There are three mechanisms for heat transfer. The most obvious is conduction. If you touch a hot stove, the heating element transfers its heat to you through the point of contact. Then there’s convection, which involves the flow of fluids. When you turn on a fan, you feel cooler even though the air temperature remains the same. Why? Well, the fan causes more air to circulate around you, causing more heat to be whisked away via conduction (what we really perceive is not temperature, but rate of heat transfer from our bodies).
Then there’s radiation, which is a little more mysterious. Think of the heating element in your toaster or conventional oven which starts to glow red hot when it’s heated up. Why is that? Well, temperature is a measure of average kinetic energy, and that kinetic energy in a solid manifests as lattice vibrations known as phonons. Due to quantum mechanics, the energy of those lattice vibrations is actually quantized. So the frequencies of light that we see emitted out of a hot body actually arise from quantized phonon transitions. The more energy there is in the lattice (the higher the temperature), the more dramatic those phonon transitions can be, resulting in higher frequencies of emitted photons. That’s why really hot things can glow white; they’re emitting frequencies all throughout the visible regime, not just lower energy red frequencies!
But even when things aren’t red hot, they’re still glowing. Human eyes just can’t see it. This is the principle behind thermal imaging. Warm things still have phonon transitions—they just manifest in the infrared. That’s how an infrared camera (or a snake!) can see the world in terms of heat.
The simplest model for the frequency spectrum of thermal emission is blackbody radiation. A blackbody is a theoretical object that absorbs all incoming radiation and reflects none. A blackbody emission spectrum is a lopsided-bell-curve-like-thing which shifts its center towards higher frequencies as temperature is increased (black curve in Figure 11). However, this model doesn’t capture how many real materials behave. Real materials preferentially emit certain frequencies based on energy levels defined by their crystalline lattice or electron orbitals. But things can get weirder: as nanophotonics teaches us, as we introduce geometric features in materials on the order of the wavelength of light, we can further manipulate their optical properties.
Radiative Sky Cooling
This idea can be taken to the extreme. Usually, when objects radiate their heat away, the effect is mitigated by incoming thermal radiation from the environment and the huge amount of energy coming from the sun. Furthermore, not all wavelengths are effectively transmitted through the atmosphere. It is hard for an object to cool radiatively when the air is blocking those frequencies! But what if a material was engineered, using principles of nanophotonics, to selectively emit at wavelengths that the atmosphere strongly transmits? And what if that material also strongly reflected incoming sunlight and thermal radiation? Then you would have a material that cools with freakish efficiency, even under direct sunlight.
This principle, dubbed radiative sky cooling, underpins Professor Aaswath Raman‘s work (see his fantastic TED Talk). Using electromagnetic simulation, Raman and his colleagues have designed specialized metamaterials that do just this. They look like mirrors to the eye (they have to in order to efficiently reflect solar radiation!). However, they are also engineered to transform their heat into thermal radiation of wavelengths between 8-13 microns, the “atmospheric transparency window” where infrared light is unimpeded by the atmosphere. These materials literally pump their heat energy to outer space! As a result, they can cool below ambient air temperature for free. It seems to defy thermodynamics; but remember, the heat of these magic materials goes from hot to cold just like thermodynamics says it should—it’s just that for normal materials, the atmosphere gets in the way.
The efficacy of these metamaterials is remarkable. Raman’s group has obtained temperatures 5°C below ambient air temperature for these materials under blue Palo Alto skies. And with very sophisticated vacuum sealing with spectrally optimized glass (to eliminate conduction and convection), Raman’s team has achieved temperatures a staggering 42°C below ambient air temperature.
This exciting technology has obvious applications for improving the efficiency of air conditioning, refrigeration, and cooling of electrical hardware (think cloud computing warehouses). However, Professor Raman wanted me to look into an unexpected application: dew harvesting.
Applying Radiative Sky Cooling to Dew Harvesting
The global fresh water demand is projected to surpass the natural supply from
the water cycle by up to 40% by 2030. There is a dramatic need to design
alternative, energy-efficient sources of freshwater. Desalination is one route for more fresh water, but it is extraordinarily energetically expensive. However, a simple dew harvesting device could be achieved with a radiative sky cooling surface, tilted slightly from the horizontal to channel water. Water vapor would condense on the cool surface and bead off into a collection chamber.
