... what is cutting?

[spinynorman]

Of course when cutting sections for electron microscopy (50-100 nm thick slices) one uses either a diamond knife or a glass knife with a freshly-broken edge. The samples being cut are typically pieces of animal or plant tissue that have been fixed (that is, treated with a cross-linking agent such as gluteraldehyde that generates covalent bonds throughout the tissue). After fixation the samples are embedded in an epoxy resin. So you have a network of biological polymers (proteins, complex carbohydrates) embedded within a matrix of synthetic polymers. In this case the sample will certainly contain be filled with individual organic molecules that are in the range 10-100 nm and larger. For example, even before crosslinking single collagen molecules are >100 nm long, and single DNA molecules can be a few cm long.

Given that smooth-surfaced (<10 nm rmsd), 50 nm thick sections are cut routinely, we have to conclude that a major mechanism of cutting in this application is the severing of covalent bonds by the glass or diamond edge. The major mechanism would be mechanical stretching and breakage of covalent bonds which for organic molecules occurs roughly over the 100-1000 pN range.

 

[Cliff Stamp]

Bonds are getting broken in general but it isn't the length of the molecules or size of the crystals which are of critical issue but the size of the individual bonds in comparison to the thickness of the actual edge. What is the typical bond length and thickness of the diamond/glass edge. Can knives actually cut through specific and isolated bonds? Steel knives are as noted orders of magnitude too thick at the edge. However can you take a diamond/glass knife and shave ice to releasing oxygen or will you just break intermolecular forces under a gross application of strain.

-Cliff

 

[Jeff Clark]

All this theory about reduced edge area increasing the localized stress seams reasonable as far as it goes, but there are some other factors that can come into play. When you apply very localized force on a hard material you can get non-linear stress concentration. When you are cutting a hard fiber you can over-stress the contact locus and start a zipper-like failure mechanism. Normally you see this as crack propagation in materials science. We also tend to think that the edge is purely wedging itself through the medium, but if the edge were flat (but extremely narrow) and the side bevels were ground so accute that they were nearly parallel you would be applying pure shear forces to push out material (a thin slice) in front of the edge. There are a mixture of shearing, wedging, compressing, forces and stress concentration effects that all come into play.

Measurements made when cutting cotton fiber may not agree with measurements made with nylon or glass fibers.

For me "cutting" is all of the wonderful things an edge can do to separate materials, whatever they may be.

PS. If you want to experiment with wire cutting go and buy some piano wire. It is extremely strong.

 

[erdvark]

Right, for hard materials there is a fracture that can occur ahead of the edge. To complicate matters even more, from what i have heard about materials like glass, water or oil can facilitate the fracture through some process that 'caps' the ends of the amorphous silicon dioxide molecules. Evidently, glass is monstrously strong in vacuum, but can break with reasonable force in air due to the presence of moisture. Also why glasscutters will wet a joint before snapping it.

 

[erdvark]

On the light thread I use, on a tensile break the area is circular so 10^-8, the thread is about 1/10 of a mm. Under a cut the area is basically width of thread (smeared out flat) * edge thickness. With edges from 0.1 to 1 micron, you would predict sharp blades would cut at about 1/10 to 1/100 the force of a tensile break. Experimentally, the thread breaks at ~kg, sharp blades are ~100 grams and exceptional ones approach 10 grams. Details can be seen in the reviews.

-Cliff

Wow, that is remarkable that it works out so well, i just made up that analysis on a whim. Do you know of academic articles that discuss the physics of the cutting mechanism?

 

[Cliff Stamp]

All this theory about reduced edge area increasing the localized stress seams reasonable as far as it goes, but there are some other factors that can come into play.

In the above I calculated in magnitude only for this reason. There are other issues such as wood fibres opening up as noted and then you have splitting vs cutting which is pretty easy to define in terms of the edge or bulk geometry suppling the cutting action.

Measurements made when cutting cotton fiber may not agree with measurements made with nylon or glass fibers.

That would be interesting to compare and see if the sharpness was of a different scale in regards to the tensile limit. You will need very thin wire though to measure sharpness as otherwise it will be heavily obscured by the measurement of cutting ability and the geometrical influences.

For me "cutting" is all of the wonderful things an edge can do to separate materials, whatever they may be.

The main point raised here is how to define what it means to cut. You could walk on a tomato and definately separate it but is that a cut? How do you define an edge - it is usually a circular defination with cut. The basic question being at what point are you cutting vs breaking/smashing and fundamentally is there a difference on a microscopic manner as to how the material is divided.

I would define cutting as the application of highly localized stress, specifically meaning you can't see damage from nonlocalized strain by eye. In Fike's video for example, as soon as he sees paper damage in the rolls he is doing test cuts on he notes it isn't a cut any more but a break. I think most people would tend to make this distinction.

