How can an ice-cube sized piece of Aerogel have the same surface area as roughly half the size of a football pitch

830 views
0

I recently watched a Veritasium video on Aerogel, where he stated “an ice-cube sized piece of Aerogel has a surface area of roughly the size of half a football pitch”. I know it’s true but I don’t understand how this is possible. Thank you

In: Mathematics

Imagine you have a block of wood. the surface area is whatever you can see, the six faces. Imagine you cut a hole in the middle of the cube. Now you can see more things, you can see the six faces (less the hole you cut); and the inside of the hole. Now imagine you cut several holes inside the hole, now you have even more surface you can see!

Aerogel is a bit like that. It’s essentially nothing but holes, and thus has a lot of “surface”. If you’d take all that “surface” and spread it out, you could cover half a football pitch with it. Sure, the blanket you created is so thin it’s practically invisible, but we never said it had to be very thick.

Take a solid cubic block of any material. The surface area (ignoring really microscopic features) is the total area of all sides of the block. Now picture that block as a sponge with lots of small holes in every part of the block. The surface area is now whatever parts of the surface area remain intact plus all those nooks and crannies, most of which are in the interior of the once solid block. This is going to be far greater than the surface area of the intact block. Now imagine that type of sponge-like construction on nearly microscopic scales. Just huge numbers of miniature small holes and tunnels cutting every which way through the material. Do this to a sufficient degree in material that can maintain structure despite being more holes than material and you end up with Aerogel, and a positively massive surface area compared to the size of the block.

To be frank, this is a really dumb way to discuss surface area, which is why it is confusing to you.

The point is that aerogel is super craggy, pitted, etc., like a complex maze, so that air (or anything) trapped inside them is highly unlikely to escape. This is why it’s a good insulator.

So at a very tiny level if you trace the surface you would have to follow the maze down through the crags to get back to the surface again, which is why the “surface area” is so large.

The reason this is a dumb way to describe it is that we usually don’t discuss surface area of other materials this way. Take, for example, a football pitch, which has a minimum (FIFA) dimension of 90mx45m. So half field is 45×45. But if you measure the “surface area” the same way you did the aerogel, you would be tracing each blade of grass up and down. But that’s not the way we measure surface area of a football pitch, and certainly defeats the purpose of using it as an example.

That ice-cube sized piece of Aerogel is ~99% air. The actual surface area of the gel includes all the parts of the gel within that cube which are exposed to air.

Here is what [it](https://str.llnl.gov/content/pages/january-2013/images/stadermann1_620.jpg) looks like when magnified.

So, have you ever seen the show Ozark? There’s a line in the show where they say Lake Ozark has more coastline than the entire state of California, supposedly due to all the inlets and fingers of the lake.

Well, think of that bit of Aerogel like Lake Ozark, but in 3D. It has so many small pits and microscopic crags in its surface, that it has more surface are than the entirety of a football field.