# Preface

We have talked about the fundamental chemistry of aerogels and mathematics, but I havenât talked to you about why aerogels are garbage.

Wait, what do you mean, Carlos? I thought you LOVED aerogels!

I do, but when you hold a small piece of aerogel in your hand and try to pinch it or poke it, it ends up looking like this:

So today, weâre going to talk about why this happens and what can we do to strengthen the silica aerogel so it doesnât break and end up looking like blue pebbles!

Wait, Carlos! Will we need your previous article to learn about what we will be talking about?

We will be talking about something different from what we have been talking about in the past dozen articles, but if you would like to take a look at it, go ahead, reader!

# Why Are Aerogels Brittle?

The pores of the aerogel are where all the thermal, optical, and mechanical properties come from. So this means the way we fill up the pores with our solvent & the liquid CO2 will determine all of the properties. Some of the properties of silica aerogel are superinsulation, lightweight, hydrophobicity, elasticity, brittleness, etc.

For example, silica xerogel is basically dried gel, which means that its mechanical properties will not have that many applications as a silica aerogel that is dense & in one piece.

The three main causes for this brittleness are the porosity of the aerogel, the OH groups, and pore size distribution.

We have already talked about the hydrophobicity of aerogels, OH Groups, and the pore size distribution via Ostwald Ripening! So finally, we have to talk about porosity & why it makes aerogels brittle!

But Carlos, will you at least explain what they all mean?

Porosity in simple terms means an object or material that is full of tiny holes for water, air, heat, etc. to pass through. We commonly use an equation/ratio to calculate the porosity.

ÎŠ is the greek letter phi, and it is the symbol used to calculate the porosity of silica gel.

V(v) is the void volume or the volume of the solid.

V(t) is the total volume of the silica gel.

This is how we can determine the porosity of aerogel! Depending on their catalysts, drying preparation, etc., aerogel can have a porosity of 80â99.8%! This means that because of all the holes that are on the surface of the silica network, aerogel has the maximum potential to be 99.8% air by volume!

Crazy!!! đ€Ż

OMG, Carlos! Thatâs insane! But how can we calculate Porosity? Is there another equation that breaks down the porosity of aerogels?

# Porosity (ÎŠ) Explained!

ÎŠ = V(v) / V(t) is the equation in its final form, but we need to dissect how we can get to this simple equation.

This equation is what happens if we break the original equation down. ÎŠ is equal to 1 - P(b) / P(s).

But how did you get there, Carlos? How do you calculate the volume, mass, and density of the particles?

All the definitions of the letters will be in the vocabulary section below, but I will explain what this means. The total volume (V(t)) divided by the total volume of our silica aerogel is 1. Thatâs where our 1 comes from the silica gel equation. In simple terms, we divide by V(t) to describe â100% porosityâ minus âP(b)â / âP(s)â.

P(b) (a.k.a. Particle Density) is the mass of the solid structure divided by the total volume.

P(s) (a.k.a. Solid Structure) is the reciprocal/opposite of P(b). P(s) is the volume of the solid mass divided by the mass of the solid structure.

Now, what do we do, Carlos?

We are almost done with the equation, reader!

Now, we have the equation simplified to V(t) - V(s)/ V(t). But when we subtract the total volume minus the volume of the solid nanostructure, we end up with V(v)/V(t)!

Wait, Carlos, isnât that the original equation we had at the beginning for ÎŠ?

Thatâs exactly right, reader! What we just solved is how to find the porosity the easier way! If we used the original equation, we would have to waste time figuring out what V(v) is without any measurements!

So does this mean we could go on to the aerogel jacket now, Carlos? đ

Weâre one article away, reader! All we need to do is talk about the refraction of silica aerogels, and we can move on to the Aerogel Windows & Jackets!

# Vocabulary đ

V(t) â Total Volume of the piece of Silica Aerogel.

M(s) â Mass of the solid of the Silica Aerogel.

V(s) â Volume of the solid of the Silica Aerogel.

P(b) â Particle Density of Silica Aerogel.

P(s) â Density of the solid structure of the Silica Aerogel.

V(v) â The Emptiness (Air by Volume) of the Silica Aerogel.

Porosity â The measurement of the emptiness, or void, of a material/substance.

ÎŠ â The Greek letter âPhiâ; the symbol used to calculate the porosity of silica gel. It is also known as the symbol for âThe Golden Ratioâ.