# What is the amputationility of a monomolecular wire weapon?

Monomolecular wire weapons are a somewhat common element in science-fiction.

Including in this this fantastic image I found while looking into this:

Is the only infeasible thing in this image that the octopus would need bones to stand like that, or is the monomolecular whip also not feasible?

Let's assume that we have the ability to construct a monomolecular wire from any real material. That uses up the hand waving allowed for this question. Which material would we use, and how effective would it be for use as a blade or whip? (I have seen blades described as either rigid or a taught wire strung in a open frame. I don't care which one is used.)

To qualify as working or feasible, I'm interested in the wire not breaking while cutting through something of various densities, like a human arm. The effort required to do so, tensile strength, sharpness, etc seem all to factor into that one metric. Limb amputation. Let's call it amputationility.

So, can I cut off an arm with a monomolecular wire made of real materials?

If no real material would work, what minimum properties of a real material would need to be modified and to what value?

Note: I considered tagging this as hard-science. But given the possible requirement of a fantasy material I've left it off. However, I want answers to be as scientific as possible. An answer of "the material needs very high tensile strength" is not satisfactory, I want to know how high the tensile strength needs to be. Numbers people, show me some numbers.

• Is that an armored octopus??? Allow me to be the first to give you a number: +1. – Frostfyre Jun 16 '15 at 19:26
• @Frostfyre I know right? The image description was fun to write "armored octopus with monomolecular whip fighting dual-dagger-wielding monkey" – Samuel Jun 16 '15 at 19:31
• Does the weapon have to be exactly 1 monomolecular wire, or can it be a bunch of them together? The main issue I see with having a single wire would be that it doesn't cut very well - the the van der Waals force would probably "heal" whatever you just cut... – Aify Jun 16 '15 at 21:08
• Re. the image, it also seems unlikely that the wire would be visible like that: it'd be super-thin, and in order to glow it would need some kind of current, like a light bulb filament. That brings up a host of other problems. – sumelic Jun 16 '15 at 21:14
• @Saidoro Actually it says in the game manual that the image came from that the "octopi have been modified to include a flexible sheathe of cartilage" combined with " A careful system of powerful muscles joined to this sheathe allows the octopus to hold itself upright." They're clearly not in zero-g in the picture, the gravity may be lower, but they still have 'bones' to get around. – Samuel Jun 17 '15 at 19:15

## 5 Answers

Graphene is what you're looking for.

With a tensile strength of 130000 MPa, it has (IIRC) the highest tensile strength in the world.

So lets make a wire-thin sword!

I envision it to probably end up looking something like this:

      >----------------------------------------------<|
|||||||                                               |
L_______________________________________________|


where the ------- represent the blade, and the <| the tip that the other end of the blade is connected to, and the ||||> represents a handle. It's important to note that the wire is being pulled taut by the <| piece at the end of the blade. The L____| represents a structure similar to that of a hacksaw, in order to hold the wires tightly.

This is a slashing/chopping weapon.

How/Why does this work?

The "Graphene wire" is really a Graphene ribbon

Graphene itself contains elastic properties, which helps with the above concept of cutting. Even if the Graphene doesn't cut right away, the elasticity will help it to continue cutting as you swing the blade through your target. "Graphene sheets (with thicknesses of between 2 and 8 nm) had spring constants in the region of 1-5 N/m and a Young’s modulus (different to that of three-dimensional graphite) of 0.5 TPa."

Graphene also has amazing shear strength. Shear modulus of graphite was reported to be ~0.44 TPa. To give you some context, the shear strength of a carbon diamond structure is ~93 GPa. 1 TPa is 1000 GPa.

To answer your question: Yes, you can.

Unfortunately, because the human body is so variable, I can't find any actual numbers regarding how much force is required to tear off a limb - however, we should note that this blade doesn't apply force the same way a sword does.

A sword cuts and splits the target because it "wedges" it apart. In this case, however, because we have a monomolecular ribbon that's completely flat, we should be able to pass through the entire target (irrelevant of what the target is made of, but assuming you gave it a good chop with no deviation in blade angle) extremely easily, since all we're severing are molecular bonds. Forces at the molecular level are at the pico-Newton level (1pN = $10^{-12}$ N); what we exert on anything using anything at any given time exerts more force than what's required. Here's some more context: One pound of force gives us 43.62 Newtons. Even a toddler could exert one pound of force by accident - so if you gave this thing to a baby and he accidentally swung it through you, good luck.

