You may know that “opposite charges attract”. Molecules that are negatively charged are attracted to molecules that are positively charged.
Well, even molecules with *no charge at all* can generate attractive forces called **van der Waal forces**. This is because electrons absolutely refuse to sit still and keep flitting around randomly, and by pure chance for an instant you might end up with more electrons on on one side of the molecule than on the otherside, making *this* side negative-ish and *that* side positive-ish. So, even uncharged molcules can basically spontaneously make themselves charged, and participate in that “opposite charges attract thing”.
The problem is that van der Waal forces are not very strong, since they disappear as quickly as they appear. To get more than a momentary blip of attractive force you need *a lot* of material generating momentary blips of force over *a large* surface area, so that it all adds up to some significant amount.
Most things don’t stick together by themselves because they don’t actually have as much surface area in contact as you would think. At the microscopic level almost everything is pretty bumpy, and you might only actually have the highest bumps of one thing touching the highest bumps of the other thing. The actually surface area in contact usually isn’t enough to create large enough van der Waals forces.
One thing glue does is it can seep into the microscopic nooks and crannies, and valleys in between peaks, and holes in porous things like paper, and fill them in to create an *actually* smooth surface between two things. This is called “wetting” and you can get a similar effect with, like, water, but water eventually evaporates and then the adhesion goes away.
So wetting alone isn’t enough. Glues also generally contain extremely long chain molecules called “polymers”, like a bunch of microscopic ropes. While they seep into the nooks and crannies these ropes can get snagged on microscopic hooks and corners and columns. They also get tangled up with each other. So you get Rope A snagged on Thing A, and then Rope A is tangled up with Rope B, and then Rope B is snagged on Thing B. This is “mechanical adhesion”.
Often glues actually create the polymer *in situ*. That is, the glue is a mix of chemicals that *would* join together into a polymer if exposed to e.g. oxygen or light or heat. So you apply the glue as a liquid for maximum penetration into the surface crevices, and only once it’s in there do all the microscopic ropes start spawning.
All this extra material forced into the space between the two surfaces is what ensures the extra surface area stays around even after the solvent evaporates.
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