http://people.csail.mit.edu/jaffer/cool/SolarScreens
	Solar Screens

• Bi-Color
• Chalmers
• Tellurium
• Nanocrystalline
• Semiconductor
• Covered CoolRoof
• Granular Aluminum Coated Cover

If the solar absorption could be reduced, even at the expense of some infrared emittance, the goal of 24-hour cooling might be possible.

Bi-Color

• Silvestrini, V., Peraldo, M., Monza, E.
  Covering Element Screening Off the Solar Radiation for the Applications in the Refrigeration by Radiation,
  US Patent 4,323,619 issued Apr. 6, 1982.

In their 1982 US patent, Silvestrini et al describe a cooling arrangement where the solar-reflective screen is separated from the infrared emitters, which are the objects or people to be cooled. For several configurations they report solar transmittance between 1.1% and 0.6% with infrared transmittance between 43% and 68%.

The solar absorption ranges from 28% to 35%, which would produce heating up to 385 W/m² at peak solar intensities. In still air, convection transports about 8 W/(m²·K); so one would expect a peak temperature rise of 48 K. Blackbody emissions at 70°C are 75% larger than emissions at 25°C. So the infrared emissivity of the screen becomes important.

The patent provides measurements for infrared transmission, but not infrared reflectivity or absorption. Simulating a 100 μm thick HDPE sheet from 8 μm to 13 μm, FreeSnell reports the average values for transmission, absorption, and reflection are 0.79, 0.11, and 0.10, respectively. The patent gives transmission of the "starting film" without pigment as 0.85.

Example 2 of the patent gives an infrared transparency of 0.78 from 8 μm to 13 μm for 7.5% by weight (1.7% by volume) of TiO₂ in 50 μm thick HDPE sheet. FreeSnell reports the average values for transmission, absorption, and reflection are 0.79, 0.11, and 0.10, respectively.

The lower HDPE sheet of the bi-color screen is filled with carbon-black or cobalt-oxide. Infrared spectral refractive-index data for these materials is not available; and the validity of using Maxwell Garnett Theory to combine the materials is doubtful.

Looking at the (FreeSnell) graphs, the transmission and absorption of the film are complementary, while the reflectance is nearly constant. From these examples, the emissivity being 0.9 minus the infrared-transmission seems a plausible assumption.

Look here for the description of SimRoof's treatment of solar-screens.

Silvestrini et al test their screen covering a 10 cm deep airspace with a selective radiator at the bottom. Simulated here is the bi-color cover 10 cm above a roof with 80% solar and infrared absorption. The conduction through 10 cm of air is 0.32 W/(m²·K); a larger air gap would give a slight performance improvement.

The scatter-plot of roof-heat-gain versus time-of-day on the left shows much less daytime heating than a high-performance CoolRoof on the right. But its night cooling is close to half that of the CoolRoof.

Bi-color Cover	CoolRoof

There are 377 hours (4% of 8760) with positive heat gain. These are correlated with the large positive screen-temperature-gains, and occur during periods of low wind-speed.

Chalmers

• Torbjorn M. J. Nilsson, Gunnar A. Niklasson,
  Radiative cooling during the day: simulations and experiments on pigmented polyethylene cover foils,
  Solar Energy Materials and Solar Cells, Volume 37, Issue 1, April 1995, Pages 93-118,
  ISSN 0927-0248, DOI: 10.1016/0927-0248(94)00200-2.

The film was produced so that f = 0.15 and d = 400 μm and the optical properties in the solar and thermal parts of the spectrum were R_sol = 0.849, τ_sol = 0.013, A_sol = 0.138, R_8-13 = 0.09, τ_8-13 = 0.33 and A_8-13 = 0.58. In simulations the corresponding optical properties were R_sol = 0.825, τ_sol = 0.011, A_sol = 0.164, R_8-13 = 0.059, τ_8-13 = 0.520 and A_8-13 = 0.421, respectively.

