What's the most surface area I can get out of something?

[BrunoPuntzJones]

Brian isnt wurking goood today.

Say I have a solid cube that is 3" on each side. 3x3 gives me 9 square inches. 6 sides, for 54 square inches in surface area. I think anyway...think I brained my damage this morning.

If I cut that cube in half, now I have 2 pieces that are 1.5"x3" on 4 sides, and 3"x3" on 2 sides. 1.5x3=4.5"sq on 4 sides is 18" then 9"x"2 for 36". Plus the other piece is 72" square inches of surface area.

At least I think that's right. I know it's not difficult at all, but my brain is a piece of shit this morning.

Carrying this out say a bazillion times, there has to be some limit that this approaches. I can't have infinite surface area. Is there a way to figure this?

What about if I have a 6x6x6 cube, and use a drill to make holes all the way through that are the size of a pencil lead, and spaced a pencil lead thickness apart. A big porous cube. That'd have to be a big ass number.

I ask because I bought some charcoal capsules one day. Each is about the size of a Tylenol. The back said that each capsule had something like 9 square meters of surface area. And couldn't I increase that by breaking one open and smashing the shit out of the stuff into an even finer powder?

 

[FoBoT]

yes, your pretty much right on it Brian

fish water filters use material like this to provide a large surface area for beneficial bacteria to grow on

 

[rivan]

Originally posted by: BrunoPuntzJones
Brian isnt wurking goood today.

Say I have a solid cube that is 3" on each side. 3x3 gives me 9 square inches. 6 sides, for 54 square inches in surface area. I think anyway...think I brained my damage this morning.

If I cut that cube in half, now I have 2 pieces that are 1.5"x3" on 4 sides, and 3"x3" on 2 sides. 1.5x3=4.5"sq on 4 sides is 18" then 9"x"2 for 36". Plus the other piece is 72" square inches of surface area.

At least I think that's right. I know it's not difficult at all, but my brain is a piece of shit this morning.

Carrying this out say a bazillion times, there has to be some limit that this approaches. I can't have infinite surface area. Is there a way to figure this?

What about if I have a 6x6x6 cube, and use a drill to make holes all the way through that are the size of a pencil lead, and spaced a pencil lead thickness apart. A big porous cube. That'd have to be a big ass number.

I ask because I bought some charcoal capsules one day. Each is about the size of a Tylenol. The back said that each capsule had something like 9 square meters of surface area. And couldn't I increase that by breaking one open and smashing the shit out of the stuff into an even finer powder?

9 square meters sounds quite high for something like that, but they do make stuff specifically to have high surface area in small packages, like bioballs, which are used to encourage bacteria growth for fishtank filtration.

 

[Tiamat]

surface area numbers can get very large especially for microporous structures.

 

[Canai]

It would probably stop when you are measuring the surface areas of subatomic particles.

 

[LS20]

Originally posted by: BrunoPuntzJones
And couldn't I increase that by breaking one open and smashing the shit out of the stuff into an even finer powder?

yes.

you wont get infiniticate surface area...but you could APPROACH it... but youre bound to how finely you canm grind it

 

[MegaVovaN]

Probably limit is when you spread the stuff 1 molecule thick.
For example, one drop of oil can be spread on water until it is 1 molecule thick layer - that's when it will have highest surface area.

If you spread your cube in a layer 1 molecule thick, it will have much more surface area than if you drilled your holes in it.

edit:

Originally posted by: Canai
It would probably stop when you are measuring the surface areas of subatomic particles.

No, because if you break it in subatomic particles, it won't be that substance anymore.

 

[Canai]

Originally posted by: MegaVovaN
Probably limit is when you spread the stuff 1 molecule thick.
For example, one drop of oil can be spread on water until it is 1 molecule thick layer - that's when it will have highest surface area.

If you spread your cube in a layer 1 molecule thick, it will have much more surface area than if you drilled your holes in it.

What if you separate every molecule though? Wouldn't that increase the surface even more?

 

[FoBoT]

Originally posted by: MegaVovaN
If you spread your cube in a layer 1 molecule thick, it will have much more surface area than if you drilled your holes in it.

that would be more like a pancake or a plane than a cube

i guess it might be a very flat rectangle

what shape are those molecules?

 

[MegaVovaN]

Canai: If you separate every molecule, you will have more surface area, but it may not be the same substance anymore - there is such thing as molecular structure. Many substances aren't individual molecules.