Thank you to Samuel for pointing out some numbers for me: "the shear strength of the Graphene ribbon is maybe 4200 piconewtons / angstrom, while fibers in the skin, like collagen, have a shear strength of only 5.5 piconewtons / angstrom." These numbers show that along the same area, the ribbon has a shear strength of over 750 times that of collagen.

Skin seems easy to cut though. What about bone? Luckily for us, most of bone's elasticity comes from the collagen in it, which means we cut bone just as easily as we do skin.

For an adult? It cuts anything, and everything, better than warm butter.

Once you finish slicing, the limb will only be held on by suction and surface tension. Any movement, and it simply slides/pops off.

However, even regarding the above saying that it is possible in theory, this tool is much better suited to a hospital setting requiring quick amputations than a battle situation.

Strictly speaking, this would work as an amputation device, but would be sorely suited for battle if the opponents also had access to similar weapons. In that scenario, please refer to Ville Neimi's answer (2 to 4th paragraph) regarding why it would suck as a weapon. Note that in normal use, the Graphene should be strong enough to be reused over and over again. The hexagonal structure of the Graphene ribbon means that even if any edge atoms are lost, it doesn't matter - No matter which atoms you lose, you will always have a suitable cutting edge.

References:

R. R. Nair, M. Sepioni, I-Ling Tsai, O. Lehtinen, J. Keinonen, A. V. Krasheninnikov, T. Thomson, A. K. Geim, I. V. Grigorieva. Spin-half paramagnetism in graphene induced by point defects. Nature Physics, 2012; DOI: 10.1038/nphys2183

http://www.graphenea.com/pages/graphene-properties#.VYCbRkZ8ork

https://en.wikipedia.org/wiki/Graphene#Thermal_conductivity

http://poplab.stanford.edu/pdfs/PopVarshneyRoy-GrapheneThermal-MRSbull12.pdf

https://web.engr.illinois.edu/~aluru/Journals/APL11.pdf

https://en.wikipedia.org/wiki/Bone

• +1 for the math and research and smart-sounding stuff. I have no idea if any of it is right, but it's really impressive nonetheless. My only qualm is that the maglev you propose would probably make the magnetic tip swing like a pendulum, rather than holding it in place relative to the orientation of the handle. That would lead to a funny defense: the defender would just swat the magnetic lump at the end, and the whole nanotube would swing back around and slice the attacker in half. – BrettFromLA Jun 16 '15 at 23:12
• Check out carbyne! en.wikipedia.org/wiki/Carbyne phys.org/news/2013-08-carbyne-stronger-material.html Might be another possible candidate. @Samuel – Mann Jun 17 '15 at 9:54
• @Bobson Burki made an excellent observation that the whip would wrap around a limb, causing a loop that could then be pulled closed. It certainly seems like an effective way to use the whip form. – Samuel Jun 18 '15 at 20:20
• Heck, I've seen special knives so carefully sharpened that people have accidentally cut off fingertips/fingers cleanly. With a monofilament blade? not a problem, though you'd have to worry about knicks... – Isaac Kotlicky Jun 19 '15 at 12:27
• Found your sword... – Isaac Kotlicky Jun 19 '15 at 12:40

I'll assume you mean "monomolecular" literally. In that case the answer is "No", you can't make practical melee weapons from monomolecular wire. You could build tools or missiles using monomolecular wire and those could have significant amputationility.

The basic issue is that a melee weapon needs to sustain repeatedly hitting the target and, most likely, armor, other weapons and coincidental objects. When that happens the atoms of the weapon will collide with the atoms of whatever is hit. No matter how hard your weapon is this will result in some of the atoms being ablated.

Most weapons are hard enough for the loss to be insignificant, maybe requiring occasional resharpening of the edge. A monomolecular weapon needs all of its atoms for its structure. Even if the material has some redundancy so it doesn't simply go "poof" or break on first impact it will be locally weakened. So repeated impacts will result in the weapon losing strength until it suddenly breaks. Probably just at the moment you are fighting for your life.

