Alternative University

Environmental Design

Energy Efficiency

Solar Reflectance
and Material Emissivity

This article provides an overview of solar reflectance and thermal radiation emittance of opaque materials.

Nature of Light

Light is energy transport via electromagnetic (EM) radiation. EM radiation has a dual nature: it behaves like waves (complete with interference, diffraction, etc.); and it is a stream of energy packets (called photons).

Each photon has a fixed amount of energy that corresponds to a particular frequency (or wavelength) of light. The higher the frequency (shorter wavelength) the more energy.

The amount of energy transported by light (called power) is an integral multiple of photons. That is a quantum quantity — there are no fractions of a photon, only whole photons.

The wavelength (corresponding to power) of a packet of light (photon) is the distance between succesive peaks of the conceptualized light wave that corresponds to that photon.

The frequency of the wave is the number of wave crests per second.

Figure 1:  Electromagnetic waves have crests and troughs similar to those of ocean waves. The distance between crests is the wavelength. The number of wavelengths per second is the frequency. [NASA]

Figure 2:  Shorter wavelength (higher frequency) has more energy. This is like a jump rope with its ends being pulled up and down: more energy is needed to make the rope have more waves. [NASA]

The portion of the light spectrum that human eyesight can see, called visibile light, is only a small part of the electromagnetic spectrum, between ultra-violet (UV) and infra-red (IR):

Figure 3:  Electromagnetic spectrum, more energy per photon (left) to less energy per photon (right). Top scale shows energy per photon, measured in electron-volts. [Wiki]

Human Vision

The human eye has nerve cell “cones” for detecting color. There are three types of cones, each detecting a different interval of the visible light spectrum.

One set of these cones picks up green colors — medium wavelengths of the visible spectrum, labelled M.

Another set of cones picks up reds — longer visible wavelengths, L. This absorption of reds happens to a lesser degree than greens.

The third set of cones detects blues — shorter visible wavelengths, S — to a much more limited degree than the greens and reds.

The human visual systems normalizes (scales) these three primary color interval inputs into the following response curves:

Figure 4:  Human vision response curves for cones of the human eye. Short (S) wavelengths of the visible spectrum are used to sense blues, medium (M) to sense greens, and long (L) to sense reds. [Wiki]

Human eyesight recognizes a “color” as a combination of those three primary color intervals. The human visual system combines colors for you to visualize a color that is between the three primary detected color peaks.

And human eyesight can “see” colors that are not on the electromagnetic spectrum. For example, brown is a color that is a combination of different colors, not itself on the EM spectrum.

White is another color that is not on the EM spectrum — rather it is a mix of all colors.

Figure 5:  Multiple frequencies of colors across the visible light spectrum will appear white to a human observer. [NIST]

Solar Spectrum

Sunlight emits visible colors which together appear white. Sunlight also includes some ultra-violet light (UV), and IR wavelengths that are near the visible light spectrum (referred to as near infra-red, NIR).

Figure 6:  Solar power spectrum. [NASA]

The solar spectrum depicted above is for sunlight in space. Some of that sunlight is blocked by Earth’s atmosphere. The following figure shows atmospheric attenuation of the solar spectrum:

Figure 7:  Atmospheric attenuation of sunlight.

The yellow curve in this figure depicts extra-terrestrial sunlight (at zero atmospheres — the top of the atmosphere), corresponding to the red curve in the preceding figure. The green curve depicts sunlight at 1.5 atmospheres (sunlight path distance through the atmosphere 1.5 times the vertical height of the atmosphere, since the Sun is not usually directly overhead).

Here is the solar power spectrum again, with additional information:

Figure 8:  Solar irradiation at top of atmosphere (yellow) and at Earth’s surface (red). Portions absorbed by gases are indicated. In addition, some wavelengths are redistributed by Raleigh scattering (causing blue sky). The “blackbody” curve indicates theoretical emission (radiation) if the Sun was a constant temperature with full emissivity. In reality, the temperature and emissivity of the Sun vary. [Wiki]

Metamerism

As mentioned above, the human visual system (HVS) records and combines three regions of the EM spectrum (tristimulus values) to visualize each color.

