The hemihelix: Scientists discover a new shape using rubber bands (w/ video)

Apr 23, 2014
This is an illustration of a helix (top), a hemihelix with one perversion marked by an arrow (middle), and a hemihelix with multiple perversions (bottom). The scale bar is 5 cm for each image. Credit: Jiangshui Huang

While setting out to fabricate new springs to support a cephalopod-inspired imaging project, a group of Harvard researchers stumbled upon a surprising discovery: the hemihelix, a shape rarely seen in nature.

This made the researchers wonder: Were the three-dimensional structures they observed randomly occurring, or are there specific factors that control their formation? The scientists answered that question by performing experiments in which they stretched, joined, and then released rubber strips. Complemented by numerical simulations and analysis of the process, the results appear in a paper published in the journal PLOS ONE.

Knowing precisely how to make the structures, predictably and consistently, may enable scientists to mimic the geometrical features in new molecules that could lead to possible advances in modern nanodevices, including sensors, resonators, and electromagnetic wave absorbers.

"Once you are able to fabricate these complex shapes and control them, the next step will be to see if they have unusual properties; for example, to look at their effect on the propagation of light," says Katia Bertoldi, Associate Professor in Applied Mechanics at the Harvard School of Engineering and Applied Sciences (SEAS).

This video is not supported by your browser at this time.
Both ends are free to rotate. Credit: Liu J, Huang J, Su T, Bertoldi K, Clarke DR (2014) Structural Transition from Helices to Hemihelices. PLoS ONE 9(4): e93183. doi:10.1371/journal.pone.0093183

The that Bertoldi and colleagues at SEAS unexpectedly encountered is a hemihelix with multiple "perversions." Helices are ; think of a corkscrew or a Slinky toy. Hemihelices form when the direction in which the spiral turns—known as the chirality—changes periodically along the length. The reversal in chirality is called a perversion.

The team was trying to make two-dimensional springs by taking two strips of rubber material of different lengths and stretching the shorter one to reach the same length as the longer one and then sticking them together, explains David R. Clarke, Extended Tarr Family Professor of Materials at SEAS. "We expected that these strips of material would just bend—maybe into a scroll. But what we discovered is that when we did that experiment we got a hemihelix and that it has a chirality that changes, constantly alternating from one side to another."

Jia Liu, a graduate student in Bertoldi's group, tested differences in the aspect ratio—the width-to-height ratio of the rubber strips—and discovered that when a strip is very wide relative to its height, it produces a helix. Further measurements revealed that there is a critical value of the aspect ratio at which the resulting shape transitions from a helix to a hemihelix with periodic reversals of .

This image shows the sequence of operations that leads to the spontaneous creation of hemihelices and helices. Starting with two long elastomer strips of different lengths, the shorter one is stretched to the same length as the other. While the stretching force, P, is maintained, the two strips are joined side-by-side. Then, as the force is slowly released, the bi-strip twists and bends to create either a helix or a hemihelix. Credit: Jia Liu

Other classes of materials would simply break when stretched to the mismatched strains that the polymers endured—likely the reason this behavior had never been observed before.

"We see deterministic growth from a two-dimensional state—two strips bonded together—to a three-dimensional state," Liu says. "The actual number of perversions, the diameter, everything else about it is entirely prescribed. There is no randomness; it's fully deterministic. So if you make one hundred of these, they'll always perform exactly the same way."

Bertoldi adds: "From a mechanical point of view you can look at these as different springs with very different behavior. Some of them are very soft and then they stiffen up. Some are more linear. Simply by changing geometry, you can design this whole family of springs with very different behavior with predictable results."

Bertoldi and Clarke believe that their findings provide important clues for how to fabricate a variety of three-dimensional shapes from flat parts.

"Intellectually, it's interesting—and we believe it is significant too," Clarke says. "There are a variety of complex shapes in nature that arise as a result of different growth rates. We stumbled quite by accident on a way to achieve fully deterministic manufacture of some three-dimensional objects."

Explore further: Morphing composite material has mighty potential (w/ Video)

More information: Liu J, Huang J, Su T, Bertoldi K, Clarke DR (2014) Structural Transition from Helices to Hemihelices. PLoS ONE 9(4): e93183. doi:10.1371/ journal.pone.0093183 . dx.plos.org/10.1371/journal.pone.0093183

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User comments : 23

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Diogenes Tha Dogg
5 / 5 (9) Apr 23, 2014
Reminds me of playing with telephone cord as a child.
Deuterium2H
5 / 5 (8) Apr 23, 2014
"Discovery?", my ass. My office phone cord does this at least ten times every day...so, do I win a friggin' Nobel Prize?
zorro6204
4 / 5 (4) Apr 23, 2014
I don't think phone cords qualify as being part of "nature". Though an argument could be made.
aaron35
Apr 23, 2014
This comment has been removed by a moderator.
mark_mnarkwynne
3 / 5 (4) Apr 23, 2014
Root wood also makes this shape. A stretched helix. Wow.

Seriously this is NOT science.
shavera
5 / 5 (5) Apr 23, 2014
Did anyone bother to make measurements of their phone cord's properties and how they got that way? Or to come up with a mathematical description of the system? I mean that's the difference between science and just saying "huh that's neat."
aaron35
Apr 23, 2014
This comment has been removed by a moderator.
Returners
2.1 / 5 (7) Apr 23, 2014
Reminds me of playing with telephone cord as a child.


Yup.

More and more p.h.d. candidates are discovering things the rest of us knew when we were like 4 years old.
aaron35
Apr 23, 2014
This comment has been removed by a moderator.
Scottingham
5 / 5 (1) Apr 23, 2014
Woo that was some nonsense aaron! I always get a kick out of the physics deniers.

