# Preface! ✨

It’s your favorite material science & nanotechnology enthusiast! Today, we will cover BET Surface Area Equations and how to calculate them for Carbon and Graphene Aerogels!

There is no article to prepare you today, reader! Let’s begin today’s topic! 😃

Author’s Note:

Not everything here is 100% accurate. I am just a kid who enjoys researching the materials of the future. If there is anything wrong here, please let time know so I can make the article more accurate! Thanks! 🙏🏽

# What Is BET Surface Area? 💡

## What Good Is It For? 🔑

To calculate the surface area of porous solids like aerogel, the BET Surface Area Equation allows calculating the total surface area by the amount of inert/non-reactive gas atoms/molecules adsorbed from the aerogel!

Secondly, when we go to the nano-scale (or a billionth of a meter), the properties of aerogel start to get. . . weird. The surface area of aerogels increases on the nanometer size/scale.

So how can we calculate this phenomenon on the nanoscale? With the BET Surface Area Equation.

BET Surface Area Equation → It measures Surface Area based on physical gas adsorption on a solid surface/material.

## But Why Does BET Work For Aerogels? 🔑

The BET Surface Area Equation only works if the solid material has these qualities:

• The material has to adsorb the molecules of inert gas.
• The material is a physical adsorber.
• The forces that attach the inert gas to the material are Van der Waal Forces.
• The layers of inert gas will form on top of each other on the surface and pores of the aerogel (aka multi-layers).
• The material is either a Type II (macropore material) or Type IV Isotherm (mesopore material). (Type I, Type III, and Type IV absorb the inert gas particles.)

However, there will be occasions where some pores of the aerogel will not be accessible for the inert gas to fill in, so a smidge of surface area will not be calculated. For those inaccessible pores, it doesn’t matter because we’re at the nano-scale (1-billionth of a meter). If the inaccessible pores were bigger than a few nanometers, then we would have a problem. 😛

For those wondering how adsorption of the inert gas would look like on the aerogel, here is a photo of that below.

## Definitions of BET Surface Area → Aerogels! 🔑

Surface Area → A measure of the total area that the surface of a 3-dimensional object covers/occupies.

BET → Brunauer, Emmett, and Teller; the scientists that created the BET Surface Area Equation.

BET Surface Area Equation → It measures Surface Area based on physical gas adsorption on a solid surface/material.

Adsorption Particles/molecules of something will collectively add up on the surface of a material. In some way, you could say the particles are “resting” on the material.

Physical Adsorption (Definition)The adsorbates stay on the surface of the adsorbent via physical forces (London Dispersion Forces, Van der Waal forces, hydrogen bonds, etc.).

Physical Adsorption (Properties) → Physical Adsorption can create multi-molecular layers on the surface of the material. Adsorption increases as the pressure of the adsorbate increases.

AdsorbateThe particles that stick or “rest” on top of the material (aerogel).

AdsorbentThe material that the particles stick to or “rest”.

Absorption Particles/molecules are moving into another substance. In some way, they are being sucked up by the material and are being spread out widely.

Mesoporous → Solids/Materials with pores between 2 nanometers — 50 nanometers in diameter; aerogels are mesoporous materials.

Isotherm → A line representing changes of volume or pressure at a constant temperature (records & calculates various pressures of gas in the sample cell/aerogel due to adsorption and desorption).

Adsorbate Cross-Sectional Area → Area/Space that is covered by the inert gas/adsorbate.

Relative Pressure → Equilibrium Adsorption Pressure (p) to the Saturation Vapour Pressure (p₀).

Saturation Vapour Pressure → There are as many molecules returning to the liquid state as there are evaporating in a closed container, and this balance of liquid and gas is known as The Saturated Vapour Pressure.

Pores → Openings/holes in a material where gas or liquid can pass.

Mesopores → Pores between 2–50 nanometers (in diameter).

Macropores → Pores that are greater than 50 nanometers (in diameter).

Mesopores → Pores that are smaller than 2 Nanometers (in diameter).

Mole → 6.02214076×10²³ particles, which may be atoms, molecules, ions, or electrons. For example, a mole of socks is 6.02214076×10²³ socks. That’s a lot.😅

Author’s Note:

I decided to move the definitions up here instead of at the end of the article because these words will show up more frequently as we go further into the article. So for me, it made sense to put them here so you won’t have to scroll down and find them. :)

## BET Surface Area Analysis → Aerogels: Fundamental Concepts! 🔑

In BET surface area analysis, the pore size and pore volume are measured and porosity using mass and volume of carbon aerogels is calculated.