-Cliff

 

[spinynorman]

To be clear, I did not mean to suggest that the *edge* of a diamond or glass knife used to cut sections for EM is "cutting through" individual bonds. But the edge certainly is placing mechanical force at the center of macromolecules that are tethered in a cross-linked matrix on both sides of the cutting edge. In other words, placing individual molecules under sufficent mechanical tension to cause the failure of individual covalent bonds. Geometry is also very important for the usual reasons (the balance between supporting the edge and cutting efficiency). For glass knives a 40 degree bevel is fairly typical.

 

[Cliff Stamp]

To be clear, I did not mean to suggest that the *edge* of a diamond or glass knife used to cut sections for EM is "cutting through" individual bonds. But the edge certainly is placing mechanical force at the center of macromolecules that are tethered in a cross-linked matrix on both sides of the cutting edge. In other words, placing individual molecules under sufficent mechanical tension to cause the failure of individual covalent bonds.

Consider the simplest case, one strand of DNA is an expoy base that is stretched out in a perfectly straight line. Now bring the edge of the knife down in the middle of sample cutting through it. Unless the edge of the knife is comparable to the individual bond length there will be many bonds under heavy strain and a high possiblity that many will break. The number would be basically edge width / bond length. This is essentially no different than just smashing it with a heavy hammer, the only thing that changes is the "edge width" is much higher so more bonds are effected. In most materials since the edge width is so much higher than the bond length, typically orders of magnitude, the edge doesn't see individual bonds any more than you feel individual molecules of air when walking through wind. It doesn't matter the size of the chains any more than it does the number of people holding hands in a chain trying to trip godzilla. His foot would plow through many of them and since the width / bond ratio is very high, a large number of bonds would be broken even though there is just one very long chain. Compare this to the same line of people trying to stop a charging horse for example and since the width / bond length is close to one, only a few bonds would be broken.

-Cliff

 

[tristram]

It seems like a really dumb question...

Fascinatingly elementary question and highly interesting/intricate answers!
thanks,
t.

 

[spinynorman]

In most materials since the edge width is so much higher than the bond length, typically orders of magnitude, the edge doesn't see individual bonds any more than you feel individual molecules of air when walking through wind.

Of course not. But a fine enough edge will see individual *molecules*. Bear in mind that the individual molecules we're talking about here routinely have 10^5 or more atoms. The cutting edge of a glass or diamond knife used on an ultramicrotome is 3-4 orders of magnitude smaller: on the order of 5 nm.

It doesn't matter the size of the chains any more than it does the number of people holding hands in a chain trying to trip godzilla.

The point that I'm making here is that when cutting with an ultramicrotome blade, cutting though severing of covalent bonds at sites adjacent to (within a nm of) the cutting edge is almost certainly more dominant than with dull blades like razors and ZDP Spydercos. Still macroscopic, yes, but at the very edge of what we'd usually consider macroscopic. Much, much less than the wavelength of visible light. Note that in this example, I'm saying that the properties of both the blade and the material being cut are atypical.

 

[HoB]

Optical magnification? Then we are back to the light problem, optical microscopes have a few hundred nm resolution.

As you point out, there isn't really a "light problem" resolution of an optical microscope is sufficient, but depth of field becomes very small, which makes imaging of 3D objects such as a knife edge pretty much impossible with a light microscope. From personal experience I would say that about 100x is about the limit. 200x is still possible, but while you gain some detail, but you loose in depth of field. In the end I found you don't get really a more telling picture.

 

[HoB]

Deleted because:

Rash, HoB.....very rash...


You got to love Pirate of the Carribean..

So really, what is the point of the last few posts. Obviously some bonds, somewhere get broken. Whether they are close to the cutting edge or not seems to me highly irrelevant. It is not that you can chose to cut between molecule A and B instead of B and C so what is the point. And what kind of bonds get broken is highly dependent on what what you are cutting and not dependent on the edge. If you are cutting through water, you are separating hydrogen bonds. If you shave off a slice of aluminum, you are separating metal bonds. If you are cutting a plastic ballpen in tow halves you are breaking covalent bond (because in first approximation the ballpen is made from one molecule).....ok, now what? Does that answer what cutting is? Me thinks not.

So getting back to "normal" cutting, leaving this science fair behind: I would suggest that cutting is easily distinguishable from breaking or cleaving as in the latter two the separation propagates by itself, once initiated. I would also propose that cutting can easily be distinguished from tearing as the main force component should run within the plane of the two newly created surfaces. To distinguish further from tearing like a sheet of paper, I would also require the main force component to run along the propagation direction of the cut (tearing a piece of paper you pull towards you and away from you but the tear propagates downwards: no cutting). This way at least push cutting would be reasonably classified. However, pull cutting, a very important component of sharpness as Cliff has pointed out many times has clearly a tearing component to it (you pull the knife towards you but the cut is popagating downwards). So obviously my "definition" is not unproblematic.

Oh, and "within a few nm" is NOT "adjacent to" when talking about molecules, atoms and molecular bonds. It is still "miles" off.