At this point it is simpler to add redundancy by making the impact point a composite of multiple molecules or crystals, just like conventional weapons are. A thin wire of "conventional" metal maybe reinforced with nanotubes or graphene gets the job done and is more robust and much simpler to engineer.

For practical monomolecular weapon you need something where the fragility and unpredictable robustness do not matter. A single use weapon such as a missile you throw away or shoot. A specialized tool used for assassination that unless you mess up you only use a single time and then dispose of. A weapon that can recover from being broken by simply producing more of the blade or whip.

The last is probably closest to what is wanted. A whip with an electric charge or a super science force field such as in the picture adding rigidity for pseudo inertia on impact could cause significant damage. And while it would almost certainly break on impact, it would be a simple matter for a microcontroller to detect the length of the whip was reduced from the change in capacitance and extrude enough new material to keep the length constant. A monomolecular whip has very little mass for a certain length so you'd probably run out of power before replacement material.

But even then it would be much easier to use a conventional material instead of an exotic monomolecular one. More robust and probably cheaper. As noted in comments, the practicality of even this limited class of monomolecular weapons is still much less than that of more conventional weapons due to marginal benefits over much more reliable solutions, so nobody would use them. Practical in theory, but not in practice. Which I am not sure even makes sense.

• Could you even effectively whip a monomolecular whip in an atmosphere? It seems like it would be as bad at trying to whip someone with a thread. – Samuel Jun 19 '15 at 17:10
• Also, as noted elsewhere, monomolecular doesn't necessarily mean a sting a single molecules. A carbon nanotube works, for instance. – Samuel Jun 19 '15 at 17:15
• @Samuel It can't have enough mass to cut by inertia, period. Ratio of surface area to mass will be too high in both air and tissue. Essentially even if it looks like a whip, you are pushing it through using whatever "force field" you have added to it. And no, I don't really think that is practical (see first paragraph). A single use garrotte or a short range missile weapon makes more sense to me. – Ville Niemi Jun 19 '15 at 17:28
• Ok, I like the single use garrotte wire if it's used for cutting. Can you expand more technically on how that can work? – Samuel Jun 19 '15 at 17:30
• @Samuel Not really. It would still have the fragility issue, so nobody would actually use it. I am afraid the "makes more sense" was strictly relative term here. It is also much easier to use a braided structure of high tensile strength fibers with hard and corrosion resistant coating. And as somebody noted being too sharp actually reduces the damage. Additionally tensile strength actually increases faster than resistance when the wire gets thicker. So the optimal thickness is probably well above where "monomolecular" really makes sense even for a garrotte. – Ville Niemi Jun 19 '15 at 17:40

I think, just like your cool picture suggests, that a whip-like weapon is what you're looking for.
Consider a whip, i.e. a strand of something (and yes, we'll use carbon-nanotubes here, because they are really, really cool!) with a handle.
Add some barbs to the end.
Keep in mind that anything that is thin enough and does not move out of the way is actually a cutting edge.

Now, you hit your opponent. The strand of carbon nanotubes will be wound around your opponent's arm, and you pull back hard. The thinness of the strand, together with the force you apply by pulling it back, and assisted by the barbs at the end, that will get hooked into your opponent's armour, clothing or flesh, result in the loop around the limb trying to get smaller, and thus cutting tissue that is in the way.

The only question remaining is: can you pull hard enough to cut through the bone? That is where it really helps if your enemy is an armed octopus: They have no bones, which will make the limb removing business a lot easier.
The downside: your octopus still has plenty of remaining limbs to make it very, very clear what he thinks about that.

As a starting point, I used How does a knife cut things at the atomic level? from Physics Stack Exchange, specifically, lemon's answer. lemon1 talked about something called nanoindentation, which is typically used as a laboratory testing technique.

For now, I'll use some of Wikipedia's equations to work this out.