As I mentioned earlier in the article, we need an inert/non-reactive gas to adsorb/“stick” to the aerogel. The forces that attach the inert gas to the material are Van der Waal Forces. Adsorption increases as the pressure of the inert gas molecules increases.

The gas must also be able to free itself from the aerogel (via desorbtion) by decreasing the pressure of the gas at a constant temperature.

The best inert/non-reactive gas for calculating the BET Surface Area is nitrogen (N₂).

Why nitrogen? Because it’s non-reactive to the carbon aerogel and is weakly bonded to the carbon aerogel via Van der Waal forces. Additionally, you can depressurize the nitrogen gas from the tubes at the nitrogen will “detach” from the aerogel. Finally, nitrogen’s electron cloud (aka the probability of finding the electrons in nitrogen) reaction to an electric field (polarizability) is low because of the very weak Van der Waal Forces.

## How Does Nitrogen Adsorption Work For Aerogels? 🔑

The boiling point of Nitrogen → 77 Kelvin | -196° Celsius.

Why this temperature?

Because the nitrogen critical temperature is 126.2 K | −146.9 ° Celsius (Properties of both gas and liquid exist at critical temperature). Anything below this critical temperature will be a gas, and the nitrogen gas can be adsorbed by the surface of the aerogel.

Because of this, the BET Theory + Equation gives you the volume of the nitrogen gas adsorbed to the surface area of the carbon aerogel.

The cross-sectional area of Nitrogen → 0.162 nm² (nanometers squared).

Why this number?

This number is used to calculate the area/space that is covered by the nitrogen gas, and this is the number for the space that is covered by (N₂).

Okay, but how can we determine the isotherm and the surface area via the BET Equation?

## IUPAC Adsorption Isotherms Chart! 🔑

Carbon Aerogels are Type IV Isotherms, which means that they form multiple layers of nitrogen gas. After the multiple layers of nitrogen cover the surface of the aerogel and all the accessible pores, they undergo capillary condensation.

Capillary Condensation → Nitrogen Gas that was trapped in the pores of the aerogel condenses (get close together; changes) into a liquid state.

Below is the Adsorption states for a Type IV Isotherm:

This graph doesn’t mean much, but when we add the key/meaning to the curves, things get a bit more understandable. . . 😉

Because we used an inert gas (nitrogen), the equilibrium adsorption pressure stays the same, but it will increase the total pressure in the system. This is why the line goes up. :)

Finally, here comes the mathematical equations to explain the rise and fall o adsorption, the BET Surface Area, and my will to stare at the computer screen. 😂

## Math Equations (Bonus)! 🔑

To find the surface area of a carbon aerogel, we need to find the monolayer adsorbed gas volume (v(m)).

Remember, carbon aerogels are both microporous and mesoporous, so we have to pay close attention to the symbol “c”, the BET constant. “c” relates to the energy of adsorption in the first adsorbed layer (monolayer). It’s an indication of the magnitude of the adsorbent/adsorbate interactions, but if the number exceeds 200, then the aerogel has a very high porosity (Hint: It Does exceed 200).

Author’s Note:

The following section will contain the equations to find the surface area of carbon aerogel. The problem is that I don’t have any numbers/values to plug into the equations. Why? Because I don’t have access to research papers with the process of finding the monolayer adsorbed gas volume. 😢

If the next section leaves you confused, I’m sorry, I tried to do my best. But I’ll see if I can get my hands on other papers to make the last section easier for you, reader. I promise! 😁🙏🏽

## Finding Surface Area! 🎉

To find the surface area of a carbon aerogel, we need to find the monolayer adsorbed gas volume (v(m)).

The answer is (thank god) described in this color-coded diagram below:

The straight line (linear) is the BET Equation (shown in red, green, blue, & purple) with values between 0.05 & 0.35, which assumes that the adsorbent isotherms (how the nitrogen gas will react with adsorbent surfaces), will increase at a steady pace when it comes to micropore filling and monolayer adsorption.

Assuming we found the monolayer adsorbed gas volume, we can finally plug in the number to find the surface area of carbon aerogels:

# Closing Thoughts! 💭

550–1400 m²/g of carbon aerogel may not sound like much, but let me use a football field as an analogy.

A football field’s surface area is 5300 m² and an average surface area for carbon aerogels is 900 meters squared per gram (m²/g).

The surface area of a football field is the playing field or where the football is in play, including the touchdown ends.

If you had 6 grams of carbon aerogel in your hand, you would have more surface area in your hand than the surface area (playing field) of a football field.

900 m²/g x 6 = 5400 m² surface area of carbon aerogels. 😮

Football Field Surface Area is 5300 m². 😮

See you soon for the final episode of “100 Nano-Stories: Bookmarked!” 🙏🏽