MIT and Penn State University engineers have found that, under good conditions, droplets of clear water on a transparent surface can produce brilliant colors, without the addition of inks or dyes.
In an article published today in Nature, the team reports that a surface covered with a thin cloud of transparent droplets and lit by a single lamp should produce a bright color if each small droplet is exactly the same size.
This iridescent effect is due to the "structural color" through which an object generates color simply because of the way the light interacts with its geometric structure. The effect may explain some iridescent phenomena, such as colored condensation on a plastic dish or inside a bottle of water.
Researchers have developed a model that predicts the color that a droplet will produce, depending on specific structural and optical conditions. The model could serve as a design guide for producing, for example, droplet-based tests or powders and color-changing inks in make-up products.
"The synthetic dyes used in consumer products to create bright colors may not be as healthy as they should be," says Mathias Kolle, an assistant professor of mechanical engineering at MIT. "While some of these dyes are more heavily regulated, companies ask, can we use structural colors to replace potentially unhealthy dyes? Thanks to Amy Goodling and Lauren Zarzar's careful observations at Penn State and Sara's model, which shed light on this effect and its physical explanation, there may be an answer. "
Sara Nagelberg of MIT, along with leading authors Goodling, Zarzar and others of Penn State, are co-authors of Kolle on the newspaper.
Follow the rainbow
Last year, Zarzar and Goodling studied transparent droplet emulsions made from a mixture of oils of different densities. They observed droplet interactions in a transparent petri dish, when they noticed that the drops looked surprisingly blue. They took a picture and sent it to Kolle with a question: why is there color here?
Initially, Kolle thought that the color could be due to the effect of rainbows, in which sunlight is redirected by raindrops and individual colors separated in different directions. In physics, the Mie scattering theory is used to describe how spheres such as raindrops scatter a plane of electromagnetic waves, such as incoming sunlight. But the droplets observed by Zarzar and Goodling were not spheres, but rather hemispheres or domes on a flat surface.
"At first we followed this effect causing a rainbow," says Nagelberg, who led the modeling efforts to try to explain this effect. "But it turned out to be something very different."
She noted that the team's hemispherical droplets broke symmetry, which meant that they were not perfect spheres – an apparently obvious but nevertheless important fact, as it meant that the light should behave differently than one hemisphere to the other. Specifically, the concave surface of a hemisphere allows for an impossible optical effect in the 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 (eg water) and a lower refractive index medium (such as air) at a high angle, so that 100% of this light is reflected. This is the effect that allows optical fibers to carry light for miles with little loss. When light enters a single drop, it is reflected by TIR along its concave interface.
In fact, once the light enters a droplet, Nagelberg found that it could take different paths, bouncing two, three or more times before going out from another angle. The way in which light rays add up at their output determines whether a droplet will produce color or not.
For example, two rays of white light, containing all the visible wavelengths of light, entering at the same angle and exiting at the same angle, could follow entirely different paths in a droplet. If a ray bounces three times, its path is longer than a radius that bounces twice, so that it is slightly backward before exiting the droplet. If this phase shift causes the waves of the two rays to be in phase (i.e., the troughs and peaks of the waves are aligned), the color corresponding to this wavelength will be visible. This interfering effect, which ultimately produces color in otherwise clear droplets, is much stronger in small droplets than large ones.
"In case of interference, it's like children are making waves in a pool," says Kolle. "If they do what they want, there is no constructive addition work, but a lot of damage in the pool or random waves. But if they grow and shoot together, you get a big wave. It's the same here: if you have live waves coming out, you get more color intensity. "
A carpet of color
The color produced by the droplets also depends on the structural conditions, such as the size and curvature of the droplets, as well as the refractive indices thereof.
Nagelberg incorporated all these parameters into a mathematical model to predict the colors that the droplets would produce under certain structural and optical conditions. Zarzar and Goodling then tested the model's predictions against the droplets they produced in the lab.
First, the team optimized its initial experience by creating droplet emulsions, whose size it could accurately control with the help of a microfluidic device. As Kolle describes it, they produced a "carpet" of droplets of the same size, in a transparent Petri dish, which they illuminated with a single fixed white light. They then recorded the droplets with a camera that circled the dish and observed that they had brilliant colors moving as the camera rotated. This showed how the angle at which light enters the droplet affects the color of the droplet.
The team also produced droplets of different sizes on a single film and observed that from one direction the color became redder as the size of the droplets increased and then returned to blue. This makes sense depending on the model, as large droplets would give the light more space to bounce, creating longer paths and longer phase delays.
To demonstrate the importance of the curvature in the color of a droplet, the team produced a condensation of water on a transparent film treated with a hydrophobic solution (water repellent), the droplets having the shape of an elephant. The hydrophobic parts created more concave droplets, while the rest of the film created less deep droplets. The light could more easily bounce into the concave droplets than the shallow droplets. The result was a very colorful elephant pattern on a black background.
In addition to the droplets of liquid, researchers have 3D printed tiny solid plugs and domes in various transparent polymer-based materials, and observed a colored effect similar to these solid particles, which could be predicted by the model of # 39; team.
Kolle expects the model to be able to be used to design droplets and particles for a range of applications that change color.
"There is a complex set of parameters with which to play," says Kolle. "You can customize the size, morphology and viewing conditions of a droplet to create the desired color."
This research was funded in part by the National Science Foundation and the US Army Research Bureau through the Institute of Military Nanotechnology at MIT.