The Sharpness of Knives.

Factual Questions
1

There was this story in the news about this cutting implement found at a caveman site. It consisted of a sharpened she’ll. But the cutting edge was a reportedly one molecule thick.

This got me thinking. Is there, just going by the law of Physics, any limit to how sharp a blade can be? And what, for that matter, is the physical definition of sharpness (of a blade, of course).

Also, could a blade theoretically be infinitely sharp? I imagine, if such a thing were possible, simply moving it through air would split atoms. Am I right?

:slight_smile: :slight_smile: :slight_smile:

2

Is there a link to this story?

3

If there was, I would have provided it right away:).

No, I don’t remember exactly where or when I first heard the story.

Actually, I think I heard it on TV, which would make adding a cite even more difficult.

Sorry.

4

I’d say that any cutting implement has a cutting edge one molecule thick, at any point. After all, some molecule has to be at the forefront, right?

5

Atoms are the bottom level of granularity in materials. (Yes, I know there are smaller levels that make up atoms but you don’t build things out of them.) So you can’t have a knife so sharp that it would cut an atom in half; the cutting edge of that knife is itself an atom.

6

You might be interested in this:

Glass is a material that was available way-back-when; if the caveman you mentioned didn’t use a shell, he might have gotten the same results from a chunk of obsidian or flint.

If sharpness is defined by the radius of curvature of the edge, then a blade with a molecular edge is about as sharp as you can get. This is handy if you can’t or don’t want to employ a sawing motion (e.g. when shaving your face, or using a planer on wood). If you add serrations to the edge, you can cut faster using a sawing motion, but that’s a different kind of cutting.

You can’t use a sharpened edge to cut through atoms; this is like asking if you can cut a baseball with a baseball bat.

7

Chuck Norris can.

[2003 humor archive OFF]

8

The word “atom” comes from the Greek word atomos, which means “uncuttable”.

Edges are sharp because they reduce the surface area being acted on by a given force. It’s hard to squeeze an orange in half, but you can cut it with a knife easily enough. That’s because the edge of the knife reduces the area under pressure and enormously increases the pressure per unit of surface.

One of the limits on how sharp an edge can be is the strength of the material, so that the edge doesn’t deform under pressure. The material has to hold together under pressure so that it will cut without breaking or bending or squishing. That’s why diamonds and obsidian can have a sharper edge than steel - the material is harder and more resistant to bending or deformation. It’s also more brittle, which is why knives and swords are typically steel rather than obsidian, but that is a trade-off knife smiths and sword smiths have known for ages - the harder the material, the sharper it can be, and also the more brittle it will be.

Regards,
Shodan

9

  1. Sharpness equals thinness, simple as that.

  2. Something that is sharp but easily deformed or broken is probably not useful, so the best knife is thin enough, strong enough, and rigid enough. (Gold leaf is incredibly thin, and therefore should be incredibly sharp, but because it’s so malleable it wouldn’t cut much of anything.)

If you’re cutting only soft things, then a knife that’s extremely thin but not very strong will still work. If you’re cutting hard tough things, then you have to sacrifice some sharpness in order to gain some strength.

There’s more to it of course, but that’s a start, isn’t it?

Oh… An infinitely sharp knife is not there at all. :slight_smile:

(Infinitely thin things disappear, don’t they?)

10

In practice, a sharp knife is a knife with a very thin edge, the thickness of which increases very slowly as you move to the back (otherwise it’s a wedge not a knife) but where the overall thinness of the blade in conjunction with the material it is made from doesn’t leave you with an impractically fragile tool. A paper-thin knife blade isn’t practical: you’d snap it off too easily.

The various materials of which sharp knives can be made are, to varying extents, inclined to flake off or otherwise fragment when you try to make the edge thinner than a certain amount. The best materials are the ones hard enough to hold an edge (i.e., the act of cutting with it doesn’t dull it quickly), durable enough that they aren’t fragile to mild impact, and not too inclined to flake or disintegrate when you sharpen them (hence capable of getting to a very sharp edge) and not so hard that they’re extremely difficult to sharpen. Carbon steel is a favorite material for these reasons, although it is natively vulnerable to rust, and the modern preference for rustproof knives has led to the embrace of what is essentially stainless steel, which has traditionally been flaky (small bits and pieces of the blade crack loose when you try to sharpen it beyond a certain point). Attempts to address that have mostly provided decent blade materials but they tend on the whole to be very difficult to sharpen, not because they flake but because they’re often so hard that the sharpening activity doesn’t do much.

