Ok let’s take this in three parts:
Pressure sensitive adhesives such as tape are a mixture of rubber (like your tires) and a type of liquid that is very slow to move but still liquid. When these are pressed against a surface, they squish themselves into the cracks of the material. The liquid material will allow you to compress it and it actually moves better when squished than it does just sitting there meaning it is now stuck in the cracks. From there, it actually resists being pulled on like a Chinese finger trap. This is what we perceived as being sticky.
There are also chemical reaction based adhesives. These don’t have to be crazy things like vulcanizing rubbers, etc. This can be something as simple as honey coming in contact with your fingers. The structure of honey allows it to absorb water into its system. This means that as it contacts your finger it takes a liking to the water on your finger and gets bound to it. The only way to get it out is to overwhelm the matrix with more water (aka licking your fingers).
Finally, when it comes to smooth surfaces (no surface is actually smooth) we go back to the first type of adhesive. The idea for smooth surfaces is to not only fill the cracks, but to make a uniform surface of adhesives that can use the small gaps in the surface to anchor it to the smooth material. For the rest of the area, it is more like a suction cup than like the tape adhesive.
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