Engineers from MIT and Penn State University have found that plain clear water droplets on a transparent surface under the right conditions can produce brilliant colors without the addition of ink or dyes.
In a paper published today in Nature the team reports that a surface covered by a fine mist of transparent drops and lit by a single lamp should produce a clear color if each small drop is just great.
This iridescent effect is due to "Structure color", whereby an object generates color simply because of the way the light interacts with its geometric structure. The effect can explain some irritating phenomena, such as the colorful condensation on a plastic bowl or in a water bottle.
The researchers have developed a model that predicts the color a drop will produce, given specific structural and optical conditions. The model can be used as a design guide for producing eg. Drop-based litmus samples or color-changing powders and in-product ink.
"Synthetic dyes used in consumer products to create bright colors may not be as healthy as they should be," says Mathias Kolle, assistant professor of mechanical engineering at MIT. "As some of these dyes are more regulated, companies ask, can we use structural colors to replace potentially unhealthy dyes? Thanks to the careful observations of Amy Goodling and Lauren Zarzar at Penn State and Sara & # 39; s modeling that brought this effect and its physical explanation to illuminate, there could be an answer. "
Sara Nagelberg of MIT together with lead author Goodling, Zarzar and others from Penn State, are Kolle's co-authors on the paper.
Follow the rainbow
Last year, Zarzar and Goodling studied transparent drop emulsions made from a mixture of oils of different density. They observed the drops' interactions in a clear petri dish when they noticed that the drops appeared surprisingly blue. They took a picture and sent it to Kolle with a question: Why is there color here?
Cole first believed that the color was due to the effect that causes the rainbow, where sunlight is diverted by rainfall and individual colors are separated in different directions. In physics, the Mie scatter theory is used to describe the way in which balls such as raindrops scatter a plane of electromagnetic waves, such as incoming sunlight. But the drops that Zarzar and Goodling observed were not spheres, but rather hemispheres or domes on a flat surface.
"Initially, we followed this rainbow-inducing effect," says Nagelberg, who led the modeling effort to try to explain the effect. "But it turned out to be something completely different."
She noted that the team's hemispherical drops broke symmetry, which means they were not perfect bullets – a seemingly obvious fact, but nevertheless an important one, as it meant that the light had to behave differently in hemispheres versus bullets. Specifically, the concave surface of a hemisphere provides an optical effect that is not possible in perfect spheres: total internal reflection or TIR. Total internal reflection is a phenomenon in which light strikes an interface between a high refractive index medium (water, for example) for a lower refractive index medium (such as air) at a high angle so that 100 percent of that light is reflected. This is the power that allows optical fibers to carry light in miles of low loss. When the light enters a single drop, it is reflected by the TIR along its concave interface.
In fact, once the light enters a drop, Nagelberg found that it can take different paths, jump two, three or more times before exciting at a different angle. The way that light rays occupy when they finish determines whether a drop will produce color or not.
For example, two white light rays, containing all visible wavelengths of light, at the same angle and leaving at the same angle, could take completely different paths within a drop. If a beam jumps three times, it has a longer path than a beam that jumps twice, so it lies slightly backwards before leaving the drop. If this phase delay results in the two beam waves being in phase (which means that the trough and cam of the waves are adjusted), the color corresponding to this wavelength will be visible. This interference effect, which ultimately produces color in otherwise clear drops, is much stronger in small than large droplets.
"When there is interference, it is as if children are making waves in a pool," Kolle says. "If they do what they want, there is no constructive effort and just a lot of mess in the pool or random wave patterns. But if they all push and pull together, you get a big wave. That's the same here: if you get waves in phase out, you get more color intensity. "
A carpet of color
The color that drops produces also depends on structural conditions, such as the size and curvature of the drops along with the droplet refractive index .
Nagelberg incorporated all of these parameters into a mathematical model to predict the colors that droplets would produce under certain structural and optical conditions. Zarzar and Goodling then tested the model's predictions against the actual drops they produced in the laboratory.
First, the team optimized their initial experiment, creating drop emulsions, the sizes that they could accurately control using a microfluidic device. They presented, as Kolle describes, a "blanket" of drops of the same size, in a clear petri dish, which they illuminated with a single solid white light. They then recorded the drops with a camera circling around the dish, observing that the drops exhibited brilliant colors that changed when the camera circled. This showed how the angle at which light is seen entering the drop affects the color of the drop.
The team also produced drops of various sizes on a single film and observed that from a single viewpoint, the color would change rescues as the droplet size rose, and then reverted to blue and cycled through again. This makes sense according to the model, as larger droplets would provide more space for jumping, creating longer paths and larger phase layers.
To demonstrate the importance of curvature in a droplet color, the team produced condensation on a transparent film treated with a hydrophobic (water repellent) solution, where the droplets formed an elephant's shape. The hydrophobic parts created more concave droplets while the rest of the film created lower droplets. Light could easily jump around in the concave drops compared to the low drops. The result was a very colorful elephant pattern against a black background.
In addition to liquid droplets, the researchers wrote 3-D printed small, fixed caps and domes from various transparent polymer-based materials and observed a similar colorful effect in these solid particles, it can be predicted by the team's model.
Kolle expects that the model can be used to design drops and particles for a variety of color-changing applications.
"There is a complex parameter room you can play with," says the colleague "You can tailor a droplet's size, morphology and observation conditions to create the color you want."
This research was partially supported by the National Science Foundation and the US Army Research Office through the Institute for Soldier Nanotechnologies at MIT.