That makes it possible for different combinations of tristimulus colors to appear like the same color to the human vision system. This phenomenon — when different combinations of primary colors appear to human vision as the same color — is called metamerism.

For example, what appears to be the same yellow color to human eyesight could be a very different mixture of colors in the real world.

Figure 9:  Yellow metamerism example. [Wiki]

In this figure, the first column visualizes a yellow ball generated with yellow light. Yellow is a wavelength on the EM spectrum, so that a light of a single wavelength is enough to generate that color.

In actual practice, a typical light source does not generate just a single wavelength, rather it could generate a narrow band of wavelengths with the single wavelength of interest (in this case yellow) predominant and a few neighboring wavelengths included in the light’s output.

Compare that to the second column, of a ball the same color generated with red, green and blue lights instead of a single yellow wavelength light. In that case, there are many more photons, from all three tristimulus color intervals, as shown in the second row of the example figure, which is reproduced here:

Figure 10:  Second row of the yellow metamerism example figure. The horizontal axis or each graph is wavelength (λ). The vertical axis is Intensity (the amount of energy, also called power).

Much more energy would be required to generate the light on the right, even though both lights will appear the same color and brightness to human vision.

The human visual system will process each of these two graphs with the human vision response curves for cones of the human eye (third row of the yellow metamerism example figure) to generate a color to see.

The resulting color and brightness of both balls looks the same, despite the huge difference in visible light energy inputs used to create the color reflection.


Reflectance and Absorption

Light striking a typical opaque object will reflect off the object or be absorbed by the object. For example, if 90 percent of the light is reflected, then 10 percent of the light is absorbed.

The color of an object we see is a reflection of light striking the object. For example, green leaves appear green because the leaves absorb the rest of the visible colors, reflecting only green light.

Figure 11:  A green object appears green because it reflects green light, absorbing all other visible light colors. [Wiki]

Consider painting an object yellow. You could obtain yellow paint and paint the object. After the object is painted, sunlight striking the object will either reflect off the object (making it appear yellow), or be absorbed by the object (the absorbed light converting into heat to heat up the object).

Say you want to reflect as much visible light as possible off the object in order to keep it cool. In that case, you could find a paint that will reflect red, green and blue in a ratio that when seen by humans will appear yellow, instead of only reflecting the narrow interval of wavelengths in the yellow part of the EM spectrum.

If the paint only reflected the yellow interval of the visible light spectrum, the graph of the reflected light would be as in the left column of the yellow metamerism example above, shown here again:

Figure 12:  Narrow band reflection.

In that case, most of the visible light is absorbed by the object. Only a narrow band of the visible light wavelengths is reflected.

On the other hand, if you find a paint that reflects a ratio of wide swaths of visible light wavelengths that combined look like yellow:

Figure 13:  Wide band reflection.

then much more visible light is reflected, leaving less visible light to be absorbed to heat the object.

This is possible to do. However, much of sunlight is not visible light. Almost half of sunlight is near infra-red, which must also be dealt with, in addition to visible light.


Heat and Radiation

Infra-red (IR) radiation is the next lower energy region of the electromagnetic spectrum after visible light. It has longer wavelengths than visible light.

Portions of IR that are near the visible light spectrum (that have wavelengths slightly longer than visible light) are emitted by the sun (are part of sunlight). That part of the IR spectrum is called near infra-red or NIR.

Longer wavelength IR is emitted by objects such as buildings, people, furniture etc. That is lower energy than the NIR that is in sunlight.

Sunlight that is absorbed by an object become heat. Heat is vibrating molecules. Materials that are hot have molecules that are vibrating more. The hotter a material gets, the more its molecules vibrate.

The molecules of cooler materials are also vibrating, but not as much as the molecules of hotter materials.

When an object has more heat than surrounding objects, it will transfer heat to the other objects. The heat transfer could be direct contact, called conduction, like conducting electricity but conducting heat instead.

Note: Materials that are good at conducting electricity, are also good at conducting heat.

In heat conduction, the vibrating molecules of hotter materials transfer some of their vibrations to the molecules of the colder materials.

This causes the molecules of the hotter material to start vibrating less, and the molecules of the colder materials to start vibrating more, thereby cooling the warmer material and heating the cooler material, until thermal equilibrium is reached.

