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This is a well-known phenomenon, and a proper explanation is needed. It seems counter-intuitive since common materials expand upon heating due to faster oscillation of atoms. There would be some reasoning to this observation with rubber that goes in opposite direction.

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  • $\begingroup$ Minor quibble: Thermal expansion occurs in common materials (e.g., metals and ceramics, whose stiffness is primarily enthalpic) because the energy curve governing bonding is asymmetric. If not for this asymmetry, then the faster oscillation would occur around the same equilibrium distance, and no expansion would occur. $\endgroup$ – Chemomechanics Jun 3 '18 at 18:06
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Here is Feynman's intuitive explanation: rubber contains very long molecules like chains. nearby atoms continuously hit this chains. of course you can imagine the stronger hitting be, the shorter will be chain. now heating rubber makes atoms faster, make them hit stronger which makes chains and so rubber shorter.

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By heating the rubber up, we increase the entropy - the amount of disorder among its molecules - and we make it pull itself tighter together. That's why a rubber band contracts when you heat it up.

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