Viscoelastic putty

Why does the same lump of putty bounce like rubber off the floor yet spread into a puddle if left out overnight?

Throw a ball of the putty at the floor: it bounces, cleanly, like rubber. Leave the same ball on a table overnight and it has spread into a low puddle.

The temptation is to say it is "somewhere between" a solid and a liquid, a compromise with half of each property. But that is not what you observed. You did not see a poor bounce and a slow flow. You saw a good bounce and a complete flow — full solid behaviour in one test and full liquid behaviour in the other, from a lump that was not altered in between.

So the question is not what fraction of each it is. It is what distinguished the two experiments, given that the material was identical in both.

List what actually differed. Not temperature, not composition, not the shape of the lump. Only how long the deformation lasted: milliseconds against the floor, hours on the table. If that is the only difference, then time is not incidental to the answer — time is the answer, and the material's identity as solid or liquid must depend on how long you look at it.

Which means we need a clock inside the material to compare against. What could tick?

The accepted account of what the putty is: a silicone polymer — long chains of alternating silicon and oxygen — with boron compounds mixed in, the boron forming junctions between chains that are genuinely chemical but genuinely temporary, breaking and re-forming continuously at ordinary temperature. That is the clock. There is a characteristic time for a junction to let go, the relaxation time, and it is the average interval over which the network can rearrange into a new stress-free configuration.

Now put the two experiments against that clock, and the puzzle resolves in one step.

Against the floor, the contact lasts a few thousandths of a second. In that interval essentially no junction lets go. The network is, for the duration, a permanently cross-linked elastic solid: it stores the deformation energy and hands it straight back, which is a bounce. On the table, over hours, every junction has released and re-formed an enormous number of times. Chains slide past one another, the stress from the lump's own weight relaxes as fast as gravity applies it, and the material has no memory of its original shape at all. That is flow.

Notice what has not happened: nothing switched. There is no threshold the material crosses, no state it changes into. The same junctions are breaking at the same average rate in both experiments. What changed is whether your experiment was long enough to notice.

Reiner gave that comparison a name in 1964, the Deborah number — the material's relaxation time divided by the time of observation — taking it from the line in the song of Deborah that the mountains flowed. His point was the one we have just reasoned to: a mountain is a solid only because we are short-lived. When the ratio is large the material reads as a solid, when small as a liquid, and the material does not get a vote.

Is this thermodynamics or kinetics? Unambiguously kinetics, and it is worth saying sharply. Thermodynamically the putty has one answer in both experiments: left alone forever, a lump of it will always end as a puddle. The bounce is not a competing equilibrium. It is the equilibrium never being reached, because you did not wait. Every "solid" behaviour this material shows is borrowed time.

That framing predicts something the compromise-material story cannot, and it is the test. If a single relaxation clock is doing the work, then anything that speeds the clock must degrade the bounce and hasten the puddle together — they are not independent properties to be traded. Warm the putty and both should shift the same way; chill it and it should both bounce better and stop spreading. Better still, the two should be interchangeable: a temperature at which the bounce has gone soft should be recoverable by hitting it faster, since only the ratio matters. That trade of rate against temperature is a well-established feature of polymer behaviour and is the signature to look for. What would refute the account? A treatment that changed one behaviour while leaving the other untouched — a putty that still bounced perfectly but no longer flowed overnight would mean two mechanisms, not one clock.

Two refinements, and the second is a real limitation.

The bounce is not evidence of stored elastic bonds in the way a steel spring's is. What returns the ball is the network being unable, in the time available, to relax the stress you put into it — better read as a failure to flow than as a stored spring. That distinction explains why the bounce is never perfect: some junctions do release even in a few milliseconds, and the energy going into those rearrangements is lost as heat, which is why the ball comes back lower than it was dropped from.

And the simplification: a real polymer has not one relaxation time but a broad spectrum of them, from local wiggles of a few atoms up to whole-chain rearrangements. The single clock is the leading behaviour, not the full description, and it is why the change from bouncing to flowing is spread across a wide range of timescales rather than being sharp. Reasoning with one relaxation time is right for understanding the phenomenon and wrong for predicting a specific material.

• Why sticky tape peels cleanly when pulled fast and stringily when pulled slowly, which is the same ratio governing adhesion instead of shape.

Every term the collection defines is gathered in the glossary.