Another form of heat transfer, besides conduction, is radiation. The hotter a material, the more heat of the material will be converted to radiation.

Figure 14:  Hot metal in a steel mill is emitting radiation to shed heat. Some of the radiation is in the visible light spectrum (“glowing”). [Wiki]

The radiation emitted by a hot object travels across space to other objects that absorb it, like NIR travels from the Sun to Earth, except that terrestial objects usually emit IR radiation that has longer wavelengths than the NIR emitted by the sun, and the space between objects is air.


Figure 15:  Maximum possible thermal radiation (blackbody curves) for Sun and Earth, with dominant (maximum) wavelengths 0.48 μm and 9.7 μm respectively (much longer wavelengths for radiation emitted by the Earth than the Sun). Coordinate axes have nonlinear scales (if scaled linearly, the curves would have long tails to the right). Actual emissions will be lower in parts due to atmospheric opacity at different wavelengths. [UCSD]

Figure 16:  Radiation emitted by the Earth (right) has longer wavelengths than radiation emitted by the Sun (left).

The emission of radiation from an object increases as the heat of the object increases. This happens when not enough conduction can cool the object.

A primary reason why conduction cannot cool an object fast enough is because the object is not in contact with enough cooler objects, or the cooler objects are not dense enough.

Consider an object that is in contact with air. Air is considered a “rarer” medium because the molecules of air are much further apart (are more rare) than the molecules of solid objects. The solid objects are thus called “dense” media.

With air having much fewer molecules to vibrate, a hotter solid object will shed more heat as IR radiation.

Figure 17:  Maximum possible thermal radiation at different wavelengths (blackbody curves) for different temperatures of a material. Coordinate axes have nonlinear scaling (logarithmic). When a material with full emissivity reaches 800 K (527°C), its blackbody curve (left tail in this figure) reaches the red end of the visible light spectrum (glowing red). Hotter materials glow or emit other visible light colors. [UCSD]

Radiant Barrier

Light striking an opaque object is either reflected or absorbed by the object. Light that is absorbed heats the object (making the object’s molecules vibrate more). In turn, this heat generates (emits) radiation to help cool the object, in the quest for objects to reach thermal equilibrium.

Building materials, furniture and people emit IR radiation to cool off. That will be the type of radiation and heat we consider in this discussion, along with the solar power spectrum.

For opaque surfaces, it has been discovered (by Kirchhoff) that for a given wavelength of the EM spectrum, the amount of light (radiation) that can be absorbed will always equal the amount of thermal radiation that can be emitted by the object at that wavelength.

This holds for any wavelength: at any single wavelength (or small enough interval thereof), the amount of radiation the surface can absorb at that wavelength will equal the amount of radiation it can emit at that same wavelength; this phenomenon is called Kirchhoff’s law of thermal radiation.

The percentage of incoming radiation the object can absorb is called the absorptance or absorptivity of the object, and the amount of radiation the object can emit is called the emittance or emissivity of the object.

Reflectance (also called reflectivity) of the object is the complement of absorption. That is, the reflectivity and absorptance must sum to equal unity (100 percent). Hence, reflectivity is the complement of emissivity.

Figure 18:  Reflectivity is the fraction of incoming radiation that is reflected off the object.

Many objects have the same reflectivity across all EM spectrum wavelengths, and thus will have uniform emissivity that is the complement of its reflectivity.

This is very useful for insulation purposes, and is the basis for radiant barrier insulation.

Radiant barrier insulation is now widely used on roofs, and is required by building codes in hot climates.

One way to set up a radiant barrier is to position shiny foil, with shiny side up (upward-facing), under an air gap below the final (upper-most) roofing. This is commonly done with metal roofing, with diagonal purlins creating an air space between the shiny radiant barrier facing and the metal roofing above.

That way, when the roofing gets hot, the air gap slows conduction heat transfer, causing the roof to get hotter, releasing more IR radiation toward the attic. But the shiny upward-facing surface reflects the IR radiation back to the roofing above, instead of absorbing it into the attic. Radiative heat loss from the roofing then goes toward the atmosphere, instead of partially into the attic.

