pretendy

If anyone wants to see a quick and direct proof of one of the most fundamental laws of the universe then they should look no further than to a chunk of rubber.

Though at first glance it might seem like elastic bands behave much like springs, and when you stretch them you store potential energy, actually no potential energy is stored in them at all! All the energy you put in is turned to heat.

So why is it that when you stretch a piece of rubber, you feel it exert a force; and when you release it, it gains enough kinetic energy to fly across the room? The answer: entropy. Or rather, the second law of thermodynamics which states that the entropy of the universe must always increase.

I’ve previously talked about how the entropy of a system is related to the number of ways of arranging the components of that system. That relates to this.

Rubber is made of polymers which are long chain-like molecules. They’re small enough that random thermal fluctuations heavily influence their shape and motion. In their relaxed state, they tangle more or less into a ball. It is possible to stretch them out, but they will want to relax back to how they were. This isn’t primarily to do with inter-atomic bonds but rather the number of ways of arranging the segments.

Here are a few frames from a simulation I made of a stretched polymer with ends tethered close together (top) and far apart (bottom).

It may or may not seem obvious that if you were to count the total number of ways the polymer could arrange itself, this number would be much greater for the stretched (top) polymer. This directly means that the stretched polymer has a lower entropy, or it is more ordered.

A rubber band is made up of trillions and trillions of these, and in its relaxed state it is at a maximum entropy. When you stretch it you are lowering its entropy (though your muscles are increasing the entropy of the universe to compensate!) and so the force you feel is the cumulative force of all the polymers ‘wanting’ to increase their entropy and relax. You are feeling the 2nd law of thermodynamics at work!

I find this concept amazing. We’re quite used to seeing the second law around us, when we see buildings get run down, milk mix with tea, etc.; but these all seem passive. They seem to happen because nothing is stopping them from happening. But in the case of an elastic band, it seems very active indeed! Entropy is forcing you to release and relax the band, and it will fly across the room or even fracture in order to achieve this.

Entropy is also the cause of many an unplanned pregnancy - the fracture of a condom is a prime example of rubber trying to maximise its entropy!

(photo adapted from sixeightthree)