Adhesive tape is an everyday item that you might think holds few secrets for us anymore. And yet there was one aspect that scientists kept puzzling over: the until recently unfathomable tape loop.

You probably have it somewhere in your closet: a roll of masking tape. Grab it and cut off a piece. Bend the ends of the tape together to make a loop (as shown in the picture below). Success? Now pull the ends apart again to again have a straight piece of tape. And… have you seen it? Something strange has just happened. When you pull on the ends, don’t let go of the loop. Instead, the loop shrinks. And only when it reaches a small size, let it go.

Tape loop. Image: Eindhoven University of Technology.

Fashion model

Thats crazy. And until recently incomprehensible. “I came across this effect a few years ago,” says Twan Wilting, PhD student at Eindhoven University of Technology. Attempts to find an explanation online for the remarkable behavior of the tape loop were unsuccessful. “I even reached out to YouTubers for an explanation, but to no avail.” And so he decided – together with some colleagues – to solve the mystery himself. Successfully. Because this month is in the magazine European Physics Letters a research article with the telling title ‘How to unloop a self-adherent sheet‘ appeared. In the paper, the scientists present a model that describes the shrinkage process of the loop and provides more insight into the ‘critical loop size’, or the minimum size a loop can have when you pull on the ends of the tape. “The model agrees very well with the experimental observations,” says researcher Jacco Snoeijer, affiliated with the University of Twente.

Making tape loops

Those experimental observations were, however, still quite difficult. Because before that, adhesive tape loops had to be made. And that sounds simpler than it is. “Because it’s a side project of mine, there was no special equipment to make perfect loops with,” explains Wilting. “And by perfect loops I mean loops where the tape sticks exactly right together. When there is a small twist, the loop will start spinning when it gets small and the loop can no longer be considered a two-dimensional problem. In addition, it was also not possible to accurately read the profile (shape) of twisted loops.” In the absence of that special equipment, Wilting and colleagues had to make the perfect loops by hand, which took quite a bit of practice and time. But the hard work paid off. Because, armed with perfect tape loops, Wilting and colleagues succeeded in describing its cancellation very accurately and explaining the remarkable behavior of the loop.

The explanation

When you make an adhesive tape loop, a contact zone is created. That’s where the tape sticks together. That contact zone has two boundaries; one at the top (referred to in the image below as point a) and one at the bottom (denoted as b). When you pull on the ends of the tape, the lower boundary will start to move up. And the upper limit will then move along at a given moment. “If the distance between points b and a is very big, you see that point a doesn’t move,” says Wilting. “Point a only starts to move when dot b comes very close, approximately when the distance between a and b becomes less than 10 times the thickness of the tape (the thickness of the tape is 0.0046 cm).”

Image: EPL, 134 (2021) doi: 10.1209/0295-5075/134/56001.

that point a at some point will move along with point b can be traced back to the difference between the curvature of the adhesive tape in point b and the curvature in point a. “The system does not want there to be a difference in curvature over a short distance. Now the tape can be in point a also lower the curvature. And it is this depression in the curvature in point a which ensures new contact between the two sides and the shifting of the point a.”

Gone Loop!

But that cannot go on indefinitely. At some point, the loop becomes too small. “First of all, it’s good to know that just like point b can move in the direction of a, point a can also move in the direction of b. In order for this to happen, energy must come from the loop that point a would ‘push’ towards point b. Now when the loop gets smaller, the bending energy in the loop increases. It is the moment when this bending energy reaches a critical height and the point a towards point b can push, which stops the process of re-contacting. Point a and b are now walking towards each other, or in other words: this is the moment when the contact breaks and the loop opens.”

It may seem like a fairly playful topic that, in the best case scenario, provides some extra conversation material when you’re standing in the store again waiting for your presents to be neatly wrapped. But nothing is less true. Such loops do not only arise in adhesive tape, but can also, for example, see the light of day during the production of graphene (1 carbon atom thick material consisting of carbon atoms arranged in a honeycomb grid). “If you don’t want loops, you can now calculate what force you need to remove such a loop. If you do want (stable) loops, you can use our model to determine the maximum forces on your material.” In addition, the research also provides more insight into blisters that can develop in a similar way in, for example, multilayer coatings. “Often people don’t want to have blisters, so they try to rub them away,” explains Wilting. “You will again have a moving contact zone and with our model you could calculate the forces present.” And so the side project of Wilting and colleagues has various applications. “I think it’s especially important because of the extra knowledge we can provide in the forces. If you don’t know what forces are involved when making or removing loops, you risk damaging your material.” And the fact that Wilting can finally let go of this problem, which has stuck with him for years, is of course also a bonus.