Since the radiant barrier surface is, by design, so effectively reflective, it therefore would have very low emissivity (according to Kirchhoff’s law for standard materials), hence could be used with shiny side down (downward-facing) above an air space to prevent downward radiation emission in the first place.

Installing the radiant barrier downward-facing (with air gap below the downward-facing shiny surface) may help because a radiant barrier surface must be clean (without dust) to be shiny enough to work effectively.

Putting the shiny surface facing down instead of up keeps it from getting dusty (thanks to gravity drawing dust particles away from the downward-facing shiny surface).

Figure 19:  Downward-facing radiant barrier on underside of roof decking (top of photograph, on rafters), in a house under construction in Atlanta (before house ceiling is installed under joists above the windows in center of photograph and under joists the photographer is standing on).

Figure 20:  Heat flow diagram of downward-facing radiant barrier on underside of roof decking in a traditional house attic. The roof heats the radiant barrier which blocks emission of thermal (IR) radiation into the attic. [PNNL]

Nonuniform Reflectance & Emissivity

An interesting variation of Kirchhoff’s law is to have reflection and emission at different wavelength intervals, so that reflectance and emissivity are not complementary overall. This can be done by combining different materials together.

According to Kirchhoff’s law of thermal radiation, reflectance and emissivity are required to be complementary only at each wavelength, not necessarily for a material overall.

Most materials have largely uniform reflectivity across the EM spectrum, and thus have essentially the same emissivity across the spectrum. In that case, reflectivity and emissivity are complementary at each wavelength and also overall.

Figure 21:  Pipes for circulating hot liquid at a solar trough electricity generating plant in Morocco. Insulation on the pipes has a shiny outer surface to reduce emissivity (thermal radiation heat loss). The shiny surface has high reflectivity and thus corresponding low emissivity as expected for standard materials according to Kirchhoff’s law. [WorldBank]

However, it is possible to design a new material to have different reflectivities (and hence different emissivities) at different wavelengths, and the material can be designed and manufactured to receive radiation in one set of wavelengths and emit radiation in another set of wavelengths.

That way, a material could have high reflectivity and high emissivity overall (instead of high and low respectively).

Likewise, a material could have low reflectivity and low emissivity overall (instead of low and high respectively).

That is how solar thermal collector surfaces are designed, such as the black collector surfaces for solar water heaters and solar trough electricity plants.

Figure 22:  “Evacuated tube” solar water heaters. These highly efficient water heating systems are popular in many parts of the world. Widespread use of these in a city results in the city requiring one less power generating station to serve residents. In these systems, a black collector tube is suspended in a vacuum within a glass cylinder. The black collector tube has low reflectivity, and low emissivity. If it had high emissivity, like typical black materials, heat would escape through the vacuum (as thermal radiation).

Standard commercial black paints (and hence black surfaces) usually have low reflectivity and high emissivity, because (in accordance with Kirchhoff’s law) reflectivity and emissivity are usually complementary.

But that compelementarity is only required at each wavelength, not overall, so that new materials can be carefully designed and manufactured to have different incoming and outgoing radiation intervals on the EM spectrum (which many materials already do) while at the same time having different reflectivities and emissivities on different parts of the spectrum (which many existing materials do not do, but can be done for newly designed materials).

This way you can design a black surface that has both low reflectivity and low emissivity, as is done for black solar thermal collector surfaces.

Figure 23:  Solar trough electricity (STE) collector, using a black collector tube suspended in a vacuum within a glass cylinder, like evacuated tube solar water heating elements. Heat transfer fluid is heated in the STE collector tubes and circulated to heat exhchangers to boil water for generating electricity with a steam turbine.

Figure 24:  Development and testing of collector tubes for solar trough electricity (STE) collectors.

Figure 25:  STE collector tubes have low reflectivity and low emissivity. [Stanford]

It is also possible to design and manufacture materials that have high reflectivity and high emissivity. That will be done for white roofing of commercial buildings.

Standard commercial white paint is highly reflective, but has very low emissivity (complement of reflectivity as expected with Kirchhoff’s law). This inefficiency has been overcome with the development of new white paints, coatings and roof membranes that are not only highly reflective, but also have high emissivity.

