# Preface! ✨

It’s your favorite material science & nanotechnology enthusiast! Time to introduce the mechanism of what happens between the interactions of the particles in the aerogel and light!

I highly recommend you read the previous article to understand the fundamentals of optical depth and how it plays a huge role in the transparency of aerogels! 😃

Don’t worry, the article below is only 5 minutes long!

Briefly, a summarization of the previous article:

• The optical depth is the quantity of light that has been removed due to absorption, scattering, and reflection.
• If the optical depth is greater than 1/e or 1, the medium/material will be opaque, and photons will either be absorbed, reflected, or scatter many times before transmitting/leaving the aerogel. This means you can’t really see what’s on the other side of the material, and it can cause a haze because of the absorption or scattering of the incoming light.
• If the optical depth is less than 1/e or 1, the medium/material will appear transparent, and photons will either transmit directly through the material without being absorbed or scattered.

But for now, let’s cover more about what the mean free path is all about!

# Mean Free Path Explained! 💡

## Definitions! 🔑

The Mean Free Path is the distance a particle or photon will travel before colliding with something and being absorbed/scattered. The symbol for the mean free path is:

If you need a better explanation, the optical depth is the number/amount of mean free paths you have traveled through a medium/material when going straight in a certain direction. For example, if the distance is one mean free path, the optical depth is 1.

## Math Equations! 🔑

With that explanation of optical depth and mean free path, this means that the optical depth can be changed, but it can be equal to an absorption coefficient times the mean free path can be equal to 1!

Tau is actually tau “τ”, which is the variable we will give the optical depth. “τ” will have a value of 1. The subscript nu “ν” is the frequency/wave speed (measured in meters per second { m/s }). “∝” is the absorption coefficient (a rate at which radiation that enters a material decreases with depth/thickness of a medium/material).

However, the absorption coefficient “∝” is comprised of two variables.

“N” → The number of absorbers/ “particles” that can potentially absorb any incoming particle or photon divided by the total volume of the material.

“σ(v)” → This means the cross-section (cm²). The cross-section is a measure of the probability of an encounter between particles and will result in either absorption or scattering.

## Aerogel Application! 🔑

If you increase the number of absorbers/aerogel particles divided by the volume/thickness of the aerogel, the mean free path will decrease. This means that we can have an optical depth of less than 1, which will allow for the aerogel to be transparent!

To put it in simpler terms, we can decrease the particle size in the aerogel but spread out the particles in the aerogel divided by the thickness of the aerogel. Because of smaller particle sizes, we can rely less on the thickness, which will allow for a smaller and smaller optical depth! :)

# Closing Thoughts! 💭

Perfect! Now we know what the mean free path can do throughout the interaction, scattering, and absorption of photons and the particles inside the aerogel, and using the mean free path corresponding to optical depth!

See you tomorrow to talk about Single Scattering Albedo! ✌🏽

# Vocabulary! 📓

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

The Mean Free Path The distance a particle or photon will travel before colliding with something and being absorbed/scattered.

Cross-Section A measures the probability of an encounter between particles and will result in either absorption or scattering.

Absorption The light is absorbed by the aerogel particles.

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

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

# cjarquin0005@gmail.com

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## More from Carlos Manuel Jarquin Sanchez

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## Carlos Manuel Jarquin Sanchez

17 |Explorando y activando