100 Nano-Stories: Refractive Index + Rayleigh Scattering + Haze!

Episode #82: Final Explanations | Optical Properties!

Carlos Manuel Jarquín Sánchez
6 min readApr 27, 2021


Preface! ✨

It’s your favorite material science & nanotechnology enthusiast! Today, I want to talk more about the refractive index of aerogels and the effects of Rayleigh Scattering on the refractive index!

The article below is essential for you to understand the optical properties given below! Don’t worry, the article is only a 7-minute read! 😃

TL;DR → Refractive Index! 🔑

  • If the refractive index moves from a higher value to a lower angle, the ray of light is going to bend farther away from the normal line.
  • If the refractive index moves from a lower value to a higher angle, the ray of light is going to bend closer to the normal line.
  • Normal LineThe light from the air comes into contact with the surface of the aerogel.
  • Refractive IndexThe reduction of speed of the light and the bending of the light as it passes from one material to another.
  • The normal refractive index in an aerogel is between 1.005 - 1.26. The lowest an aerogel’s refractive index has ever been recorded is 1.0026, which is a smidge lower than the refractive index of air. (1.0029)

Author’s Note:

This was only an overview of the aerogel properties and how to calculate aerogel’s refractive index. If you are still confused, please read the article above to grasp all the concepts in their entirety.

Now that we have a good explanation, let’s move on to how the refractive index can determine how much haze & scattering occurs in our aerogel!

Refractive Index + Rayleigh Scattering! 💡

Connection! 🔑

Refraction/Scattering occurs because there is a difference in the refraction index between the air and the aerogel.

Author’s Note:

For today, we will use the refractive index of aerogels as 1.25.

Air Refractive Index → 1.0029

Aerogel Refractive Index → 1.25

However, the reason why scattering also occurs is that the aerogel is amorphous silica.

Amorphous means that the material structure (aerogel particles) is not in the form of a crystal. The aerogel particles do not have a defined/clear structure, which allows for the scattering of light to occur with the photons in the air.

Crystalline Silica Structure vs. Amorphous Silica Structure

The scatterers in the silica aerogel are the particles themselves. The size of the particles is around 50 nanometers, but the size of the particles will vary depending on the sol-gel process and the drying/reaction conditions.

Rayleigh Scattering Equations! 🔑

Normally, Rayleigh Scattering will only occur if the particles are smaller than 1/10 of the specific wavelength of light. (Particle Size << 1/10 (λ)). In the case of silica aerogels, the most common light that enters the aerogel is sunlight, which has a wavelength of around 500 nanometers.

1/10 of 500 nanometers is around 50 nanometers, which perfectly matches our size of the aerogel particles, but remember, the size of the particles could vary on other reaction conditions when making the aerogels.

But because of the silica aerogel, the scattering depends on the nanostructure of the silica particles (how they are arranged in amorphous silica).

The equation below is how to calculate the scattering intensity in a silica aerogel that has particle sizes of around 50 nanometers:

I = Scattering Intensity.

I₀ = Intensity of Light.

R = The distance the light is taking to scatter in the aerogel.

λ = The wavelength of the light entering the aerogel (mostly sunlight)

d = Diameter of the light scattering in the aerogel.

θ = The scattering angle of the light after it’s deflected by a particle in the aerogel.

n = Refractive Index of the aerogel.

1 + cos² = The measurement of the angle, you will measure from the cosine angle.

In this equation, this where the Intensity of the scattering is inversely proportional to the wavelength of light that is passing through the aerogel (blue light). In this case, the equation below can represent the relationship between the scattering density and the wavelength of the blue light:

This means that the scattering density is inversely proportional to one over the wavelength of light to the power of 4. Shorter wavelengths of light tend to be scattered more in the aerogel (Blue, Violet, UV Light).

Because most silica aerogels are amorphous, meaning that the aerogels particles aren’t arranged in a crystal-like structure, the Rayleigh Scattering occurs because it is blocking out all the larger wavelength of light that is transmitting through the aerogel.

This scattering may look nice at first glance, but this scattering is what hinders us from being able to reach transparency/clearness. (Hello, Optical Depth!) 😉

The Rayleigh Scattering in the aerogel is the light that is reflecting off/scattering in the aerogel because the particles are called haze.

In a previous article, I described the equation that MIT Professors and researchers have used for calculating haze.

The haze equation is the diffused transmittance of light divided by the sum of the diffused transmittance of light and the direct transmittance of light!

Closing Thoughts! 💭

There are two ways to eliminate the haze:

  • Aerogel Particle Size.
  • Overall Transmittance in Ultra-Violet (UV) Light, Visible Light, and Infrared (IR) Light.

See you tomorrow to explain more about calculating the transmittance in aerogels to mitigate the haze in aerogels! ✌🏽

Authors Note:

This was one of the final explanations of the optical properties of aerogel! I will post a few more, but I will be moving on to more of the chemistry side of aerogels soon to complete the iconic “100 Nano-Stories: Bookmarked!” 🎉

Vocabulary! 📓

Amorphous → The material structure (aerogel particles) is not in the form of a crystal /doesn’t have a defined/clear structure.

Refractive IndexThe reduction of speed of the light and the bending of the light as it passes from one material to another.

HazeIn aerogel, haze is defined as a lack of transparency, or that the aerogel looks somewhat cloudy rather than clear.

Density Mass per unit volume of a material/substance. (m / v)

Optical Depth → The quantity of light that has been removed due to absorption, scattering, and reflection; τ.

TransparencyAll the light will pass through a material, and it won’t be reflected, absorbed, or scatter in a material.

Direct Transmission Passes through the aerogel without changing direction.

Diffuse Transmission Passes through the aerogel at an angle, the angle of the light is no longer 0 degrees.

AbsorptionThe light is absorbed by the aerogel particles.

Diffuse ReflectionLight enters through the aerogel and is reflected the way it entered through the aerogel at an angle.

Scattering In terms of light, it’s the change of direction of electromagnetic radiation/light from its original path (direction).

Connect →🔗



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