The difference, and novelty of what they did was that they were able to create a shape with multiple 'perversions' (their word, not mine). I have seen those hemihelixes on phone cords, but only one at a time, or one then a few regular loops then another. I have never seen a phone cord do what that rubber can do. It just isn't stretchy enough.
aaron35
Apr 23, 2014
This comment has been removed by a moderator.
Returners
2.5 / 5 (4) Apr 23, 2014
Woo that was some nonsense aaron! I always get a kick out of the physics deniers.

The difference, and novelty of what they did was that they were able to create a shape with multiple 'perversions' (their word, not mine). I have seen those hemihelixes on phone cords, but only one at a time, or one then a few regular loops then another. I have never seen a phone cord do what that rubber can do. It just isn't stretchy enough.


I used to do that when I was a kid. There is nothing too special about that. Sure, it's been engineered to make the effect more consistently and useful, but it is doable with a normal 80's era phone cord.
NoTennisNow
5 / 5 (3) Apr 23, 2014
How you return the phone cord to it's original shape? Are the hemihelix's (hemihelicies?) stable?
DonGateley
5 / 5 (2) Apr 23, 2014
@NoTennisNow: too damn stable for me. I have never figured out how to get rid of one. No matter what I do a distortion remains. :-)

I am curious what will happen when he lets go of the ends of that multi-perversion thingy, though.
dustywells
5 / 5 (3) Apr 23, 2014
As I was reading this, my first thought was: "Phone cord," my second thought was: "delayed April fools joke." However, this discovery does have potential in many fields once we get past the "I knew this already" bias. After all, graphene was just soot a decade ago.
aaron35
Apr 24, 2014
This comment has been removed by a moderator.
Expiorer
1 / 5 (2) Apr 24, 2014
I also discovered a new shape while taking a dump this morning.
Young_Kyun_Choi
3 / 5 (2) Apr 24, 2014
Wow, look how many scientifically uneducated people equalize sporadic, episodic observations with controlled experiments! Maybe they came from back in the 15th century when the idea of empirically studying of nature by experiment was still in its infancy.
Young_Kyun_Choi
3 / 5 (2) Apr 24, 2014
Also, the article aaron35 linked had little to explain the discovery described in this report, as the structures investigated in the two articles were different and the researchers in the aaron's article did not attempt to describe or explain formation of regular structure made of repeated hemihelices.
Young_Kyun_Choi
4 / 5 (4) Apr 24, 2014
So all you mean commentators should be ashamed of yourself unless you contemplated on the principle underlying this phenomenon, related it to the elastic property of the material, and systematically varied each system variable while controlling all other variables.
antialias_physorg
5 / 5 (4) Apr 24, 2014
The cucumber vine tendrils are doing these shapes routinely. Yes, it's a "duh" science

It's not 'Duh' science. This is not about finding the helix type but about characterising when and how it happens. The energy terms involved are very interesting because they point the way to manufacture of similar structure - possibly switchable structures between 'regular' and these helix types.

Helix structures are used in technology. There's a high probability you're actually looking at one right now (the liquid crystals in your monitor). If it's easy to switch between the two this could lead to energy savings (and ultra fast reacting monitors), as a 'perverse' helix should not rotate light, while a regular helix does. I.e. you don't have to straighten the entire path out as you have to do now.
mark_mnarkwynne
1 / 5 (4) Apr 24, 2014
Did anyone bother to make measurements of their phone cord's properties and how they got that way? Or to come up with a mathematical description of the system? I mean that's the difference between science and just saying "huh that's neat."


mathematics is not science, but you already know that I am sure.
A phone cord gets that way due to the nature of the materials used, ie flexibility and bend radius, the nature of the manufacturing of the cable as in twisted wiring to reduce interference so the phone cord shape is a set of multiple different factors combined. All mathematically calculated during design. Engineering lad.

you can translate this to maths, yes of course. Is that scientific? No. Mathematics are a scientific tool. Nothing scientific can be derived purely from Mathematics.
charlimopps
5 / 5 (3) Apr 24, 2014
"Mathematics is the science of Quantity" - Aristotle
"Mathematics is the science that draws necessary conclusions" - Benjamin Peirce
"Mathematics is the science of formal systems" - Haskell Curry
"Mathematics is the science of numbers, quantities, and shapes and the relations between them" - merriam webster dictionary

So you might not want to be so arrogant and insulting before you even bother to open a dictionary. ;-)
Shootist
5 / 5 (1) Apr 24, 2014
"Discovery?", my ass. My office phone cord does this at least ten times every day...so, do I win a friggin' Nobel Prize?


didja publish a paper properly describing the topology?
Jeppe
5 / 5 (1) Apr 24, 2014
The discovery isn't the shape per se. It is that the number and interval of the 'perversions' in the helix shape is determined by the aspect ratio of the 2 bands being bonded together. The important part is that the changes in chirality are not random.
TiagoTiago
not rated yet Apr 24, 2014
Isn't this the same thing that happens when you try to put a higher dimensional 2d flat surface in 3d space, or in other words, when you make a disc have a bigger circumference than it should have for it's diameter? Don't some mushrooms and sea animals have wavy shapes like that?
Liquid1474
not rated yet Apr 26, 2014
"mathematics is not science, but you already know that I am sure."


Wow that is an asinine statement; unfortunately you can't realize that. Here I will help you:
The Riemann hypothesis
The Poincaré conjecture
Fermat's Last Theorem
Yang–Mills existence and mass gap...

These questions and associated discoveries MAY have engineering applications but are NOT studied to produce better phone cords Skippy;
IamVal
not rated yet Apr 30, 2014
my telephone cord and slinkies have been pulling this bullshit for the entirety of my nearing 3 decades