# Staying cool this summer

Many green energy solutions originate as condensed matter physics problems. Prominent examples include electricity production via solar cells, brighter and more efficient lighting via LEDs, and thermoelectric materials for converting waste heat into electricity.  Another promising but less well-known approach is using metamaterials for passive—no power input required– daytime radiative cooling.  This may one day supplement or replace air conditioners or be incorporated in clothing.  Just what we need with summer upon us.

A recent Science paper illustrated how a species of ants in the Sahara Desert uses special triangular hairs on the top part of its body to cool themselves in the middle of the day in temperatures up to 158° F [1].  This work was also highlighted in a New York Times article.

Left: SEM image of Sahara silver ant head.
Right: SEM image of ant hairs. Notice that they are corrugated on the top surfaces, have a triangular cross-section, and are of different sizes. From Ref. [1].

The engineering requirements for daytime radiative cooling are high reflectivity at visible wavelengths, where the solar spectrum is peaked, and high-emissivity (corresponding to low reflectivity, aka high absorptivity) at mid-infrared wavelengths, where the blackbody spectrum of a human or a hot building are peaked (~9 microns).  This originates from Kirchhoff’s law of thermal radiation, which states that the absorptivity ($\alpha_\lambda$) and emissivity ($\epsilon_\lambda$) must be equal at a given wavelength ($\lambda$) in order to maintain equilibrium.  However, the overall absorption and emission is weighted by the solar spectrum ($I_{\lambda,sun}$) and the blackbody spectrum of the hot body ($I_{\lambda,body}$), respectively.

Total absorptivity: $\alpha =\frac{ \int^\infty_0 \alpha_{\lambda,body}I_{\lambda,sun} \mathrm{d}\lambda}{\int^\infty_0 I_{\lambda,sun}\mathrm{d}\lambda}$

Total emissivity: $\epsilon = \frac{\int^\infty_0 \epsilon_{\lambda,body}I_{\lambda,body} \mathrm{d}\lambda}{\int^\infty_0I_{\lambda,body} \mathrm{d}\lambda}$

The values above might not be equal, even though emissivity and absorptivity must be equal at a given wavelength.  An object which is highly reflective at visible wavelengths is not effectively heated up by absorbing energy from the sun.  Meanwhile, an object which has high emissivity (aka high absorptivity aka low reflectivity) at mid-IR wavelengths can effectively radiate heat, provided the atmosphere has sufficient transparency, which it does for radiation with wavelengths between 8 and 13 microns.  An example of the latter is a plant leaf: their high emissivity at mid-IR wavelengths allows them to cool below ambient temperature at night, which is why you find dew condensed on the grass in the morning.  If a single material or structure has high reflectivity at visible wavelengths and high emissivity at mid-IR wavelengths, there is the possibility of passively cooling below ambient temperature in the middle of the day.

These engineering requirements are generally hard to achieve in bulk materials, and this is where metamaterials—composites or structures engineered to have properties not found in bulk materials– come in.  Recently, passive daytime radiative cooling has been predicted [2] and achieved [3] in engineered photonic structures.

Returning to the desert ants, their hairs are an example of a natural photonic metamaterial which passively cools them in the middle of the day so they can venture out for a snack while their predators are hiding from the heat.  The hairs’ shape, size, and surface all conspire to reflect visible light.  The triangular cross-section permits total internal reflection for a range of incidence angles (see figure below).  The cross-sectional size of the hairs is comparable to the wavelength of visible light, which allows for the trapping and re-radiation of light via a process called Mie scattering.  A given cross-sectional area will give enhanced reflection at a single wavelength, but the polydisperse distribution of hair sizes allows for broadband coverage.  Finally, surface roughness allows for diffuse scattering of visible light at the surface of the hair.  As for mid-IR absorption, the paper says that the hairs act as an antireflective coating at these wavelengths, though they do not specify the mechanism.  Most likely, the sub-wavelength size of the hairs present an effective medium with an effective index of refraction to incoming mid-IR light, and the triangular shape helps produce a gradient of the refractive index which minimizes reflection due to index mismatch with air.  Another factor might be that the size of the hairs (and they appear to grow in a single layer) is roughly comparable to ¼ of the wavelength of mid-IR light, and quarter-wave-thick layers are frequently used in antireflective coatings.   And it really works.  Both in vacuum and in air, the ant is able to stay 10° C cooler with the hairs than without.

Total internal reflection happens for a range of incidence angles, and is one mechanism by which the ants’ triangular hairs reflect visible light.

It sounds too good to be true—cooling a body or an object passively in full sunlight—but the Sahara Desert ants (Ref. [1]) and the experiments in Ref. [3] show that it is really possible to achieve this feat by manipulating the optical properties of materials.

Thermal images of the ant head show that radiative cooling works both in vacuum and in air, and that the hairs are the source of this phenomenon.

References:

[1] N. N. Shi et al. Science (2015), Advance online publication

[2] E. Rephaeli et al. Nano Lett.,  13 (4), pp 1457–1461 (2013)

[3] A. Raman et al. Nature515 pp 540–544 (2014)