11

IIRC, in Batman Beyond there was an assassin called Curare who wielded a sword with a blade one molecule thick.

12

Jim B: Also, calcium carbonate isn’t totally insoluble in water, so if you find a cavemans knife carved from a seashell, I’d bet there isn’t a single molecule left of the original edge, but it’s all shaped from subsequent weathering.

13

Monomolecular wire

14

First of all, I must recommend to the OP (and anyone else whose interest is piqued) the following article:

It’s an outstanding, accessible discussion of what makes a knife sharp and why it’s hard to make sharp knives that last. It also gets the technical/metallurgical details right to an impressive degree.

[Emphasis added]

This is absolutely nitpicking, but diamond and obsidian don’t get sharper than steel because they’re harder or stronger–their hardness and strength make them useable at all.

We should be careful to differentiate between a blade’s sharpness and the strength and hardness of the underlying material. Diamond and obsidian blades can be sharper than steel, but not because they’re harder or stronger: it’s because they have a finer and narrower edge.

For example, you can make similarly sharp knives out of both glass and diamond. The diamond blade is harder and stronger; it will stay sharp much longer than a glass blade. But it’s not necessarily much sharper than a new glass blade.

(I imagine you’re quite aware of this, Shodan; it doesn’t invalidate any of your points).

One reason obsidian can be made sharp more easily than steel is that obsidian has no crystal structure–it’s volcanic glass–and steel does.[sup]1[/sup] While some martensitic inclusions are smaller (and much harder) than other grains in the same material, they’re both a lot bigger than the molecules that represent the lower limit of a glass or obsidian blade. It’s possible to grind an edge that’s finer than the width of the grains, but conventional knife-sharpening reaches its limit at this point.

With glasses like obsidian, you can knap a sharper edge than you could grind into a metal blade.

Diamonds also have a crystal structure, but I’m not sure what its size is relative to that of, say, a nice heat-treated steel. Diamonds are exceedingly hard and often enormously strong, so a diamond blade would feel very sharp if you could use one to slice a tomato. But they’re so small (a few millimeters long) and so expensive (several thousand dollars) that no one is making dinner with these things.
[sup]1[/sup] There’s such a thing as metallic glass; it’s made by cooling liquid metal very quickly. Yes, you can buy a knife made from a metallic glass, but they’re not as much of a materials slam dunk as one might imagine.

15

Huh! The Subtle Knife was so sharp it could cut through from one universe to another.

16

I owe you a beer. About 50 years ago, I read a sci-fi story about a wire so thin that if you strung it across a doorway, anybody walking through would be cut in half. About 30 years ago, something reminded me of it, and I tried to find it again. I was pretty sure it was by Larry Niven, but I couldn’t find it.

Your link led me to “Thin Edge,” by Gordon Garrett, and that was it. No wonder I couldn’t find it; if you had asked me whether I had ever heard of Gordon Garrett, I would have said no. But the story holds up, so I’m surprised I haven’t heard of him, and I’ll look for more.

ETA: and now that I’ve googled him, I see that he more often goes by “Randall Garrett,” and of course I’ve heard of him.

17

Ringworld, I think.

Nessus, a Pierson’s puppeteer, got one of his heads cut off by a piece of monomolecular wire (or maybe it was a piece of “Shadow Square” filament - I don’t remember)

18

BTW, when I said a blade ‘infinitely sharp’, I was speaking purely philosophically.

Interestingly enough, though, is that what was meant by the wire/Universe thing?

:slight_smile:

19

Stone Age Technology Still Makes the Best Blades – Awesci – Science Everyday

20

A knife is a type of wedge, if I remember my simple machines correctly.