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10/05/2005
Gold Popping Off
Last week, we discussed shockwaves around exploding stars as a
source of cosmic rays. After posting the column, I found a
colorful picture of a shockwave around an exploded star on the
cover of the September 23 issue of Science. Science is a very
selective journal publishing papers in virtually all fields of
science. For example, that issue of Science also had a paper on
waves generated by last year’s horrific tsunami. On a vastly
smaller scale, another paper was titled “Jumping Nanodroplets”.
In this paper, A. Habenicht of the University of Konstanz in
Germany and his coauthors describe experiments on tiny gold
droplets jumping off surfaces. Offhand, jumping gold droplets
sounds like a frivolous subject. However, Habenicht et al. point
out that the behavior of small droplets on a surface is very
important in certain applications. For example, most of us use
inkjet printers that squirt tiny droplets of ink at the paper. Those
little droplets had better not bounce off the paper if we want a
printed copy of our file.
Similarly, when we spray trees or plants to ward off insects or
disease we want those small droplets in the spray to stick to the
leaves of the plant. On the other hand, I’ve seen reports that self-
cleaning windows may be in our future. If you have a self-
cleaning window, you want any water droplets or other particles
that land on the window to bounce or roll off. My VW Jetta
should have such windows – too often do I hop in only to find a
passing bird has left its calling card on my windshield!
To set the stage for the jumping droplets, let’s talk about energy.
A moving droplet has a kinetic energy, energy due to motion,
given by a simple formula, times the mass of the droplet times
its velocity squared. (You might notice that, except for the ,
this formula is very similar to Einstein’s energy equals mass
times the velocity of light squared. This is the energy that would
be released if the droplet were completely transformed into
energy.) There’s another kind of energy we should consider here
surface energy. A liquid droplet wants to be a spherical ball –
that gives the least surface area. It takes energy to deform a
spherical droplet, say into a flat floppy pancake with more
surface area. If the liquid pulls itself together in a ball, it releases
that surface energy expended to flatten it.
If you’re uncomfortable with the concept of energy in a
deformed droplet, consider a rubber band. If you deform it by
stretching it, you put kinetic energy into the stretching. The
stretched band has more energy. If you let go of the rubber band,
that deformation energy is converted to kinetic energy in the
moving band and that kinetic energy can sting if the band hits
your skin as it returns to its normal state.
Another factor affects what happens when a droplet lands on a
surface. If the liquid wets the surface, the droplet tends to spread
out and not reform as a droplet. Those avian calling cards on my
windshield seem to be in this category. If the droplet doesn’t wet
the surface it lands on, then it will tend to ball up again and may
bounce off. It’s the nonwetting case of concern in the Science
article. When a droplet hits a surface its kinetic energy is used in
deforming the droplet. The kinetic energy becomes surface
energy. If the droplet pulls itself together again into a spherical
shape, that excess surface energy becomes kinetic energy again
and the droplet pops off the surface.
The German workers concentrated on the second half of the hit-
bounce of a droplet. They looked at what happens when you
start with deformed droplets on a surface and they become
spherical droplets. Would the surface energy in the deformed
droplets really change into kinetic energy and cause the droplets
to jump off the surface? The researchers used a form of graphite
called pyrolytic graphite as their material on which to study
droplets of gold. Unlike the graphite in your pencil, pyrolytic
graphite is quite hard and smooth, and isn’t wet by molten gold
to any appreciable extent.
They evaporated patterns of solid gold in the form of tiny
triangular shaped deposits on the graphite. The amount of gold
in each triangle was enough to form a droplet of around 200
nanometers in diameter. (Remember, nano means billionths – a
nanometer is a billionth of a meter, which is about 3 inches
longer than a yard. For comparison, I measured a hair on my
arm with my calipers as between 25 and 40 thousand nanometers
in diameter. It would take over a hundred of those nanodroplets
side by side to equal the width of that hair.)
Now, how to melt the gold triangles? Habenicht and crew
zapped the sample with very short 10-nanosecond pulses from a
laser. The intensity in the laser beam varied across the beam so
that some of the triangles were heated more than others. As a
result, after pulsing, some of the triangles were unchanged;
others were partially melted and starting to pull together to form
spherical droplets. In the areas covered by the more intense
portions of the laser beam there was nothing – gold droplets had
formed and jumped off the pyrolytic graphite.
The researchers concluded that the surface energy of the
misshapen droplets forming from the triangular deposits did
indeed convert to kinetic energy and spur the jumping droplets.
A skeptic might say, “Hey, you’re zapping these droplets with a
laser beam. Doesn’t that supply the energy to knock off the
droplets?” That sounds like a plausible argument but the
German workers didn’t just look at the samples after pulsing
with the laser beam. They actually measured how fast the
jumping droplets were moving!
To do this, they deposited the gold triangles on glass instead of
the graphite. This allowed them to shine the laser through the
glass onto the bottoms of the gold triangles. The experiment
reminded me of popping popcorn in a pan. Nothing happens
until the temperature reaches the popping point, when the kernels
pop and jump off the bottom of the pan. That’s what happens
with the gold droplets. When the intensity of the laser beam
reaches a critical value, gold droplets ball up and pop off the
glass at a speed of roughly 60 feet a second. Increase the beam
intensity and the gold droplets keep popping off at the same
speed. This supports the conclusion that the laser just melts the
gold and doesn’t supply the energy to pop the droplets. Not until
the intensity is several times that critical value do the droplets
move significantly faster, at temperatures estimated to be near or
at the boiling point of gold.
How did they measure the speed of these teensy droplets? When
the gold droplets jump off the top of the glass, they pop up into a
thin sheet of laser light from another laser a few millimeters
above the glass. The droplets scatter that light. By measuring the
scattering, the researchers can calculate a distribution of particle
velocities. Most of the droplets are jumping off the glass at
about the 60 feet a second velocity.
One final point. I’ve implied that all the kinetic energy converts
to surface energy and vice versa. Actually, energy conversion
processes are generally far from 100 percent efficient; otherwise,
your SUVs would run a lot longer between visits to the gas
station. The German workers also made theoretical calculations
and ran a few experiments varying the size of the gold droplets.
As expected, heavier droplets didn’t fly off as fast as lighter
droplets. Comparing experiment and theory, they concluded
only about 20 percent of the surface energy was converted to
kinetic energy, still enough to make those droplets jump.
Allen F. Bortrum
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