🔬 optics

Robust Radiative Cooling in Functionalizable Silica Microsphere Paints

This study demonstrates that the radiative cooling performance of optically thick silica microsphere paints is robust to variations in particle diameter (2–8 µm) within the multiple-scattering regime, allowing microsphere size to be optimized for processing or surface chemistry without compromising cooling efficiency.

Original authors: Jorge Burgos, José Rodrigo Magana, Ares Lladós, Javier Pascualena Ferré, Sara Núñez-Sánchez, Juliana Jaramillo Fernández, Cefe López, Pedro David García

Published 2026-06-02

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CC BY 4.0

Original authors: Jorge Burgos, José Rodrigo Magana, Ares Lladós, Javier Pascualena Ferré, Sara Núñez-Sánchez, Juliana Jaramillo Fernández, Cefe López, Pedro David García

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you have a special kind of paint that acts like a "thermal mirror." Instead of just reflecting sunlight to keep things cool, this paint also acts like a radio antenna, beaming heat straight out of your house and into the cold vacuum of outer space. This process is called radiative cooling.

The scientists in this paper were trying to figure out if the size of the tiny glass beads mixed into this paint matters for how well it works.

Here is the simple breakdown of what they found:

The Setup: A Crowd of Glass Beads

Think of the paint as a thick layer of tiny, disordered glass marbles (microspheres) sitting on a surface.

The Goal: To bounce sunlight away (so the sun doesn't heat it up) and to glow with infrared heat (so it can dump that heat into space).
The Question: Does it matter if the marbles are tiny (2 micrometers) or larger (8 micrometers)? Usually, in optics, size is everything. If you change the size of a lens or a mirror, the light behaves differently.

The Experiment: Testing Different Sizes

The team made four different batches of this "photonic glass" paint, using glass beads of four different sizes: 2, 4, 6, and 8 micrometers. They made sure all the paint layers were about the same thickness (roughly 25 micrometers).

They then took these samples outside on a sunny day in Barcelona to see how they performed. They measured:

How much sunlight they reflected.
How much heat they emitted into the sky.
How much cooler they got compared to the surrounding air.

The Big Discovery: Size Doesn't Matter (Once You're Thick Enough)

Here is the surprising part: All four sizes worked almost exactly the same.

To understand why, imagine a crowded dance floor:

The "Single Step" View: If the dance floor were very thin, a dancer (a photon of light) might only bump into one or two people before leaving. In that case, the size of the dancers (the beads) would matter a lot.
The "Deep Crowd" View: The scientists made their paint layers thick enough that a photon of light has to bounce around hundreds of times before it can escape. It's like being in a massive, dense crowd where you lose track of who you bumped into first.

Because the light bounces around so many times (a state the scientists call the "diffusive regime"), the specific size of the individual beads stops being important. The light behaves like a collective wave moving through a crowd, rather than bouncing off individual people.

The Results in Plain English

Sunlight Reflection: All four paints reflected over 93% of the sun's energy, regardless of bead size.
Heat Emission: All four paints were excellent at glowing heat into the sky (emissivity between 0.91 and 0.95).
Temperature Drop: When the sun was shining, all the paints stayed roughly the same temperature as the air. In the late afternoon and at night, they all cooled down about 4.8°C below the ambient temperature.

Why This is a Big Deal

Usually, if you want to make a high-tech material, you have to be incredibly precise. You might need to sort your glass beads to ensure they are exactly 4.0 micrometers, not 4.1 or 3.9. That is expensive and difficult.

This paper shows that because the paint works by "collective bouncing," you don't need that level of precision. You can use a mix of sizes, or choose a size based on what is easiest to manufacture or what chemical properties you need (like making the paint stick better to a specific surface), and the cooling performance won't suffer.

The Bottom Line

The scientists proved that for this type of "super-cooling" paint, once you make the layer thick enough, the exact size of the glass beads becomes irrelevant. This makes it much easier and cheaper to mass-produce these paints for real-world use, allowing engineers to focus on other things (like making the paint durable or colorful) without worrying about ruining the cooling effect.

