Firstly, it’s not breaking the molecular bonds. Secondly, there is heat in the form of friction, it’s just negligible.
Scissors work less using the laws of chemistry and more the laws of physics. It’s design allows a lot of force ie you grasp, to be exerted onto a very tiny point on the paper, this breaks the paper. As you close the scissors they continue to open this tear.
Atoms combine with other atoms to create molecules. Molecules create bonds with other molecules, and their bond is strongly dependent of their atomic structure.
It takes a given amount of energy to break those bonds. When you mimick a scissor with your fingers, you finger surface is so high that the deformation energy is divided by all of the molecules beneath, which is insufficient to break the bond.
With scissors, you are concentrating the same amount of energy in the metallic edges. The concentrated tear is indeed locally energetic enough to break the bonds and cut the paper.
However, it won’t be able to cut through, say, tempered steel, whose bonds are harder and its structure makes it hard to concentrate deformation energy.
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