# Why does glue stretch straighter than string?

So I have some bottles of lemonade and I peeled the labels off both of them, revealing the glue underneath. When these bottles were next to each other the glue stuck. I pulled them apart and it forms into long thin strands like this:

What's more interesting is that when the bottles are pushed back together, the strands remain in tension and if they happen to slacken, they always return to tension over time, eventually becoming very thin and snapping.

This image shows approximately what happens, first (top left) we begin to move the bottles apart, then (top right) we have the thin, straight strands from the photo, then moving the bottles back together we get some slack (bottom left), but the slackness starts to disappear (bottom right) and goes back to tension.

What is it about glue that makes it behave differently from string (which would remain slackened in that well known $y=\cosh(x)$ catenary shape? Why do the strands become extremely thin, eventually snapping? Answers, even if heavy on the maths/fluid dynamics/mechanics are perfectly acceptable.

• Do you need a necessarily quantitative answer ? Jun 12, 2015 at 10:30
• @Gaurav not strictly, although it would be interesting to see some mathematics, or a model of the forces/viscosity at work. Jun 12, 2015 at 10:39

The glue used on plastic bottles is usually based on polyisobutylene or something similar to it. This has long hydrocarbon chains in it, and when the material is at equilibrium the polymer chains form a tangled network much like a mass of tangled wool.

If you quickly stretch the polyisobutylene then the chains cannot untangle themselves because the timescale for diffusion of the chains is (much) longer than the timescale of the stretching. So what happens is that the chains get stretched out into a long thin conformation. This has a higher free energy than the normal tangled network, so there is a restoring force. In effect it's like stretching a spring, though the force in the polyisobutylene is largely entropic rather than mechanical. The polyisobutylene flows back because of the restoring force, though it will not flow back into exactly the same shape becvause there will be some permanent rearrangement of the chains as the material flows.

• So this is more of a polymer dynamics problem? The system moves towards some kind of disorderly configuration (because entropy typically increases) i.e a mash of tangled chains stuck on the bottles, rather than highly extruded chains. You're saying that provides the force to keep the elongated parts in tension at all times as they are pulled onto the bottle surface, preventing it from drooping too much, right? Thanks for this answer. Are there any mathematical models of polymers that can be used to simulate this on a computer? Jun 12, 2015 at 10:59
• @Histograms: it's more than 20 years since I worked in polymer science, and I'm afraid I've forgotten most of what I knew at the time. At the time simulation of polymer dynamics was a difficult problem, but then computers were far slower than they are now. I'm sure there must be people working in this area if you Google for it. Jun 12, 2015 at 11:05
• The 'free energy' feature of the stretched polymer means that (at 'high' temperature) it will relax to an unstretched state, taking up heat as it does. The strained glue is out of thermal equilibrium, relatively easy to calculate. The computation of relaxation rate depends on LOTS of weak interactions between molecules, a very complex problem. Jun 19, 2016 at 6:14

I would assume the difference between the string and the glue is that the tendency to achieve minimum surface energy in the glue case.

The glue shrinks in length so that it can decrease in surface area, while the string need not since it does not have a particular tendency for minimum surface energy.