100 Nano-Stories: Beer-Lambert Law!

Episode #67: Liquid & Gas + Absorption Coefficients!

Carlos Manuel Jarquín Sánchez
5 min readApr 13, 2021

Preface! ✨

It’s your favorite material science & nanotechnology enthusiast! It’s time to introduce another concept in creating transparent aerogels!

For all the new readers, I highly recommend checking out the previous article on the single-scattering albedo to understand some of the topics we will be discussing!

Don’t worry, the article is only 3 minutes long! 😃

A brief overview of the single scattering albedo is:

  • Single-Scattering Albedo is used to define the scattering and absorption in a medium/material.
  • Equation → ωλ = σ(s)/ β(e)
  • ω = Single-Scattering Albedo symbol.
  • σ(s) = The Scattering Coefficient.
  • β = The Extinction Coefficient. (sum of absorption and scattering coefficient).
  • λ = Wavelength Symbol.

But for now, let’s move on to the Beer-Lambert Law!

Beer-Lambert Law Explained! 💡

Definitions! 🔑

The Beer-Lambert Law relates the logarithmic dependence of loss of radiant energy/intensity through a medium/material. The direction of the energy can be ignored. In the case of aerogels, the energy comes from the light itself.

The Beer-Lambert Law states that there is a dependence between the transmission of energy (light) through the aerogel and the product of the absorption coefficient (all the light that is absorbed by the aerogel) and the length/distance of the material from one end to the other.

Abbsorbant Coefficient Equations! 🔑

However, the absorption coefficient is composed of many other constants that we need to be wary of.

The absorption coefficient is made up of this equation:

β(a) = A/d

β(a) → Absorption Coefficient (determines how absorbent the material will absorb certain wavelengths of light). Usually measured in cm^-1.

A → Absorbance in the material. The equation for absorbance is log10(I/I(0)).

I(0) → Original intensity of the light (before it passed through the material).

I → Intensity of the light after it passed through the material.

d → Distance/Length the light traveled through the material.

Basically, if the Absorbant in the material results in 0, the transmissivity of light/transparency in a material is 100%. If the absorbency ends up in 1, the transparency of the material is 10%. This means that absorbance has a logarithmic dependence on transmissivity/transparency.

The smaller the number for absorption, the more transparent our aerogels can be! 😁

Transmissivity Equation! 🔑

Now that we know what the meaning of our absorption coefficient is about, we can move on to the bigger picture of the Beer-Lambert Law!

We mentioned in the absorbance coefficient that we need to divide the final intensity of a specific wavelength of light over the initial intensity of a specific wavelength of light.

The (x) located to the final intensity (I) means it is flowing in the x-direction (x can mean either up, down, left, right, etc., you can decide the direction if it makes it easier for you to understand 😄)

In this case, we can have two ways of expressing the transmission equation (shown below):

But in the end, we end up with the transmissivity (t) of a certain wavelength of light. The (x) means the distance traveled. (t) is the transmittance, which is the light that was able to be directly transferred to the other side of the material without scattering or being absorbed.

Aerogel Applications! 🔑

With these equations, we can calculate the haze in any aerogel, whether it is transparent, silica, polymer, etc.

To calculate haze, we would use this equation:

T → Transmissivity.

If you notice, it follows a similar equation as the absorbance (log10 (I)/I(0)).

What is happening in this equation is the haze that an aerogel that scatters more than absorbs will result in a higher haze than a partially absorbing medium at the same optical depth (“distance”).

The reason this phenomenon occurs is that absorption does not contribute to the haze/opaqueness in the aerogel (because once absorbed by the particles in the aerogel, it can no longer escape/scatter around).

This way, we can calculate the diffuse intensity of the aerogel, and the overall transmittance, or the light that makes it through the other side without being scattered!

Closing Thoughts! 💭

Well, that was a little tough to write, but as Manasi Patil once said:

“It's the hard that makes it beautiful!”

I will be talking a bit more about organic chemistry for the next article! See you soon! ✌🏽

Vocabulary! 📓

The Extinction Coefficient → A sum of the absorption coefficient and the scattering coefficient; β(e).

Single-Scattering Albedo Defines the scattering and absorption in a medium/material.

Absorption Coefficient(β(a))

Scattering Coefficient(β(s))

Wavelength Symbol → λ

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.

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.

The Beer-Lambert Law A relation of the logarithmic dependence of loss of radiant energy/intensity through a medium/material. The direction of the energy can be ignored. In the case of aerogels, the energy comes from the light itself.

Connect →🔗



Personal Newsletter


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