Commercial buildings already have white roofs to sharply reduce air conditioning load. (To see examples, use a mapping app in satellite mode to see white roofs on commercial buildings near you.)

In the future, white roofs on buildings will have high emissivity in addition to high reflectivity.

Figure 26:  White roof on a retail store in Las Vegas sharply reduces air conditioning costs of the building. [Walmart]

Figure 27:  White roofs efficiently cool buildings, sharply reducing the size and usage of air conditioning systems in hot climates. High emissitivity will be incorporated into white roofs to further improve cooling efficiency.

Radiative Sky Cooling

Continuing with the idea of designing materials to have high reflectivity and high emissivity, there is yet another trick we can rely on to further increase emissivity: emitting IR radiation in wavelength bands that are especially easy to pass through the atmosphere.

This creates materials that are actually cooler than their surroundings in equilibrium. Such materials will be developed and used to provide natural cooling without electricity or other energy.

The atmosphere has bands of electromagnetic wavelengths that are transparent to IR radiation. These materials will be specially designed to emit thermal IR radiation in those bands to more easily escape the atmosphere, and as a result increase emissivities of materials in those wavelength bands.

The new materials are being developed as white paint, mirrors, and translucent sheets with reflective backing.

These surfaces do not absorb solar irradiation, while emitting IR radiation during day or night in the high-flow IR-transparent portions of EM spectrum that easily pass through the atmosphere to outer space and are referred to as “atmospheric windows”.

These new materials are cooler than their surroundings because the surroundings emit thermal radiation in wavelengths that do not pass as easily through the atmosphere to outer space, causing the atmosphere to act as somewhat of a blanket on the surroundings.

Water pipes will be attached to the materials, to cool water that can be circulated to indoor radiative cooling systems which currently use heat pumps.

Figure 28:  Rooftop sky radiator panels. [Stanford]

Additional applications will include precooling water for traditional HVAC systems:

Figure 29:  Schematic diagram of an evaporative/radiant cooling system for a floor of a multi-floor office building, augmented with a rooftop sky radiator. Since there is no air handling, fresh air for occupants must be provided by a separate system. [PNNL]

This diagram shows a commercial hydronic cooling system augmented with rooftop sky radiator panels to pre-cool the circulating water.

For a passive house (instead of an office building): insulation, sealing and an HRV (ERV) would provide fresh air and narrow indoor temperature fluctuations; less than 15 radiant cooling surfaces would be needed; the chiller (rooftop evaporative cooler) would not be needed; the storage tank could be optional or small; the only energy needed would be electricity to power the fan of the HRV and power the water pump to circulate water from the roof panel to the radiative cooling surfaces (which could be switched to providing radiant heating with a heat pump in winter).

Figure 30:  Evaporative cooling system chillers on the roof of a high school. For a passive house, the chiller would be eliminated, or replaced with a heat pump.

Figure 31:  Water tubing and heat exchanger plates in a wall under construction, before wall boards hide the tubing and plates. These types of systems are also available for floors and ceilings. Warm or cool water will circulate in the tubing, heating or cooling the wall which will emit or absorb thermal radiation to heat or cool the room respectively. In passive house construction, heating and cooling of the water is accomplished with a heat pump. In the future, radiative sky cooling could assist or replace the heat pump for cooling.

Energy Efficient Windows

Energy efficient windows are glass windows with multiple panes of glass and inert gas fill between the panes.

Figure 32:  Energy-efficient window.

Figure 33:  Energy-efficient window, with a removable storm window (on the exterior facade of the building) to protect the window from storms and wildfires.

The gas fills, between the panes of glass, reduce conduction and convection heat transfer. Thermal radiation heat transfer is reduced with window coatings that are applied to the glass panes during manufacturing.

Conduction is the transfer of heat (molecular vibrations) by direct contact of materials, as explained above. In this case, if the space between glass panes was air, conduction would heat up a film of air along the glass pane surface on the warmer side of each air gap between panes.

Convection is heat transfer by movement of a gas or liquid: when a film of air is heated by conduction, it gets lighter (molecules move further apart in order to have more room to vibrate), causing it to weigh less (per liter) and rise above other air that is heavier (not as warm), creating air currents (called convection) that displace the film of air with cooler air that then conducts heat and itself rises away in a convection loop.

