Tikalon Blog by Dev Gualtieri

Whiter Whites

September 5, 2014

Some people prefer to see the world as black and white , but the reality is that nothing is that certain. Scientifically, pure black and pure white are technologically useful, but they are difficult to obtain. I wrote about various aspects of white and black in some previous articles (Thin and Black, August 2, 2013, Paint it Black, February 13, 2013, Very White and Very Black, November 23, 2011, and White Roofs, March 19, 2012).

One measure of the whiteness of an object is its diffuse reflectivity , known also as albedo (from the Latin, alba, "white"). Albedo is the ratio of reflected to incident light, but it's defined at each wavelength of light. What this means is that something that's black at visible wavelengths might be white at other wavelengths. The purest white has an albedo of one, and the purest black has an albedo of zero.

Uncooked, polished, white jasmine rice from Thailand.

The characteristic aroma of white jasmine rice comes from 2-Acetyl-1-pyrroline (C₆H₉NO).

(Photograph by Takeaway, via Wikimedia Commons.)

The natural world has a wide range of albedo. The expression, "pure as the driven snow ," is a misnomer, since fresh snow has an albedo of only 0.85. Fresh asphalt , however, is fairly close to pure black, having an albedo of just 0.02. The albedo of the Moon is about 0.135.

Two technologically useful white materials are barium sulfate , which has an albedo of better than 97% at visible wavelengths, and Teflon (PTFE), with an albedo better than 98%. Coatings of these materials are used as diffuse reflectors on the inside surface of integrating spheres for photometric and radiometric measurements.

Obtaining a good black poses a problem, since the surface of any material with a refractive index n different from air (n=1) will necessarily reflect light according to the reflectance equation,

where n₁ and n₂ are the refractive indices of air and your material (in any order). Glass, for example, gives a reflectance R of about 4% at normal incidence, so a black glass is still just 96% black.

The solution to the reflectance problem is to have a textured surface in which incident light is multiply scattered from low reflectance surfaces before it's returned. One black material that incorporates texture to produce a better black is black gold, which is formed when gold is evaporated under an argon or nitrogen pressure of about 750 millitorr . Under these conditions, the gold atoms cool and cluster before attaching to a substrate, forming a black layer.[1-2] The process works for other metals, as well.[3]

Before the discovery of graphene, carbon nanotubes were the darlings of materials science, and these offer a means of building highly textured black surfaces. Scientists from Rensselaer Polytechnic Institute grew arrays of vertically aligned carbon nanotubes to create a super-black material that reflected just 99.955% of incident light at visible wavelengths.[4-5] Japanese scientists created similar arrays in 2009 to produce a broadband black absorber operable from 0.2 - 200 μm.[6] Similar research has been pursued by NASA.[7]

As you look at the world around you, there are a few things, such as some flower petals, that are colored white. One unusual example of a natural white is the coloring of the Cyphochilus beetle, sometimes called the "ghost beetle." The high albedo of this genus of beetle arises from the texture of its scales. The properties of these scales has been elucidated by an international team of scientists from the Università di Firenze (Firenze, Italy), Harvard University (Cambridge, Massachusetts), the Massachusetts Institute of Technology (Cambridge, Massachusetts), Exeter University (Exeter, UK), and Cambridge University (Cambridge, UK).[8-9]

Cyphochilus beetle. (left image and right image by Lorenzo Cortese and Silvia Vignolini, licensed under the Creative Commons Attribution 4.0 International License.)

A white surface will arise from random scattering centers of high refractive index in a thick layer.[8] These scattering centers must reflect all wavelengths of light equally, at least in the visible light spectrum.[9] The Cyphochilus beetles appear white because of an anisotropic network of chitin filaments that comprise their scales.[9]

These chitin filaments are extremely thin, too thin to reflect light very well on their own. In the beetle scales, however, their tight packing allows an efficient scattering of light, and the anisotropy of the packing produces the white color.[8-9] The multiple scattering has the lowest transport mean free path of any low-refractive-index system discovered to date.[8]

Scanning electron micrograph of the cross-section of the scales of the Cyphochilus beetle.

(Fig. 1b of ref. 8, licensed under the Creative Commons Attribution 4.0 International License.[8])

Says research team leader, Silvia Vignolini, of the Cavendish Laboratory,

"Current technology is not able to produce a coating as white as these beetles can in such a thin layer... In order to survive, these beetles need to optimize their optical response but this comes with the strong constraint of using as little material as possible in order to save energy and to keep the scales light enough in order to fly. Curiously, these beetles succeed in this task using chitin, which has a relatively low refractive index."[9]

A random collection of scattering centers by themselves wouldn't give rise to such an intense white as with the chitin material. It's the particular arrangement of the filaments that allows this, and this high-brightness white comes from a material with a low mass per unit area.[8-9] The artificial production of such structures would have many applications, such as making whiter paper, plastics and paints.[8] Says Vignolini,

"The lessons we are learning from these beetles is two-fold... On one hand, we now know how to look to improve scattering strength of a given structure by varying its geometry. On the other hand the use of strongly scattering materials, such as the particles commonly used for white paint, is not mandatory to achieve an ultra-white coating."[8]

The research was funded by the European Research Council and the Biotechnology and Biological Sciences Research Council.[8]

Whiter Whites

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