Why a rubber band pulls back

Take a wide rubber band, press it flat against your upper lip, and stretch it hard and fast. It goes warm — you can feel the heat against the thin skin there. Now hold it stretched a moment so the warmth fades, and then let it snap back to its slack length while it still touches your lip. It goes cool. Stretching heats it; releasing chills it.

A steel spring does not behave this way in any noticeable degree, and that is the first clue that a rubber band is elastic for a reason that has almost nothing in common with a spring.

The spring is the intuitive picture, and it is the wrong one. Bend or stretch a piece of metal a little and you are prying its atoms slightly apart against the stiff bonds that hold them in a lattice. That takes work, and the work is stored in the strained bonds like water held behind a dam. Let go and the bonds snap the atoms back to their preferred spacing, handing the energy back. The restoring force is stored energy trying to get out. This is what most people imagine is happening inside a rubber band too — that stretching it winds up some molecular spring, and the pull you feel is that spring wanting to unwind. It isn't. In rubber the bonds are barely strained at all, and the energy stored in them is almost beside the point. The pull comes from somewhere stranger.

Rubber is a tangle of very long molecules — polymer chains, each one thousands of links long, heaped together like a bowl of cooked spaghetti and then tied to each other here and there by permanent cross-links. (That tying is what vulcanizing does; it is the difference between the useless sticky sap that weeps from a rubber tree and the springy solid in the band. The cross-links let the chains writhe and jostle freely but stop them from ever sliding fully past one another and flowing away.) The crucial fact about one of these chains is that, left to itself, it is not straight. It is a random tangle — a walk that turns a random direction at every link — and a walk like that almost never wanders far from where it began. It doubles back, coils, crosses itself. There are an astronomical number of ways for a long chain to be crumpled into a compact heap, and only a vanishingly small number of ways for it to lie out straight and extended, end to end. Crumpled is not one option among many. Crumpled is essentially all of the options.

So consider what you do when you stretch the band. You take those chains, which are sitting crumpled because crumpled is overwhelmingly the most probable way to be, and you drag their ends apart, forcing them toward the rare, extended, orderly shapes. You have hardly touched their energy — the bonds are not being pried apart the way a metal's are. What you have changed is their disorder, and you have changed it in the costly direction: you have taken a system with countless available shapes and squeezed it down toward the few. And the chains are not still. They are seething with heat, every link kicked and jostled by thermal motion, constantly trying on new configurations. A chain jiggling at random among its possibilities is overwhelmingly likely to fall back into some crumpled shape, simply because there are so many more of those to fall into. That statistical drift — trillions of restless chains, each far more likely to coil than to stay extended — is, added up, a steady tug pulling the two ends of the band back together.

That is the restoring force. Not stored bond-energy straining to escape, but disorder reasserting itself; not a spring wanting to unwind, but a crowd of writhing chains wandering back into the shapes there are simply more of. The band pulls back because coiled is more probable than straight, and heat is the thing doing the pulling.

Once you see that the force is made of disorder and driven by heat, the two upside-down things about a rubber band stop being tricks and become the whole point.

The warmth on your lip is the first. Stretching the band forced its chains into order — dropped their disorder — and that lost disorder has to go somewhere. It leaves as heat, which is why the band warms in your hand as you pull it. Let it relax and the chains rush back to their crumpled tangle, disorder floods back in, and to supply it the band pulls heat from your skin: it cools. A steel spring, storing ordinary energy in ordinary bonds, does nothing of the kind. This warming-on-stretch was noticed by John Gough in 1805, feeling exactly what your lip feels, decades before anyone could say why.

The second is stranger and you can rig it up on a table. Because the whole restoring force is the product of thermal jostling, it gets stronger when the band is hotter — hotter chains kick harder and drift home more insistently. The pull of a stretched rubber band is very nearly proportional to its absolute temperature. So hang a weight from a rubber band, one that stretches it to some resting droop, and then warm the band with a hairdryer. Everything else in your kitchen lengthens when you heat it; the loaded rubber band does the opposite. It contracts, and lifts the weight. Heat a steel spring and it sags a little; heat a stretched rubber band and it hauls harder. String the spokes of a light wheel with rubber bands, warm the bands on one side only, and the wheel will turn on its own toward the heat, forever if you keep the lamp on — a little engine run entirely on the fact that warm disorder pulls tighter than cool.

There are not many places in ordinary life where you can put your hands directly on entropy — on the plain counting fact that disordered arrangements vastly outnumber orderly ones, and that this lopsidedness alone can push and pull on the world. A gas driving a piston is one. A rubber band is the other, and it is the one you can hold. The next time one snaps back, notice that nothing inside it is sprung or wound or storing your effort as tension in a strained bond. What snapped it back was only that there are far more ways to be tangled than to be straight, and a band full of restless heat will always, on average, find its way back to the many.