# 100 Nano-Stories: Haze In Transparent Aerogels (Math)!

## Episode #56: Haze Equation!

# Preface!✨

It’s your favorite material science & nanotechnology enthusiast! Finally, we can begin our dive into Transparent Aerogels! If you are confused,** I highly recommend understanding the concept of transparency in aerogel below!**

Briefly, transparency means that all the light will pass through a material without being absorbed or reflected. This reflection/absorption is what creates **haze.**

Now let’s move on to the mathematical concepts for haze!

# Haze Equation Explained! 💡

## Equation! 🔑

Let’s begin with showing you the actual equation itself!

This may look easy to understand, but allow me to explain the equation piece-by-piece!

## Simplification! 🔑

Collimated light will enter the boundary/surface of the aerogel. **Collimated light **means that the light is parallel and will want to disperse/spread as least as possible. This collimated light will enter at an angle of 0 degrees **(θ = 0).**

But once the light enters the aerogel via the pores on the surface, **the light will interact with the aerogel particles and begin to scatter throughout the aerogel** causing the light to have a new direction than parallel throughout the aerogel.

In this situation, there are four outcomes for the light in the aerogel:

**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)**Absorption**(The light is absorbed by the aerogel particles)**Diffuse Reflection**(Light enters through the aerogel and is reflected the way it entered through the aerogel at an angle)

This is where the equation comes in handy! 😁

## Explanation! 🔑

Let’s focus on the first part of the equation!

To calculate the haze, we divide the Diffuse Transmittance over the Total Transmittance.

But Carlos, what is the rest of the Total Transmittance?

The Total Transmittance is the sum of the Diffuse Transmittance and the Direct Transmittance of the light that passes through the aerogel.

**We are ignoring the absorbed and reflected light because that is what causes haze! We want a percentage of efficiency in how much light passes through to the other side of the aerogel!**

*So to sum it up, 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! 💭

While it is possible to achieve close transparency, it is hard to achieve a low haze in an aerogel because of the interaction between the light and the silica particles and the network of the aerogel structure for solar/thermal/window applications. But the other reason why it is hard to calculate the maximum transparency is the aerogel particles and nanostructures themselves. The size of these particles makes calculating transparency a big challenge.

But I’ll tell you more about possible solutions tomorrow (with some mathematical formulas!) ✌🏽

# Vocabulary! 📓

**Collimated Light → **The light is parallel and will want to disperse/spread as least as possible.

**θ → **Lowercase Greek letter for the word “Angle”/ Theta.

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

**Transparency → **All 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.

**Absorption → **The light is absorbed by the aerogel particles.

**Diffuse Reflection → **Light enters through the aerogel and is reflected the way it entered through the aerogel at an angle.

# Bonus Resources! 💻

# Previous “100 Nano-Stories!” 🔖

*© 2021 by Carlos Manuel Jarquin Sanchez. All Rights Reserved.*