 

[Cliff Stamp]

The point that I'm making here is that when cutting with an ultramicrotome blade, cutting though severing of covalent bonds at sites adjacent to (within a nm of) the cutting edge is almost certainly more dominant than with dull blades like razors and ZDP Spydercos.

As noted the number of points of contact would be less because the edge width is reduced, however as for "seeing" individual molecules; the intermolecular distances between the large organics as well as the binder media would also have to be smaller in scale than the edge thickness to isolate points of contact and the sample highly perpendicular inorientation and the knife would require a similar scaled edge length.

Note plant fibres for example are much longer than edges are wide but still does the edge "see" individual fibres when you cut through some leafy plants? It is interesting to note that organic chains can be that long, especially cm, many materials are similar in scale, crystal structures for example can be much larger than the width of a typical knife edge. Do you have an references to the edge thickness of the nm scale? In particular I would like to see pictures contrasting the edges with normally sharpened steel blades as Verhoeven has done.

Whether they are close to the cutting edge or not seems to me highly irrelevant.

It is often an argued distinction that cutting will focus the bond separation at the edge and is intra-bond while breaking is more of a van der walls issue.

I would suggest that cutting is easily distinguishable from breaking or cleaving as in the latter two the separation propagates by itself, once initiated.

I am not sure what you mean by propogates by itself. If I take a hammer and smash a piece of wood the breaking stops once the energy of the hammer is dissipated. Now there is some continuing of the fractures away from the immediate site of impact but we have already agreed that this is the case for cutting as well and that the bonds are not broken individually at the edge. Consider for example the microstructure under the immediate layer which make contact with the edge. If the top layer is so highly distorted that it breaks it isn't unreasonable to think that the breaking may be more than one "molecule" deep.

I would also propose that cutting can easily be distinguished from tearing as the main force component should run within the plane of the two newly created surfaces.

This is an interesting perspective however consider rocking cuts or dynamic cuts in general. These will all have a large component of the main force at the contact area perpendicular to the surface of the media being cut, but another component will be parallel as in tearing.

-Cliff

 

[DGG]

It seems like a really dumb question. But I mean how is cutting different from, say, breaking? A knife cuts because the edge is very thin, which focuses the pressure on a small area. Well, with more pressure over a larger area, you can still separate material. I dunno, like a dull and damaged lawnmower blade still 'cutting' the grass. This question partially comes from some thinking about how a knife can cut through a bulletproof vest. Is it just that the contact area of a bullet is just so large in comparison to an edge, that despite the large amount of force driving it it still can't generate the same pressure as a blade?

It is really simple. It is the process of dividing a material into more than one part.

What's all this talk about steel, etc.

http://www.clinicon.com/diamondlaser.html

 

[DGG]

Now I'm scared to cut anything... What if I split an atom???

Just make sure it is a "beer atom" so you get some fizz!

 

[HoB]

It is often an argued distinction that cutting will focus the bond separation at the edge and is intra-bond while breaking is more of a van der walls issue.
-Cliff

That is nonsense from a chemical point of view. Either way material will separate along the line of least resistance. Since van-der-Waals forces are generally weaker than covalent bonds it is likely to separate there if the possibility exists. But this is a moot point as it depends on what you are cutting. If you are cutting an ultrahigh density polymer you are cutting or tearing covalent bonds one way or another. Same if you are cutting metal. There is only one kind of bond in the metal so you are not separating van-der-Waals bonds whether you break it or cut it or tear it. Even on an ultramicrotome the edge is much bigger than a bond so it is still a dumptruck driving through a chain of people holding hands.

Wood is not really a resonable testing platform. Wood is essentially a fiber composite it doesn't really break, especially not accross the grain. What I mean with self-propagating break or fracture is best explained on glass or metal. Once you initiate the crack, the crack propagates under the smallest applied forces. You can not stop a crack half way through. Once a crack is present it will continue by itself or under force that are much smaller than needed to initiate the fracture. You may be lucky that it doesn't fall apart immediately but the structural integrity is lost the moment the crack is initiated. In materials of sufficient hardness and brittleness like glass, you can actually see the crack selfpropagating. Obviously, some materials do not break (like some polymers), they rupture or tear but they don't break. While when cutting metal for example, you can stop the cut halfway through, without the material losing any more structural integrity than from the material removed.

 

[Cliff Stamp]

That is nonsense from a chemical point of view.

Yes, I didn't propose that arguement, just noting it is a common argued distinction. In the above I was using van der walls in a sloppy way meaning anything that held the substance together an an intramolecular/atomic sense versus the individual intermolecular/atomic bonds. As I noted the bond and intra grouping distances are very large compared to edge thicknesses, in steels knives it is almost macroscopic vs microscopic.

[glass]

Once you initiate the crack, the crack propagates under the smallest applied forces.

Ok, easy to understand in regards to a glass cutter and then actually breaking it to separate the glass. However it is hard to argue for your breaking/cutting distinction along that viewpoint as for example I can "cut" a watermelon Gallagher style with a sledgehammer with that defination.

-Cliff