Samples		TSol	RSol	ASol	T8-13	R8-13	A8-13
15% ZnS in 400 μm thick polyethylene	Measured	0.013	0.849	0.138	0.33	0.09	0.58
15% ZnS in 400 μm thick polyethylene	Simulated	0.011	0.825	0.164	0.520	0.059	0.421

A 1 mm thick aluminium plate was sprayed with matt black paint several times, with drying in between. By weighing a small reference plate the paint thickness was estimated to be at least 100.um, which makes the plate an almost black body - like emitter of thermal radiation. Spectrophotometric measurements showed that the painted plate had R_sol = 0.045 which means that A_sol = 0.955. In the thermal spectral region the corresponding values were R_8-13 = 0.09 and A_8-13 = 0.91.
...
The ZnS pigmented foil was subsequently fixed to cover the box at a height of 50 mm above the radiator.

Chalmers Cover	Bi-color Cover

There are 995 hours (11% of 8760) with positive heat gain. The performance is not as good as the bi-color screen due primarily to the black roof. Replacing it with a white roof and increasing the separation to 10 cm brings the daytime cooling closer to the bi-color screen (481 vs 377 hours of positive heat gain). Night cooling is also inferior because of the polyethylene thickness being 400 μm vs 100 μm.

Chalmers Cover over White Roof	Bi-color Cover

Tellurium

• T. Engelhard, E.D. Jones, I. Viney, Y. Mastai, G. Hodes,
  Deposition of tellurium Films by decomposition of electrochemically generated H₂Te: application to radiative cooling devices,
  Thin Solid Films 370 (2000) 101-105.

Table 1
Optical functions values, R_8-13, A_8-13, T_8-13, R_Sol, T_Sol and A_Sol as defined in the text.

Sample	T8-13	R8-13	A8-13	TSol	RSol	ASol
Polyethylene	0.813	0.156	0.030	0.891	0.078	0.031
Mn-O coated polyethylene	0.801	0.170	0.029	0.725	0.173	0.102
Te Film	0.652	0.221	0.137	0.047	0.123	0.830

With the Te layer on top, the reflection and absorption from top and bottom differ. FreeSnell calculates the following values for 50 μm HDPE (not LDPE) without and with a 0.12 μm layer of Te on top:

Sample	Side	T8-13	R8-13	A8-13	TSol	RSol	ASol
HDPE	either	0.914	0.085	0.0	0.841	0.101	0.058
Te Film on HDPE	top	0.610	0.349	0.042	0.078	0.563	0.358
Te Film on HDPE	bottom	0.610	0.321	0.070	0.078	0.470	0.450

Tellurium 8-13 numbers are reasonably close to those measured by Engelhard et al, but the solar numbers are not. FreeSnell's simulation of the HDPE with tellurium (ordinary-ray) in the infrared (on right) matches well with the graph in the paper; but the solar response (on left) has more than 3 times the transmission.

Neither changing to the extraordinary-ray nor varying the tellurium thickness resolves the difference; and such changes spoil the infrared match.

The problem is that tellurium is a semiconductor. Room-temperature tellurium has a direct band-gap of 0.32 eV (3.87 μm), which lies in between the two wavelength regions plotted. Solar radiation, nearly all of which has more energy than 0.32 eV, will be absorbed and inject carriers into the conduction band. That carrier cloud in turn makes the tellurium more metal-like and reflective.

That would be good news except that those carriers will also reflect thermal-infrared radiation. A screen covered with tellurium will not allow radiative cooling during daylight! An unscreened CoolRoof will have better daylight performance than tellurium screens.

The only loose end is why (in the plot to the right) does the absorption transition occur at 2 μm rather than 3.87 μm?

Nanocrystalline

• Mastai, Y., Diamant, Y., Aruna, S.T., and Zaban, A.
  TiO₂ Nanocrystalline Pigmented Polyethylene Foils for Radiative Cooling Applications: Synthesis and Characterization,
  Langmuir,17, 22, 7118, 7123, 2001, 10.1021/la010370g.

"The ideal shield should secure complete reflection of the solar radiation and complete transmission of the IR window region (8-13 μm)."