FoBoT: Didn't know OP wanted to preserve a geometrical shape. I don't know what shape molecules are, not my cube But I guess if they are square, it could be a very flat rectangle.

edit: (geometrical SHAPE, not geometrical cube)

 

[Canai]

Originally posted by: MegaVovaN
Canai: If you separate every molecule, you will have more surface area, but it may not be the same substance anymore - there is such thing as molecular structure. Many substances aren't individual molecules.

FoBoT: Didn't know OP wanted to preserve a geometrical shape. I don't know what shape molecules are, not my cube But I guess if they are square, it could be a very flat rectangle.

edit: (geometrical SHAPE, not geometrical cube)

Right, but if we're not going to the subatomic level, then the greatest surface area would be the smallest single pieces that the substance can be while still being the substance. Single molecules (assuming we're talking about any 'pure' substance).

 

[FoBoT]

so would pure elements be able to have a larger area than other stuff?

or is a blob of an element, like gold, still organized into molecules even though the whole thing is all one element, only gold atoms for instance

 

[gorcorps]

The technical physical limit you can get a material down to while it still being that material is it's unit cell. The size and number of atoms in a unit cell depend on the material in question, so in order to figure this out you'd have to specify the material. Many unit cells are just cubes, but there's a few with awkward shapes like hexagons. Most pure metals have a fairly simple cubic structure so the easiest way is to assume you're talking about a pure metal.

Take for example pure copper. Copper has a 'face-centered-cubic' crystal structure, meaning it's unit cell has a copper atom at each corners of the cube, as well as one in the middle of each face. Check wiki for an atomic radius... which is 135 picometers (135*10^-12 meters). Using geometry arguments you can find the side length of a copper unit cell to be 381.8 picometers. So calc surface area on that and you get 8.748*10^-19 sq. meters of surface area per unit cell, or 1.356*10^-15 sq. inches.

This isn't the best way to go about this as you really should treat each atom as a sphere and figure out the SA that way, but you get the idea. I'm a materials engineer... and I have no life

 

[MegaVovaN]

Originally posted by: gorcorps
The technical physical limit you can get a material down to while it still being that material is it's unit cell. The size and number of atoms in a unit cell depend on the material in question, so in order to figure this out you'd have to specify the material. Many unit cells are just cubes, but there's a few with awkward shapes like hexagons. Most pure metals have a fairly simple cubic structure so the easiest way is to assume you're talking about a pure metal.

Take for example pure copper. Copper has a 'face-centered-cubic' crystal structure, meaning it's unit cell has a copper atom at each corners of the cube, as well as one in the middle of each face. Check wiki for an atomic radius... which is 135 picometers (135*10^-12 meters). Using geometry arguments you can find the side length of a copper unit cell to be 381.8 picometers. So calc surface area on that and you get 8.748*10^-19 sq. meters of surface area per unit cell, or 1.356*10^-15 sq. inches.

This isn't the best way to go about this as you really should treat each atom as a sphere and figure out the SA that way, but you get the idea. I'm a materials engineer... and I have no life

excellent post :thumbsup:

 

[gorcorps]

Originally posted by: MegaVovaN

Originally posted by: gorcorps
The technical physical limit you can get a material down to while it still being that material is it's unit cell. The size and number of atoms in a unit cell depend on the material in question, so in order to figure this out you'd have to specify the material. Many unit cells are just cubes, but there's a few with awkward shapes like hexagons. Most pure metals have a fairly simple cubic structure so the easiest way is to assume you're talking about a pure metal.

Take for example pure copper. Copper has a 'face-centered-cubic' crystal structure, meaning it's unit cell has a copper atom at each corners of the cube, as well as one in the middle of each face. Check wiki for an atomic radius... which is 135 picometers (135*10^-12 meters). Using geometry arguments you can find the side length of a copper unit cell to be 381.8 picometers. So calc surface area on that and you get 8.748*10^-19 sq. meters of surface area per unit cell, or 1.356*10^-15 sq. inches.