Inert gases are used instead of air, because the higher molecular masses of the gases suppresses convection. Many windows use argon, or argon mixed with krypton.

Molecular masses:

Radiation is the transfer of heat as electromagnetic radiation, described above in this article and referred to as thermal radiation.

Thermal radiation would emit from a warmer pane of glass toward the cooler pane, in each gap between glass panes.

A coating (that reflects IR) on the cooler pane could reflect the radiation back. Likewise, a coating on the warmer pane could be low-emission (“low-e”) to prevent the thermal emission from initiating in that direction.

The two coatings just described (high IR reflectance and low IR emissivity) could be the same coating, maintaining high visibility through the glazing in both directions (optical reciprocity).

Visibility through a window refers to imaging coherence through the glazing, measured as visible light transmittance (VT) and haze (h).

Visibility and haze requirements limit the possible kinds of coatings that are available, for example not supporting particular combinations of allowing while blocking different thermal radiation wavelength bands.

Besides glazing properties, the window frame and any other possible thermal bridges are of importance.

Window frames leak much more heat that window glazing, and may catch fire during fires (depending on the window frame’s material exposure) causing the window to fall out and spread a wildfire through the window opening into the house.

Careful condsideration must be paid to choosing window frames, to reduce heat transfer and reduce fire danger. New types of window frames are being developed, for example wood frames with exterior metal cladding.


Metamerism and Photonics

An energy-efficiency drawback, of energy efficient windows, is the requirement for imaging coherence (transparency) through glazing, which precludes many energy-efficiency options, such as use of metamerism.

Other building materials do not have that requirement, thereby providing much more opportunity for using reflection and emission to reduce detrimental heat transfer.

Metamerism was already discussed above, to reflect more light for a given perceived color. However, as mentioned, that only applies to the visible light spectrum.

Heat transfer applications for architectural design must also account for IR radiation, not just visible light characteristics. The visible and IR spectrums must be used together.

Also important is to account for the ability of different wavelengths of EM radiation to pass through the atmosphere.

Some wavelengths are blocked by the atmosphere. The atmosphere is said to be “opaque” to those wavelengths.

Some wavelengths can pass through the atmosphere. Those wavelengths of EM radiation are said to “transmit” through the atmosphere

The degree to which the atmosphere blocks a wavelength of EM radiation is called the “opacity” of the atmosphere at that wavelength.

The degree to which the atmosphere transmits a wavelength of EM radiation is called the “transmittance” of the atmosphere at that wavelength.

Transmittance is the opposite of opacity (they are complements). Here is a graph showing the opacity of the atmosphere (useful for determining whether astronomical observations are possible at the Earth’s surface):

Figure 34:  Atmospheric opacity graph for astronomy. [NASA/Wiki]

And here is a graph of the transmittance of the atmosphere, for the portion of the EM spectrum from 0.2 to 70 μm:

Figure 35:  Atmospheric transmittance (top) and causes of opacity at corresponding wavelengths. The wavelength bands of high upgoing transmittance (IR radiation escaping to outer space) are called “atmospheric windows”, to the right of which Carbon Dioxide (CO2) blocks IR radiation from escaping to outer space. Another band of wavelengths blocked by CO2 is to the left of water vapor absorption that is to the left of the atmospheric windows in this graph. [USNA]

There are other atmospheric windows, in the adjacent lower energy portion of the EM spectrum:

Figure 36:  Spectral transmittance showing longer wavelength radiation transmission on the right. The atmospheric window region on the left in this figure is on the right of preceding and following figures. [NOAA]

However, the longer wavelengths, on the right of that figure, are not in the range of typical (passive) architectural object emissions. For our purposes, the solar power spectrum and neighboring thermal infra-red emission spectrum are used:

Figure 37:  Solar spectrum and thermal infra-red emission spectrum. The human vision response curves (left) are as described earlier. More atmospheric windows are shown in this thermal infra-red emission spectrum than in the preceding figures (at bands blocked by carbon dioxide), because sparse narrow bands of atmospheric transparency can be found there if higher resolution is used. The main emission bands of interest for our purpose are in the dense transparency region we have labelled “Dense Lobes” in this figure. [Nature]

It is possible to develop different color coatings, that appear to be the same color but have different thermal IR emissions, if the color is matched metamerically (is not actually the same color, but looks like the same color).