The Young's modulus of the thing being cut, $E$, is related to the stiffness of the contact, $S$ and the indentation depth, $h$, by $$E=\frac{1}{\beta}\frac{\sqrt{\pi}}{2}\frac{S}{\sqrt{A(h)}}\tag{1}$$ where $$A(h)=\sum_{n=0}^{n=7}C_nh^{2^{-(n-1)}}$$ Doing some re-arranging, $$A(h)=\left(\frac{S\sqrt{\pi}}{E\beta2}\right)^2$$ Setting these two equal gives us $$\left(\frac{S\sqrt{\pi}}{E\beta2}\right)^2=\sum_{n=0}^{n=7}C_nh^{2^{-(n-1)}}$$ Let's solve for $S$: $$S=\frac{2E\beta}{\pi}\sqrt{\sum_{n=0}^{n=7}C_nh^{2^{-(n-1)}}}\tag{2}$$ If we say that $C_0=C_1=C_2=. . .=24.5$, and $h$, the thickness of the human arm, is about 0.1 meters, and $E$ is about 14, then, for one tip, I find that the stiffness needed is . . . $\approx$ 1,196,000 Newtons/meter; the force needed is 196,000 Newtons. That's only if one tip is used. Add on more tips on a smaller scale, and this could be feasible. You would get smaller tips, and so smaller identations for each one, but it could work. Perhaps.

The important thing to gain from this is that the types of tips used in nanoindentation can be quite effective. A (paywalled) study also mentioned in lemon's answer showed that the different types of nanoindenters used in the process can produce slightly different results. Fortunately, the Wikipedia page on the devices produces a nice starting point for research . . . which led me nowhere. Curses.

What was I even trying to get at? Consider a long piece of barbed wire. Now make the barbs tiny - really tiny - and lined on every piece of the wire. Then turn each barb into something like a nanoindenter. Now you've got quite the weapon. The reason I covered nanoindenters was that I wanted to see if it would be possible to pick a design such that the shape would be more important that the composition.

In any event, the resulting weapon would look like this:

        ||
--------||
||---x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x
--------||
||


The tip of each "x", though, would be in the shape of a nanoindenter.

1 Note to any potential editors: the username is all lowercase.

• The Young's modulus is given for bone on the linked Wikipedia article: Human Cortical Bone, GPa: 14, psi: 2.03×10^6. Where does the summation to seven come from? – Samuel Jun 19 '15 at 19:47
• @Samuel That's embarrassing. I didn't check the list. The summation comes from the expression for $A$ given in the Wikipedia page; I put it like that for simplicity. – HDE 226868 Jun 19 '15 at 19:48
• Wouldn't this be ineffective as a weapon? It sounds like it would be rough, and the barbs would only produce superficial cuts. I don't quite understand why multiple nanoindenters would be useful. – sumelic Jun 19 '15 at 19:49
• @sumelic Lots of tiny barbs would, I think, do quite a bit of damage. Scaling down the nanoindenters a bit more would make it more effective. – HDE 226868 Jun 19 '15 at 19:51
• Oh, I see. It should be to 8 then. As you do now have the value for bone, can you find S and show the numbers? Perhaps one of these indenters would provide a more accurate representation. – Samuel Jun 19 '15 at 20:13

No way. The positive answer(er)s all fail to take into account a) how exceedingly small a molecule is, b) how many molecules there are in a body (and how much they interact with one another) c) how a chain has to weather the sum of all forces acting on it and d) that a force acting perpendicularly on a chain can not simply be colinearized as is, but will lead to a colinear force many times the former magnitude.

Have a breaking strength of 1TP like one answer gave for graphene: One Pascal is one Newton of force (100 grams in earth gravity) on one square meter. So 1TP means 10^12 Newtons per square meter! Yay! But consider the cross section of a molecule: Let's be generous and set it to 2nmx2nm - thats (2*10^-9)^2. So the breaking force for that single molecule is: 4*10^-6 Newtons ... the force gravity exerts on four tenths of a milligram of mass. You could lift four fruitflies with that! (Yay?) Any molecule encountered by the "whip" on it's way through flesh will need to be acted upon by a force - shear intermolecular-bonds, shove it out of the way, resist adhesive forces... and at any one time, the whip traversing something as small as the human finger would encounter (lowballing) 10^5 molecules - so any of those molecules could be acted upon by (in the mean) 4*10^-11 Newtons - that's just about ten times the force needed to break a hydrogen bond (weakest bond there is http://www.picotwist.com/index.php?content=smb&option=odg) and just a fourth of the force need to break a noncovalent bond. And we haven't even begun figuring in the multiplicators coming into play because the "whip" has these forces acting perpendicular to itself.

The "whip" will drift towards its target, strike with undetectable force, and then break at the first tug. Possibly there is a papercut along the way.