This isn't the best way to go about this as you really should treat each atom as a sphere and figure out the SA that way, but you get the idea. I'm a materials engineer... and I have no life

excellent post :thumbsup:

I try

 

[gorcorps]

And just to get more precise: When you figure out SA using cubes like that you assume no void space in between the atoms... which isn't true. So like I said before you should use spheres for a more accurate representation.
There's 4 atoms per unit cell:
-1 on each corner, but only 1/8 of those atoms are part of this cell... and there's 8 of them. So all the corner pieces equal 1 atom
-1 on each face, but only 1/2 of those are part of the cell... and there's 6 of those. So all the face pieces equal 3 atoms
3+1=4 atoms total

SA of a sphere= 4(pi) r^2 where r is the 135*10^-12 we got from wiki. Multiply that by 4 atoms and you have a total TRUE SA of 9.16*10^-19 sq. meters instead of the 8.748*10^-19 we assumed w/ the cube. Not a big change, but enough to think about.

 

[Cerpin Taxt]

An interesting, relevant, albeit strictly academic principle:

http://en.wikipedia.org/wiki/Banach-Tarski_paradox

 

[FoBoT]

thank you for the awesome info gorcorps

 

[soydios]

maximum ratio of surface area to volume is a flat plane. minimum ratio is a sphere.

a sheet can be folded into a small volume.

 

[BrunoPuntzJones]

Sorry for taking so long to reply. Nice posts gorcorp.

I was thinking originally something like a cube of carbon, something that will stay elemental all the way down to basic structure. Which I guess you could get down to one molecule thick.

Say you have a 6"x6"x6" cube of carbon (assuming you get down to a chunk of some type of 100% carbon, not just a chunk of coal). Anyway to calculate out the surface area if you were to smush it down to unit cell thickness (theoretically)?

I'm guessing no one worries about someone creating a splitting device and taking that chunk of carbon and engulfing the Earth...then again, perhaps it's already been done, but at such a small thickness you'd never know...

Try to prove that negative

 

[gorcorps]

Carbon (in it's pure uncompressed form) is one of those tricky bastard ones that likes to assemble itself into hexagonal prisms instead of cubes... so the SA isn't as easy to calculate. It's still doable using the sphere method though. Compressed carbon though (diamond) forms a similar face-centered-cubic structure to the copper, but not quite as easy.

 

[MegaVovaN]

Originally posted by: gorcorps
Carbon (in it's pure uncompressed form) is one of those tricky bastard ones that likes to assemble itself into hexagonal prisms instead of cubes... so the SA isn't as easy to calculate. It's still doable using the sphere method though. Compressed carbon though (diamond) forms a similar face-centered-cubic structure to the copper, but not quite as easy.

Have fun trying to break a diamond down to 1 unit thick film

 

[Fenixgoon]

Originally posted by: gorcorps
And just to get more precise: When you figure out SA using cubes like that you assume no void space in between the atoms... which isn't true. So like I said before you should use spheres for a more accurate representation.
There's 4 atoms per unit cell:
-1 on each corner, but only 1/8 of those atoms are part of this cell... and there's 8 of them. So all the corner pieces equal 1 atom
-1 on each face, but only 1/2 of those are part of the cell... and there's 6 of those. So all the face pieces equal 3 atoms
3+1=4 atoms total

SA of a sphere= 4(pi) r^2 where r is the 135*10^-12 we got from wiki. Multiply that by 4 atoms and you have a total TRUE SA of 9.16*10^-19 sq. meters instead of the 8.748*10^-19 we assumed w/ the cube. Not a big change, but enough to think about.

so pick something that's HCP instead of FCC not that it'll fix the voids entirely (damn you gibbs!) but it'll help


<--- in college for materials

 

[gorcorps]

Originally posted by: Fenixgoon

Originally posted by: gorcorps
And just to get more precise: When you figure out SA using cubes like that you assume no void space in between the atoms... which isn't true. So like I said before you should use spheres for a more accurate representation.
There's 4 atoms per unit cell:
-1 on each corner, but only 1/8 of those atoms are part of this cell... and there's 8 of them. So all the corner pieces equal 1 atom
-1 on each face, but only 1/2 of those are part of the cell... and there's 6 of those. So all the face pieces equal 3 atoms
3+1=4 atoms total

SA of a sphere= 4(pi) r^2 where r is the 135*10^-12 we got from wiki. Multiply that by 4 atoms and you have a total TRUE SA of 9.16*10^-19 sq. meters instead of the 8.748*10^-19 we assumed w/ the cube. Not a big change, but enough to think about.

so pick something that's HCP instead of FCC not that it'll fix the voids entirely (damn you gibbs!) but it'll help


<--- in college for materials

Very true, which is why I started talking about Carbon afterwards .

slightly off topic: which school? I'm in materials as well at the Colorado School of Mines