That would allow us to change the thermal properties of a colored object without noticably changing the color.

This has been done by Stanford researchers, documented in their open-access article in Nature (see References below), which we discuss now.

As a base to start from, consider the color black. For human vision to see black, each of the tristimulus values (primary colors) would be zero or near zero. That would correspond to a black object reflecting little or no light.

The following diagram shows a graph, of the reflectivity of standard commercial black paint, for wavelengths of the visible light spectrum:

Figure 38:  Reflectivity of standard commercial black paint in the visible light spectrum. Only about 5 percent of visible light of any wavelength is reflected. [Nature]

Here are graphs showing the absorptivity and emissivity of that paint:

Figure 39:  Standard commercial black paint: abosrptivity (complement of reflectivity) in the solar power spectrum (left); emissivity in the thermal emission spectrum (right). Emissivity in the dense lobes of atmospheric windows (approx. 8 to 13 μm) are about the same as absorptivity in the solar spectrum, as would be expected with Kirchhoff’s law. [Nature]

Next, consider how a standard commercial light pink paint compares to that black paint:

Figure 40:  Reflectivity of a standard commercial light pink paint in the visible light spectrum, compared to standard black paint. More than 20 percent of visible light reflects off the paint at some wavelengths of the spectrum, and almost 40 percent at longer wavelengths, thereby reflecting more visible light than the black paint. [Nature]

The human vision system combines that combination of visible light wavelengths to perceive a light pink color.

Here are graphs of the the absorptivity and emissivity of that light pink paint compared to the black paint:

Figure 41:  Absorptivity (left) and emissivity (right) of standard commercial light pink and black paints, slightly lower for the pink paint than for the black paint. [Nature]

Stanford researchers have developed a system to design and manufacture thin colored photonic surfaces (coatings) that substantially adjusts the reflectance and emissivity of a coating as needed (to change its thermal properties in sunlight) without noticably changing the color (using metamerism).

As an experiment, they developed two light pink surfaces, that appear to be the same color as a standard commercial light pink paint, but with very different thermal properties in sunlight:

Here is a visible light reflectivity graph of those two experimental light pink thin surfaces, and the standard light pink and black paints for comparison:

Figure 42:  Visible light reflectivity graph of two experimental light pink thin surfaces (denoted “Hot” and “Cold”), and standard commercial light pink and black paints (denoted “Paint” and “Black paint” respectively). The light pink colors appear to be very similar (inset, top of graph). [Nature]

Visible light reflectivity curves of the experimental light pink surfaces are similar to the light pink paint, but exaggerated. The similarity of the peaks and lows causes metamerism to produce colors that appear very similar in human vision.

Also notice in this figure that exaggeration which is asymmetric (variance occuring only to one side of the pink paint curve) is in portions of human vision that sense less — at shorter and longer wavelengths. Moving the errors to portions of the spectrum less noticable to human vision helps with metamerism.

Here is overall color sensitivity of human vision relative to the solar spectrum:

Figure 43:  Photopic (color) vision response curve in bright sunlight. The human eye mostly “sees” green and yellow, with higher sensitivity of green. Much of the blue of bright sunlight is not seen by the human eye. [McCluney]

The errors (asymmetric reflectivity variance of the two experimental light pink materials) are in the regions away from where human eyesight is better able to detect wavelengths of visible light, making those errors have less effect on human vision.

Here are graphs of the aborptivity and emissivity of the two experimental light pink thin photonic surfaces, and standard light pink and black paints for comparison:

Figure 44:  Absorptivity (left graph) and emissivity (right graph) of two experimental light pink photonic surfaces (denoted “Hot” and “Cold”), standard light pink paint (denoted “Paint”), and standard black paint (“Black paint”). [Nature]

As mentioned, asymmetrical absorptivity (reflectance) variance relative to standard pink paint tends away from photopic vision response wavelengths, helping to utilize metamerism.