Radiative sky cooling has been used before for this purpose. However, cooling is not the only factor in the efficiency of dew harvesting. Patterning hydrophilic and hydrophobic regions on the surface is critical; hydrophilic regions cause
condensation, and hydrophobic regions cause efficient collection. However, no
attempts have been made to simultaneously optimize a dew condenser for radiative cooling and its surface-water interactions. This is the objective of our design.
Designing Surface Wettability
Before we talk about the electromagnetism techniques we need to optimize a metamaterial for radiative sky cooling, let us first focus on the wettability properties we want so that our dew condenser effectively attracts water for condensation but also allows it to shed. Wettability measures how a liquid clings to a solid surface.
We first need hydrophilic (water loving) regions on our dew condenser so that water condensates in the first place. Due to the dew’s attraction to the hydrophilic surface, these droplets will emerge with high probability and grow to be large and flat. Using some materials parameters, I roughly simulated the behavior of a hydrophilic dew condensing substrate. A maximum droplet size can be found by setting the surface adhesion force equal to the gravitational pull along the inclined plane of our condenser (experiments have found an incline of 30° is favorable).
A water-loving surface sounds pretty good for something that’s meant to collect water. However, a hydrophilic surface can lead to large films of water covering the condenser, which would ultimately impede radiatively sky cooling. Furthermore, if the surface is too hydrophilic, water may shed too infrequently for it to be a good harvester. Enter, the hydrophobic (water-fearing) surface.
The hydrophobic surface has fewer nucleation sites (points where condensation first occurs), but more frequent shedding. As a result, water is collected steadily instead of sporadically. The game is to figure out an optimal proportion of hydrophilic and hydrophobic sites, as well as the geometry of the patterning.
As has been done in the literature, we experiment with patterning hydrophilic dots on a hydrophobic substrate to aim for the best of both worlds. I recreated an experiment by Choo et al. in simulation.
Now we have an idea for how we want to pattern hydrophilic and hydrophobic regions on our substrate. But how do we achieve these different material properties in practice? One option is to literally pattern two different materials. However, introducing etched patterns into a material can change its wettability properties too! Etching a grating into a material (in this case SiO2) introduces air pockets which repel water and render the surface hydrophobic; this is known as the Cassie-Baxter state. Hydrophilic regions can be based on SiO2 planes which exhibit natural hydrophilicity. In the next section, these SiO2 designs will also be leveraged for their optical properties for radiative cooling.
Optimizing Emissivity for Radiative Cooling
Light can be manipulated in surprising ways when we introduce geometric features on the order of the wavelengths of light. So for the infrared wavelengths we’re interested in for thermal radiation, we need to engineer structures on the micron-scale.
The same SiO₂ grating we used to obtain the hydrophobic surface can be optimized for radiative sky cooling. A silver mirror underneath the grating reflects incoming radiation and directs emission skywards, while SiO₂’s infrared emission is fine-tuned by the periodic grating. Our electromagnetic simulation method is based on Kirchhoff’s law of thermal radiation. In the infrared regime, the absorptivity of a material is the same as its emissivity. The implication of this is that we can numerically simulate bouncing various wavelengths off our structure and measure the absorption and reflection to predict its thermal radiation spectrum.
To enhance thermal radiation within the atmospheric transparency window, we leverage a special type of optical mode that emerges in these SiO2 gratings: surface phonon polaritons (sorry for the technobabble). These resonances are surface modes caused by the coupling a photon to a phonon (those aforementioned quantized lattice vibrations which are the mechanism for thermal radiation). We run an optimization for the dimensions which result in these modes helping us emit more radiation skyward while simultaneously reflecting radiation outside of the atmospheric transparency window. The optimized dimensions are depicted below.
The optimized SiO2 grating demonstrates outstanding selectivity for emission in the atmospheric transparency window in simulation (Figure 11). As the hydrophobic grating will constitute the majority of the surface area of the dew harvester, this will provide the cooling power necessary. A hydrophilic SiO2 slab also demonstrates reasonable emissivity in the window, but less selectivity.
Using two length scales simultaneously, one optimized for surface collection, the other for selective emission, we can achieve high performance on both fronts. This two-pronged design for dew harvesting is the first of its kind. Professor Raman left Penn for UCLA, so this design has remained theoretical. But if manufactured, this dew harvester with special wettability and radiative sky cooling could be an efficient, alternative source for freshwater.
On a personal level, this research effort is what made me fall in love with light and nanophotonics. Who would expect that Maxwell’s equations could predict thermal radiation, especially this magical form of it that feels like free energy!? Thinking about the world from this approach is like growing a new set of eyes. It’s intoxicating, and I can’t wait for what else I’m going to see.
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