Harvard scientists create the hemihelix

Researchers from Harvard University have accidentally stumbled upon a shape called the hemihelix. While a related shape, the helix, is one of the most common structures in nature, the hemihelix is more complex and rarely seen.

A helix is a 3D spiral structure, much like a corkscrew or a slinky toy. Hemihelices form when the direction or handedness in which the spiral turns - known as the chirality - changes or reverses periodically along the helix’s length. This reversal in chirality is called a perversion.

The team discovered the shape when they set out to fabricate new 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.

“We expected that these strips of material would just bend - maybe into a scroll,” said David R Clarke, Extended Tarr Family Professor of Materials at the Harvard School of Engineering and Applied Sciences. “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.”

Writing in the journal PLOS ONE, the researchers said that in its simplest form, a helihelix “consists of two helices of opposite chirality joined by a perversion”, but that “a recent, simple experiment using elastomer strips reveals that hemihelices with multiple reversals of chirality can also occur, a richness not anticipated by existing analyses”.

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. Image courtesy of Jiangshui Huang.

To better understand whether the observed 3D structures were randomly occurring or whether specific factors controlled their formation, the scientists stretched, joined and released rubber strips, then numerically simulated and analysed the shape-forming process. Their experiments can be viewed on YouTube.

By testing differences in the aspect ratio, or the width-to-height ratio of the rubber strips, the authors discovered that when a strip is wide relative to its height, it produces a helix. Further measurements revealed that there may be a critical value of the aspect ratio at which the shape transitions from a helix to a hemihelix, with periodic reversals of chirality.

The authors suggest that this phenomenon has not yet been observed because other classes of materials simply break when stretched to the mismatched strains used in these tests.

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. Image courtesy of Jia Liu.

“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,” said co-author Dr Katia Bertoldi, an associate professor at Harvard.

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

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