Table 1. Optical Function Values of the Different TiO2 Pigmented Shields

sample	TiO2film thickness (μm)	TSol	RSol	ASol	T8-13	R8-13	A8-13
A	0.12	0.610	0.381	0.009	0.765	0.172	0.063
B	0.45	0.412	0.581	0.007	0.731	0.154	0.115
C	0.75	0.273	0.712	0.015	0.681	0.162	0.157
D	1.08	0.220	0.684	0.096	0.651	0.153	0.196
E	1.82	0.166	0.763	0.071	0.546	0.178	0.276
sub-μm TiO2		0.323	0.601	0.076	0.391	0.174	0.435
PE		0.891	0.078	0.031	0.813	0.151	0.036

Mastai et al Sample C	Mastai et al Sample E

Unfortunately, they sacrificed solar reflection in the pursuit of transparency. Even for example E (the highest reflection sample) too much solar radiation reaches the roof, overwhelming cooling during daylight hours.

"... these measurements underestimate the transmittance values, since scattered transmitted radiation is not counted."

Higher solar transmittance only makes the daytime situation worse.

Mastai et al Sample C	Mastai et al Sample E

Semiconductor

• K.D. Dobsona,1, G. Hodesa, Y. Mastaib,
  Thin semiconductor films for radiative cooling applications,
  Solar Energy Materials & Solar Cells 80 (2003) 283-296.

Table 1
Values of the optical functions, R_8-13, A_8-13, T_8-13, R_Sol, T_Sol and A_Sol, of various materials for application in radiative cooling devices.

Samples	TSol	RSol	ASol	T8-13	R8-13	A8-13
LDPE 50 mm	0.891	0.078	0.031	0.813	0.156	0.031
Pigmented ZnS (50 mm)	0.346	0.540	0.114	0.641	0.193	0.166
Pigmented ZnO (50 mm)	0.403	0.429	0.168	0.582	0.184	0.234
PbSe HC NTA (200 nm) T=25°C	0.09	0.274	0.636	0.508	0.186	0.306
PbS HC NTA (200 nm) T=25°C	0.168	0.468	0.364	0.741	0.154	0.105
PbS HC TSC (150 nm) T=25°C	0.138	0.372	0.490	0.642	0.143	0.215
Pigment ZnS coated with PbS film	0.04	0.331	0.629	0.488	0.162	0.350
Pigment ZnO LDPE coated with PbS film	0.03	0.286	0.684	0.406	0.155	0.439

Covered CoolRoof

For deployment above a roof, the bi-color screen is over-designed in that the black bottom layer is not needed if the roof itself reflects solar radiation. Covering the CoolRoof analyzed earlier with just the white HDPE sheet (10 cm air gap) reduces the solar heating and increases the infrared emissions so that there are only 217 (2.5% of 8760) hours of net roof heat gains. Other than one hour at 22 W/m², the net heating of the roof over a typical year is always less than 12 W/m². Because the thermal transmission of the screen improves from 0.62 to 0.78, the nighttime cooling is 80% of that for the CoolRoof alone and 36% greater than for the bi-color screen.

Covered CoolRoof	Bi-color Cover

The peak screen heating is actually greater than for the bi-color screen. But because the screen's emissivity is lower, screen heating contributes less to roof heating.

Covered CoolRoof	Bi-color Cover

The bi-color cover cools itself (not the roof) below ambient more than the covered cool-roof. Again, this is because the thicker screen is more emissive, reducing the cooling available to the roof.

Covered CoolRoof	Bi-color Cover

Plotting net-radiative-transfer against ambient (dry-bulb) temperature shows that, while night cooling is nearly always available, day cooling is not reliable.

Covered CoolRoof—Diurnal Cooling	Covered CoolRoof—Nocturnal Cooling

Granular Aluminum Coated Cover

Reflection, Absorption, Transmission, 0.2 μm−2.0 μm	Transmission, Absorption, 8 μm−13 μm

FreeSnell Simulation

Sample	Side	TSol	RSol	ASol	T8-13	A8-13
30.nm layer of 80% Al in 13.um HDPE film	top	0.118	0.722	0.159	0.795	0.017
30.nm layer of 80% Al in 13.um HDPE film	bottom	0.118	0.679	0.202	0.795	0.019

There are 232 hours of net heat gain, nearly all of them less than +12 W/m².