Putting the squeeze on paper

By BBC News Online science editor Dr David Whitehouse

Crumple a sheet of paper in your hand and you will end up with a ragged little ball that no matter how hard you try to squash it further, you just cannot squeeze any more.

Curiously, physicists have had great difficulty explaining this seemingly simple phenomenon: why a flimsy piece of paper can be so strong when scrunched up. Now, they may be on the way to an answer.

In the journal Physics Review Letters, normally a repository of loftier areas of physics such as quantum mechanics, non-linear optics and gravitation, can be found a revealing analysis of the crumpled paper conundrum.

It is all to do with topology, the science of shapes, and exactly where the energy goes that you use to crumple the piece of paper.

Saturated system

A team of researchers determined how the size of a crumpled wad of paper varied with the force applied to it.

Looked at with a physicist's eye, a crumpled sheet of paper is actually an assembly of edges and points inside which the energy used to compress the wad is stored.

So is there a limit to how much you can squeeze a wad of paper because there is a limit to the number of folds it can endure?

Experiments showed that, as expected, as the wad is compressed further and further, the number of edges and points increases. Eventually, the system becomes saturated and it requires a tremendous squeeze to supply enough energy to make the wad even a tiny bit smaller.

Thinking they had the problem solved physicists including Sidney Nagel of the University of Chicago, US, devised a simple model for a crumpled sheet.

Power law

It predicted that when squeezed by a steady force, the paper sheet should swiftly collapse towards a final fixed size. However, their experiments showed the idea was wrong.

To find out what was really going on the puzzled researchers next crumpled a circular sheet of ultra-thin and strong aluminised Mylar inside a piston-device designed to exert a steady force.

To their surprise, instead of approaching some final value, the size of the Mylar clump continued to decrease, even over three weeks after the weight was applied.

They found that the relationship between the height of the wad and the applied mass was what is termed as a power law, a fairly common form of relationship found in nature.

Now, all they have to do is to understand why.