Technical Summary: Robust Radiative Cooling in Functionalizable Silica Microsphere Paints

Problem Statement
Passive daytime radiative cooling (RC) relies on materials that simultaneously exhibit high solar reflectance (>90%) and strong thermal emission within the atmospheric transparency window (ATW, 8–13 µm). Disordered coatings based on silica (SiO₂) microspheres are a promising scalable platform for this purpose, utilizing multiple Mie scattering to enhance reflectivity and porous structures to boost emissivity. While particle-size optimization is traditionally considered critical for maximizing single-scattering efficiency, the behavior of these systems in the "multiple-scattering" or diffusive regime remains unclear. Specifically, it is unknown whether the microsphere diameter significantly influences radiative cooling performance once the coating thickness ( $L$ ) greatly exceeds the transport mean free path ( $l_t$ ). Current literature suggests that optimization is vital for single-scattering efficiency, but it is not established if such constraints persist when collective light transport dominates.

Methodology
The authors investigated this question by fabricating and characterizing disordered photonic glass coatings using commercial silica microspheres with nominal diameters of 2, 4, 6, and 8 µm. The coatings were deposited onto highly reflective substrates to a uniform thickness of approximately 25 µm. The study employed a multi-faceted characterization approach:

Optical Spectroscopy: UV-Vis reflectance and mid-infrared emissivity were measured to determine solar reflectance and ATW emissivity.
Coherent Backscattering (CBS): Measurements were conducted to quantify the transport mean free path ( $l_t$ ) and confirm the operation of the coatings within the diffusive transport regime ( $L \gg l_t$ ).
Outdoor Thermal Characterization: Long-term monitoring of coating temperatures under direct sunlight (Barcelona, October 2025) compared against ambient air and reference substrates.
Dissipated Power Measurements: A resistive heater was used to impose controlled temperature differences ( $\Delta T = 5–30$ °C) to measure net cooling power ( $P_{net}$ ) and estimate solar absorption via energy balance analysis.

Key Results

Diffusive Regime Confirmation: Coherent backscattering measurements revealed transport mean free paths ( $l_t$ ) ranging from ~3.7 µm (for 2 µm particles) to ~7 µm (for 8 µm particles). In all cases, the coating thickness ( $L \approx 25$ µm) was significantly larger than $l_t$ (by factors of 3.5 to 7), confirming that light transport is governed by collective multiple scattering rather than individual particle resonances.
Spectral Invariance: Despite measurable differences in microscopic scattering properties and $l_t$ , the macroscopic optical properties remained robust. All coatings exhibited solar reflectance between 93.6% and 95.3% and ATW emissivity between 0.91 and 0.95. These values varied by less than ~3% across the full diameter range.
Thermal Performance: Outdoor thermal measurements showed that all four coating sizes maintained temperatures nearly identical to ambient air during peak solar irradiance (~800 W/m²). In the late afternoon, all coatings achieved a maximum temperature reduction of 4.8 °C relative to reference surfaces. Post-sunset, they cooled up to 3.7 °C below ambient.
Cooling Power: Nighttime radiative cooling powers ranged from 44 to 61 W/m² across the different particle sizes, showing no systematic dependence on diameter. Thermally estimated solar absorptions (5.5–7.6%) aligned closely with spectroscopically measured values (4.8–6.4%), validating the thermal measurements.

Key Contributions and Significance
The primary contribution of this work is the demonstration that radiative cooling performance in optically thick, disordered photonic glass coatings is robust to variations in microsphere diameter when the system operates deep in the diffusive regime.

The paper claims that once the condition $L \gg l_t$ is met, the cooling performance becomes insensitive to the exact particle size. This finding challenges the conventional necessity of precise particle-size optimization for enhancing solar scattering in thick coatings. The authors posit that in this limit, light propagation is governed by collective transport properties rather than individual particle resonances.

Significance for the Field
The authors argue that this diameter invariance is a defining feature of radiative cooling in diffusive coatings. This robustness has practical implications for material engineering:

It decouples thermal performance from strict constraints on colloidal assembly and particle-size control.
It allows the selection of microsphere size based on other factors, such as surface chemistry requirements or processing constraints.
It facilitates the integration of radiative cooling with the broader toolbox of colloidal chemistry, enabling functionalization and chemical tuning without compromising thermal efficiency.

The study concludes that scalable, multifunctional cooling materials can be developed without the need for the precise particle-size control previously assumed necessary, provided the coatings remain optically thick and operate in the diffusive limit.