In Larry Niven’s Ringworld (or one of the sequels, there’s something called Sinclair Molecule Chain which is effectively string made of fibres, each one of which is a single molecule for the entire length of the reel, therefore to cut/break the stuff, you have to break the molecular bonds.
so how strong would such a thing be? (if it was real) - what is the strength of the strongest known molecular bond? (Ideally expressed in terms that I can understand, so scaled up to a piece of thin string made of many strands, each one having the molecular bond as it’s strength)
I’m not a scientist, but until some come along, I’ll tell you that molecular bonding can be of various types: hydrogen bonding, valence bonding, and ion bonding. Hydroen bonding is the weakest, and this is what DNA uses. That’s why the strands separate quite easily.
In valence bonding, atoms will share one or more electrons. Ion bonding is merely the chemical attraction between positive and negative ions. Salt is an example of ion bonding: a positive sodium ion with a negative chlorine ion. When broken, two ions are produced. When valence bonding is broken, two atoms are produced. Ion bonds can be broken by electrolysis, such as found in batteries. I would guess valence bonding would be the strongest, especially if more than one electron is shared.
This sounds like a great Fermi problem. One of those where you just play around with factors of ten, and end up with something in the right ballpark. However, I fail miserably!!!
Assuming that we are talking about intramolecular bonds, I’d venture a guess. Most intramolecular bonds are on the order of 1 - 10eV (breaking them causes visible light).
1 eV = 1.602 x 10[sup]-19[/sup]J
Assuming that the you can order the atoms more or less close packed we’d have a cross section of about
1Å[sup]2[/sup]=10[sup]-20[/sup]m[sup]2[/sup] / bond.
This doesn’t seem very impressive at all!
Assuming that you have a 1mm[sup]2[/sup] rod of the material, it would only require 1.6x10[sup]-7[/sup] J to break it. Thats 1.6x10[sup]-7[/sup]Nm!!
What’s wrong with my reasoning?
Most likely my assumption that one could transfer all the applied energy into breaking the bonds in one layer. I assume that the elasticity of the bonds in the other layers would distribute the applied force.
Or am I completely wrong with my assumptions of 1eV,1Å[sup]2[/sup]? (It’s been a while since I measured these things…)
Right. Hydrogen bonds are indeed weak individually, they merely have a strong collective effect (they explain why water has such high melting and boiling points). Ionic bonding can be quite strong (I’ll get to this in a bit), and covalent bonding can also be pretty powerful. There’s also stuff like van der Waal’s (I think I spelled that wrong) interactions, but we don’t normally call those a bond.
Now then, let’s look at some covalent bonds. The strongest are going to be triple bonds, so let’s just take N[sub]2[/sub], molecular nitrogen. The bond strength is about 950 kJ/mol, or about 10 eV. I’m not sure how to put that in simple terms, because I don’t know how you’d scale it up to a molecule the size of a string. For what it’s worth, the thermal energy at room temperature is roughly 1/40 eV.
For ionic bonds, you can use Coulomb’s law. Looking at NaCl, the bond length is 2.4 Angstroms, giving a bond strength of about 6 eV. MgO, with twice the charge on each ion, has a bong length of 1.8 Anstroms, for a bond energy of about 32 eV.
Individually, these bonds are very weak on our scales, but if you take a really really long molecule and pull on the ends, the energy would probably be distributed roughly evenly throughout the chain. Let’s take a 1 meter long molecular rope with a bond energy of 1 eV. You’ll have something like 10[sup]10[/sup] bonds, so you’d need 10[sup]10[/sup] eV to break it. This still isn’t a lot. Now consider if you had a bundle of these fibres a mm thick. Ballpark figure, a molecule might be a few Angstroms, so we’ll say that we’ve got 10[sup]13[/sup] molecules in the fiber (remember, the number of strands would go as the radius squared). So for a mm thick fiber one m long, now we’re talking 10[sup]23[/sup] eV to break it, or 10000 J. This is the same energy it would take to lift Joe average 30 feet, roughly speaking. Impessive, eh?
Now I may be as thick as a whale omelette, but a chain is as strong as it’s weakest link, isn’t it? so a long molecule is going to be as strong as the weakest bond therein, not the sum of them (or am I wrong?)
Well, I checked my old high school chem book (and I do mean old, 1955) and I see the errors of my ways. The bond is a covalent bond and covalence is the number of electrons one atom contributes to produce the bond. And valence is the number representing the capacity of an element’s atomic weight to combine with, or displace, atomic weights of other elements, the unit of such capacity being that of one atomic weight of hydrogen or chlorine. Stated more briefly, the valence of an element is the number of atoms of hydrogen, or of chlorine, which the atom of the given element can combine with or displace.
Mangetout, I’m no expert on energy transfer, but while it’s true that a chain is only as strong as the weakest link (i.e. the super long molecule will break at the weakest bond), when you have chemical bonds like this, you have to take into account the way that the energy is distributed.
Right, so to break a chemical bond, basically all you have to do is put enough energy into it and eventually it’ll come apart. Now, let’s say I pull on one end of a molecule. Okay, so I’m putting energy into the first bond. What will happen is that this energy will reorganize, and try to distribute itself throughout the entire molecule. The time scales for this are normally very quick by macroscopic standards. So what you have to do is get enough energy into the weakest link in the chain, fighting the tendency for the energy you put into the molecule to redistribute itself throughout the whole thing. I assumed that the time scale for this would be so fast as to be virtually instantaneous, and therefore, you’d have to put enough energy in to break most all the bonds in order to get enough into any one bond to snap it. Does that make sense?
Now I may be as thick as a whale omelette, but a chain is as strong as it’s weakest link, isn’t it? so a long molecule is going to be as strong as the weakest bond therein, not the sum of them (or am I wrong?)
You’re right. What g8rguy has calculated is the energy required to break a molecular chain, which is rather different from the maximum force it will bear. (Consider a glass rod and a rubber rope of appropriate thickness so they can each support the same load. They have equal strength, but the rubber rope is tougher - you have to put in a lot more energy to actually break it.)
Regarding the OP - a few points.
A single molecule doesn’t have to have atomic-scale thickness. A diamond is a single molecule. So is a carbon nanotube.
Most fractures of materials aren’t the result of direct pulling-apart of atomic bonds. Instead, they are the result of propagating failures such as crack propagation (brittle fracture) or dislocation movement (ductile fracture.) These can be regarded as “catalysts” for fracture, greatly weakening the material.
The theoretical strengths of materials without cracks or dislocations are very much higher than those seen in ordinary materials. E.g. mild steel has a typical ultimate tensile stress of 400 MPa, but the theoretical strength of dislocation-free mild steel is about 20000 MPa.
Dislocation-free metal fibres have been produced in laboratories which approach these theoretical strengths. These fibres are called “whiskers” (a term which unfortunately has been adopted by the composite materials industry for any very thin fibre) and have exhibited measured UTS values of 25000 Mpa.
Carbon nanotubes have been tested to UTS values of 63000 MPa, and theoretically could be as strong as 300,000 MPa.
What do these figures mean in comparison with Niven’s Sinclair molecule chain? Well, for a 0.1 mm diameter fibre:
mild steel supports 320g
a tungsten whisker bundle would support 20 kg
a current carbon nanotube bundle would support 50 kg
a future carbon nanotube bundle may support 240 kg
That’s very strong, certainly good enough to make a good cheesewire or cut your fingers off. I can’t remember how strong Sinclair molecule chain was meant to be, but I’m guessing stronger than these figures suggest.
Is a diamond really a single molecule? so cutting one involves breaking molecular bonds? (aha! - is this why they cut more cleanly through certain planes?)