nitric acid. Instead of dropping to a minimum as the amplitude
is increased, the mean elevation increases monotonically in bicarbonate. Of course, the zeta
potential of the surfaces does depend on the pH, which is quite different in these 3 electrolytes;
however all 3 cases correspond to like charge on the two surfaces. Nonetheless we see opposite
trends in the electrolytes.
20-minute talk presented in the session on “Electrokinetic Self-Assembly” at the International
Electrokinetics Conference, Pittsburgh, PA, June 14, 2004.
Slide 9
Connection between Normal Motion and
Aggregation: Electroomotic Flow
z
Downward Flow → Decreases Elevation → Disaggregation
z
Upward Flow → Increases Elevation → Aggregation
9
ELKIN 2004
We saw a pair of particles move apart in KOH; similar studies with bicarbonate show pairs
moving together. This opposite behavior is also seen in the normal motion of single particles.
There is a simple explanation for the strong correlation between normal motion of a single particle
and the lateral motion of pairs: the same electroomotic flow causes both.
The advantages of studying single particle behavior is 1) we can follow the motion in far greater
detail and 2) the motion of a sphere normal to a plate is axisymmetric, meaning that mathematical
models are 2D. In contrast, the lateral motion of pairs of particles is inherently a 3D problem.
20-minute talk presented in the session on “Electrokinetic Self-Assembly” at the International
Electrokinetics Conference, Pittsburgh, PA, June 14, 2004.
Slide 10
Effect of Frequency on Mean Elevation
Mean Elevation (normalized)
4.6 or 6.2 µm PS bead in 0.13 mM over ITO Electrode (5 Vpp)
1.4
1.2
1.0
0.8
0.6
KOH (6.2 µm)
NaHCO3 (6.2 µm)
HNO3 (4.6 µm)
simulation
0.4
0.2
0.0
101
102
103
104
Frequency (Hz)
10
ELKIN 2004
There are even more striking differences in behavior with electrolyte choice when frequency is
varied rather than amplitude. In KOH the particle is drawn closer to the electrode at virtually all
frequencies and in bicarbonate the particle is pushed away at all frequencies.
In nitric acid, a reversal is observed at a moderate frequency. Unfortunately, we do not yet have
the corresponding aggregation behavior.
Notice that at very high frequencies, all of the electrolytes show the particle tending to the nofield elevation.
20-minute talk presented in the session on “Electrokinetic Self-Assembly” at the International
Electrokinetics Conference, Pittsburgh, PA, June 14, 2004.
Slide 11
Brownian Motion Dominates at High Frequency
6 µm PS bead in 0.13 mM KOH over ITO Electrode (5 Vpp)
no field
(stochastic)
400 Hz
(more deterministic)
2,000 Hz
(stochastic again)
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ELKIN 2004
At high frequencies, the normal motion of the particle appears to become stochastic again. This
slide compares trajectories measured with no field, moderate frequency and high frequency.
At moderate frequencies, the particle is moving up and down in a deterministic fashion,
producing a trajectory which looks very different from the other two trajectories on this slide. Of
course, this is because the motion of the particle at moderate frequencies is primary the up and
down deterministic oscillations.
By contrast, at high frequencies, the motion appears to be primarily stochastic again. If it is
indeed stochastic, we ought to be able to apply the same analysis technique to measure interaction
forces which we have applied in the absence of any electric field.
20-minute talk presented in the session on “Electrokinetic Self-Assembly” at the International
Electrokinetics Conference, Pittsburgh, PA, June 14, 2004.
Slide 12
Analysis of Stochastic Fluctuations in Elevation
4.6 µm PS bead in 0.13 mM HNO3 over ITO Electrode
1.8
700
1.6
Probability Density
800
Elevation (nm)
600
500
400
300
200
100
1.4
1.2
1.0
0.8
0.6
0.4
0.2
0.0
0
0
5
10
15
20
25
30
6 0
Time (min)
p ( h ) = Ae −φ( h ) kT
200
300
400
500
600
κ = 26.5
nm (nm)
Elevation
(IS = 0.13 mM)
-1
Potential Energy (kT)
Boltzmann's Eqn
100
5
4
3
hm = 170 nm
2
<ψ> = 5.6 mV
1
0.045 pN
(PS diameter = 5.4 µm)
0
0
100
200
300
400
500
600
Elevation (nm)
12
ELKIN 2004
For purely stochastic motion, we deduce the PE profile by applying Boltzmann’s equation to the
histogram of elevations measured over a long period of time.
In this case, that leads to a linear increase in potential energy with elevation at large elevations.
The slope of that line is the net weight of the particle, which is small fraction of a piconewton in
these experiments.
We will now apply the same analysis to the fluctuations in elevation observed at 10 kHz.
20-minute talk presented in the session on “Electrokinetic Self-Assembly” at the International
Electrokinetics Conference, Pittsburgh, PA, June 14, 2004.
Slide 13
A/C Field Causes Particle to Get Lighter in HNO3
4.6 µm PS bead in 0.13 mM HNO3 over ITO Electrode (10 kHz)
6
Potential Energy (kT)
5
4
0000 V/m
4132
6198
7438
3
E
2
1
0
0
100
200
300
400
500
600
700
800
900
Absolute Height (nm)
13
ELKIN 2004
The slope of the linear portion of the profile is decreased, suggesting that an upward forces is
being exerted on the particle by the a/c field. From the amount of decrease in slope, we can infer
that upward force.
20-minute talk presented in the session on “Electrokinetic Self-Assembly” at the International
Electrokinetics Conference, Pittsburgh, PA, June 14, 2004.
Slide 14
Force is Nonlinear in E
0.15mM KOH, 10kHz
KOH
(attractive)
Force (pN)
0.1
HNO3
(repulsive)
1.78
0.01
1.68
1
10
Electric Field (kV/m)
14
ELKIN 2004
Here you see the force exerted as a function of the applied field strength. It is repulsion in nitric
acid and attractive in KOH. In either case, the dependence on field strength obeys a power law
with an exponent slightly less than 2.
20-minute talk presented in the session on “Electrokinetic Self-Assembly” at the International
Electrokinetics Conference, Pittsburgh, PA, June 14, 2004.
Slide 15
Conclusions
z
Added new dimension (z) to video microscopy (x,y) study of
self-assembly
¾ normal motion of single sphere is axisymmetric (2D)
¾ lateral motion of pairs is 3D
z
Normal motion of single particle correlates with lateral
aggregation of 2D ensemble (at least at low frequencies)
¾ KOH: decreased elevation and disaggregation of pairs
¾ NaHCO3: increased elevation and aggregation of pairs
z
Strong dependence on electrolyte
¾ KOH, NaHCO3 and HNO3 show very different trends with frequency
and amplitude of E
z
More than one E2 force is suggested
¾ low frequency → current is primarily Faradaic
¾ high frequency → current is primarily capacitive (non-Faradaic)
for the rest of the story ...
see poster #38 by Jeff Fagan, 6:00pm today
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ELKIN 2004
20-minute talk presented in the session on “Electrokinetic Self-Assembly” at the International
Electrokinetics Conference, Pittsburgh, PA, June 14, 2004.