100 Nano-Stories: Nomenclature Of Aerogels!

Episode #60: Fundamental Symbols In Aerogel Math!

Carlos Manuel Jarquín Sánchez
3 min readApr 6, 2021

Preface! ✨

It’s your favorite material science & nanotechnology enthusiast! Finally, we can begin our dive into Transparent Aerogels! We will be discussing many aspects behind the Radiative Transfer Model, Equation, and Theory!

Shoutouts to MIT for the research papers! :))

Check out the previous article for more explanation on The Radiative Transfer Equation (RTE)! Don’t worry, it’s only a 3-minute read! 😃

In the meantime, allow me to introduce the Nomenclematures that we will be discussing to break down the models behind the transparent aerogel research and theories!

Nomenclatures Explained! 💡

Definitions! 🔑

Nomenclatures mean a system of names, symbols, and terms for a certain branch of science, mathematics, arts, etc.

For example, there are certain rules you have to learn to understand calculus, soccer, quantum physics, etc. These rules, equations, or laws are nomenclatures for that specific branch of interest!

Now that we know what Nomenclatures mean, let’s explain some of the common nomenclatures we will encounter in mathematical aspects of aerogel technology!

Main Nomenclatures Of Aerogel! 🔑

e(b) → Blackbody Emissive Power.

K(R) → Mean Extinction Coefficient.

n → Index Of Refraction.

q̇ → Heat Flux (W m^-2).

R(total) → Total resistance (Pressure).

Tnλ → Spectral Transmittance (Light).

ε → Porosity.

λ → Wavelength.

σ → Stefan–Boltzmann Constant.

β → Extinction Coefficient.

∝ → Deformed Factor.

Definitions! 🔑

ε This is the symbol used for porosity (Epsilon). It’s used for arbitrarily small positive quantities in mathematical analysis. It will approach zero, but not reach zero.

∝ → In aerogels, this “deformed factor” can be used to describe the small stresses that can occur under capillary tension/pressure when drying the aerogels. It changes the shape of the aerogel (either on the corners or the interior of the silica framework) via applying pressure.

e(b) → The energy of thermal radiation emitted in all directions per unit time from each unit area of a surface at any given temperature via Black body Radiation. If the blackbody emissivity is 1, it will emit all its potential blackbody radiation. If the blackbody emissivity is 0, it will reflect all the radiant energy of the object at a certain temperature.

n → It’s a measure of the bending of a ray of light when passing from one medium/object into another object/material.

q̇ → It’s the rate of heat energy that passes through the surface of a material. The unit to express the rate of heat energy is W/m².

σ → A constant of proportionality in the Stefan-Boltzmann Law, which in simple terms, it’s used to measure the amount of heat radiated from the black body of the total “power” transferred via all wavelengths of light increasing because of the temperature of the subject/material. (5.67 × 10− 8 W/m2K4).

β → A measure of the rate of diminution/reduction of transmitted light via scattering and absorption for a medium/material.

Closing Thoughts! 💭

This was a brief introduction to many symbols that we will have to encounter on our mathematical journey through aerogel technologies via thermodynamics, chemistry, and optics!

Author’s Note:

I may not be 100% accurate, since I do not have enough knowledge on these topics and background to give you a clear response, but I will be talking to scientists on these topics and learning higher-level math as quickly & efficiently as possible to express these discoveries in simple terms! 😄

See you tomorrow for Van der Waal Forces! ✌🏽

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