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Why does paper crumble on getting wet? This is something I have noticed hundreds of times but cannot think of an explanation.
Does it have anything with water disturbing the intermolecular forces between cellulose micro fibrils in paper or something else?
Also, one peculiar observation is that it does not crumble immediately but only after the water evaporates? Why?
Polymer properties in water often relate to the relative strength of polymer-polymer interactions versus polymer-water interactions. For example, the solubility of amylose > amylopectin > cellulose is attributed to how strongly molecules of each of these polymers interact with water molecules compared to other molecules of themselves.
In the paper making process, the cellulose fibers of paper dry out and interactions with water tend to get replaced by interactions with nearby polymer molecules. The resulting structure is strong because of polymer-polymer interactions as well as purely physical effects (e.g., "matting" of fibers, and surprisingly strong surface-surface interactions), all of which is enhanced by the compression and tension forces placed on the paper during its manufacture (google it to see photos).
When paper is later made wet, the entrance of water eventually disrupts these interactions, leading to local regions of what you might think of as micro solubility. Then, when the paper dries out again as you describe, it probably does so without any compression/tension forces on the paper, thereby reducing the extent to which the matting of the fibers and chemical interactions between polymers takes place, and so it crumbles because of those micro regions of "solubility".
(Disclaimer: The above is just rationalizing off the top of my head. But since it is based on expertise as a PhD Chemist for nearly three decades, I'd give it a 70+% chance of being accurate ;)
The real science begins when you test the above ideas: For example, one test would be drying out paper under different degrees of compression and/or for different time periods and then testing the crumbling behavior. Another might be to wet the paper while it's under different degrees of compression. But the best test of the above ideas would be if there were some way to assay the extent of polymer-polymer versus polymer-water interactions -- no doubt such interactions result in very different vibrational modes. So there, I've outlined a Ph.D. thesis for you.
This is best understood as a macroscopic mechanical process: Most "everyday" paper is nothing more than cellulose pulp that is processed into an aqueous slurry, aligned and layered to a desired thickness, and then pressed to remove most of the water. The pressing process creates mechanical links (or "entanglements") between cellulose fibers.
If you add water to this dry cellulose (which is hydrophilic) you are partially undoing the last step of manufacturing: As it absorbs water and expands, some of the mechanical links are torn. (If you want to "recycle" the paper, you only have to mechanically agitate it with an excess of water to continue to break those links and return it to a slurry.) Where those links are broken the paper is only held together by water-polymer bonds. If you then let it dry without pressing or other action to restore the broken mechanical links, the paper crumbles along the lines of larger broken mechanical links.
All this is simply due to hydrogen bonds being created and destroyed. Cellulose is a rather long linear molecule with plenty of $\ce{-O-H}$ groups attached along the chain. When dry, hydrogen bonds are created randomly between $\ce{OH}$ groups from neighboring cellulose molecules. Not all $\ce{OH}$ groups are included in the final arrangement. The existence of a carbon framework products a more or less stiff network, hold together by hydrogen bonds.
When cellulose is wetted, all those cellulose-cellulose hydrogen bonds are replaced by hydrogen bonds between cellulose and water, plus multiple bonds water-water. The whole is not so rigid, as the carbon framework is not fixed any more to another carbon network. The cellulose molecules can easily move by breaking and creating all the time new hydrogen bonds with water. This is why dry paper is hard, and wet paper crumbles.
