Researchers at Harvard have characterized the hemihelix, a shape rarely found in nature, from rubber bands, in a study that could offer insight into the fabrication of a range of three-dimensional shapes from flat parts, and even the development of new molecules.

Although helices, 3D structures shaped like a corkscrew, are one of the most common structures in nature, hemihelices are more complex, being formed when the direction of the spiral – its chirality – changes along its length, a reversal known as a “perversion”. As reported in PLOS ONE [Liu et al. PLOS ONE (2014) DOI: 10.1371/journal.pone.0093183], the surprise discovery occurred when the team was trying to manufacture new 2D flexible helical springs for a cephalopod-inspired imaging project and unexpectedly encountered a hemihelix with multiple perversions.

Hemihelix produced by perversions in chirality
Hemihelix produced by perversions in chirality

Their springs were made from two strips of rubber material of different lengths. The shorter strip was stretched to the same length as the longer one, before the undeformed strip and the pre-stressed strip were glued together. On examining the differences in the aspect ratio of the rubber strips through numerical simulations and analysis, it was found that when one of the strips was significantly wide compared to its height, it produces a helix, but that there was a critical value of this aspect ratio at which the resulting shape moves from a helix to a hemihelix with periodic reversals of chirality.

“We discovered that a wide range of possible shapes can be attained in a simple stressed system by controlling the geometry of the cross-section.”Katia Bertoldi

They found this very simple method allowed them to create a variety of shapes. Although other classes of materials would just break when stretched in this way, they expected the strips to bend, but found instead they obtained a hemihelix that had a chirality that changed, constantly alternating from side to side. As study leader Katia Bertoldi said “We discovered that a wide range of possible shapes can be attained in a simple stressed system by controlling the geometry of the cross-section.”

The work showed the potential of identifying robust mechanisms to generate complex 3D shapes from flat strips, providing the basis for the development of a range of more intricate shapes. The next stage is to investigate how these different shapes can affect the properties of the structures, such as their effect on the propagation of light. Being able to produce the structures in a predictable and consistent way could also help mimic the geometrical features in new molecules, and lead to advances in a range of nanodevices.