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Consider a piece of paper. If I pull on it in the right way it tears into two pieces. However, if I push those two pieces together, they do not spontaneously form a single piece. What happens at the microscopic level when the paper tears such that the process is irreversible?

My instinct is that in the fully formed piece of paper the fibers are strongly interwebbed, and so there is a large amount of (electrostatic?) energy stored at the boundaries between the fibers. To tear the paper, one must overcome this barrier, but I don't see what could have happened to make it difficult to re-introduce all those surfaces with one another. It almost seems like an entropy argument might work but I'm not sure how.

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  • $\begingroup$ Johanson Blocks -- taken to the extreme, as in Second Foundation. $\endgroup$
    – Carl Witthoft
    Commented Sep 28, 2015 at 12:30

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Paper is a mesh of fibres usually mixed with a binder and some clay. The fibres will in turn have some microstructure depending on their origin (cloth, wood, etc). Ultimately the paper is composed mostly of cellulose molecules.

When you tear paper you are mostly pulling the mesh of fibres apart. If you look at the torn edge closely you'll be able to see the fibres sticking out of it. You will probably also fracture some fibres, and that fracture process will depend on the microstructure within the fibres. The clay particles are small and rigid, and they are likely to just separate from each other rather than fracturing. Some of them will spring off the surface as a fine dust.

Given all this complexity, the chances of you reassembling the torn pieces into anything approaching their original configuration are essentially zero.

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  • $\begingroup$ So the guess in the OP is correct. All right, but can we be any more specific about the structural difference between whole paper and the torn edges? $\endgroup$
    – DanielSank
    Commented Sep 28, 2015 at 16:42
  • $\begingroup$ Of course, one could always recycle the paper, at which point it is redissolved into the various fibers and stuff, and remade into paper. But, that is no different from recycling metals or glass or... $\endgroup$
    – Jon Custer
    Commented Sep 28, 2015 at 22:52
  • $\begingroup$ @John Rennie What if the paper was torn in space, would it tend to weld back together as metal does when touched together? $\endgroup$
    – Jitter
    Commented Sep 29, 2015 at 3:16
  • $\begingroup$ @DanielSank: I'm not sure how specific it's possible to be. In any composite material fracture is a complex process. If you tear cloth or break wood you get similarly irregular edges for basically the same reason. $\endgroup$
    – John Rennie
    Commented Sep 29, 2015 at 5:12
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    $\begingroup$ @DanielSank: velcro is made with flexible hooks on one surface that latch onto fibre loops on the other surface. It is a purely mechanical mechanism with no intermolecular forces involved. $\endgroup$
    – John Rennie
    Commented Sep 29, 2015 at 5:45
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I suspect that this question is resolved in the same way as for metal? Perhaps you've seen the famous (visionary) lecture by Feynman on nanoscience (before it existed), he argued for what is now known as cold welding, using an argument that I think applies to paper too. I reproduce a relevant quote from Feynman's celebrated "Feynman lectures on physics" here, which shows the main idea:

The reason for this unexpected behavior is that when the atoms in contact are all of the same kind, there is no way for the atoms to “know” that they are in different pieces of copper. When there are other atoms, in the oxides and greases and more complicated thin surface layers of contaminants in between, the atoms “know” when they are not on the same part.

The only thing is that, with paper, it's infinitely more complex to "put the pieces back together" in the right fashion because of the highly nontrivial structures at the edge. To be clear, the answer I'm proposing is: It isn't irreversible, in principle.

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    $\begingroup$ "when the atoms in contact are all of the same kind" applies to metal, but not to the highly heterogeneous mixture in materials like paper. $\endgroup$
    – Emilio Pisanty
    Commented Mar 1, 2019 at 17:43

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