Outside of the metamerism window, the “hot” material jumps to high absorption of incoming near infra-red (NIR) radiation like the black paint (right side of the left graph), while the “cold” material drops to lower absorptivity, going up where there is less incoming NIR radiation to absorb.

In the thermal emission graph (the right graph), emissivity of the “hot” material drops through the sparse (thinly banded) atmospheric window of carbon dioxide blocking, and through the water vapor blocking (opaque) region, to low emissivity (retaining heat) along the dense lobes atmospheric windows, unlike the black paint which has high emissivity in this most important of emission windows, making the “hot” surface that is colored light pink much hotter than the black paint.

The “cool” pink surface, on the other hand, jumps to high emissivity in the dense lobes region, thus emitting much more thermal radiation to outer space than the “hot” material could (after already having absorbed much less heat than the “hot” material in the first place).

Compared to the standard commercial light pink paint, the “cool” pink material has slightly less emissivity in the dense lobes (atmospheric windows) than the pink paint. But it has much higher reflectivity (lower absorptivity) in the incoming NIR bands (left graph), making it much cooler than the light pink paint, because it absorbs much less NIR radiation than the paint, while only being slightly less effective than the paint in shedding excess heat through thermal radiation to outer space.


Color Temperature

Photopic Vision


References

 1.  Wei Li, Yu Shi, Zhen Chen, Shanhui Fan, Stanford University, “Photonic thermal management of coloured objects”, Nature, 2018. doi/pdf

 2.  Eden Rephaeli, Aaswath Raman, Shanhui Fan, Stanford Univ., “Ultrabroadband Photonic Structures To Achieve High-Performance Daytime Radiative Cooling”, Nano Letters, 2013. pdf

 3.  Yao Zhai, Yaoguang Ma, Sabrina N. David, Dongliang Zhao, Runnan Lou, Gang Tan, Ronggui Yang, Xiaobo Yin, Univ. of Colorado (& Wyoming), “Scalable-manufactured randomized glass-polymer hybrid metamaterial for daytime radiative cooling”, Science, 2017. doi/pdf

 4.  Dongliang Zhao, Ablimit Aili, Yao Zhai, Shaoyu Xu, Gang Tan, Xiaobo Yin, Ronggui Yang, “Radiative sky cooling: Fundamental principles, materials, and applications”, Applied Physics Reviews, 2019. pdf

 5.  N. Fernandez, W. Wang, K. Alvine, S. Katipamula, “Energy Savings Potential of Radiative Cooling Technologies”, Pacific Northwest National Laboratory, 2015. pdf

 6.  Eli Goldstein, Dennis Nasuta, Song Li, Cara Martin, Aaswath Raman, “Free Subcooling with the Sky: Improving the efficiency of air conditioning systems”, Purdue, 2018. pdf

 7.  Xiulin Ruan, “Radiative Cooling”, Purdue, 2020. pdf

 8.  Haiwen Zhanga, Kally C. S. Ly, Xianghui Liu, Zhihan Chen, Max Yan, Zilong Wu, Xin Wang, Yuebing Zheng, Han Zhou, and Tongxiang Fan, “Biologically inspired flexible photonic films for efficient passive radiative cooling”, Proceedings of the National Academy of Sciences, 2020. pdf

 9.  Eliane Coser, Vicente Froes Moritz, Arno Krenzinger, Carlos Arthur Ferreira, “Development of paints with infrared radiation reflective properties”, Polymers (Polimeros), 2015. pdf

 10.  Ross McCluney, “Selecting the Right Glass for Solar Shading”, ASHRAE Seminar, 2004. pdf

 11.  Geoff Smith, “Glass, daylighting and lighting”, UTS Applied Physics and Institute of Nanotechnology, Australia, 2005. pdf

 12.  Julian (Jialiang) Wang, Donglu Shi, Univ. of Cincinnati, “Spectral selective and photothermal nano structured thin films for energy efficient windows”, Applied Energy, 2017. pdf

Copyright © 2021 Arc Math Software, All rights reserved
Arc Math Software, P.O. Box 221190, Sacramento CA 95822 USA
Disclaimer   Contact
2021–Sep–22  19:41  UTC