Chirality through buckling

The tremendous interest in chirality originates not only from understanding its crucial role in living and non-living systems, but is also spurred by potential technological applications such as enantioselective catalysis and separations, optical devices, and sensors. While at the molecular scale a couple of systems have been reported to show spontaneous symmetry breaking followed by amplification of this initial bias to molecules of single handedness, extension of these principles to larger length scales has remained a fundamental challenge. Since a general characteristic in these molecular systems is the presence of specific enantioselective molecular interactions that are not applicable to higher-scale systems, fundamentally different concepts need to be developed to achieve complete chiral symmetry breaking at larger length scales.

Left: Stability diagram from the buckling analysis. Upon reaching a critical swelling ratio, each individual supported plate buckles into either half or full sinusoids depending on its aspect ratio $l/h$. This results in the formation of either achiral or chiral patterns. Right: Demonstration of reversible achiral and chiral pattern formation by swelling. The color-coded arrows in the insets indicate the handedness of vertices.

We succesfully reported chiral symmetry breaking followed by full amplification to yield uniform chiral patterns of single handedness in micro/macroscale structures. Guided by extensive theoretical analysis, we used buckling in supported cellular structures to reversibly switch between achiral and chiral configurations. Furthermore, we show that the sign of chirality can be encrypted, read out, and overwritten in the architecture and demonstrate the generality of this novel mechanism using different length scales, geometries, materials and stimuli. Importantly, the scale-independent behavior of the proposed process allows us to scrutinize the kinetic processes of both the nucleation which causes the symmetry breaking, and the subsequent propagation of this chirality which is assisted by a self-correction mechanism to yield uniform patterns of single handedness.

We have discovered a fundamentally new way of generating chiral structures with desired handedness, exploiting buckling in supported cellular structures. Despite many studies on buckling of surface-attached plates and freestanding structures, little is known about mechanical instabilities in surface-attached cellular structures. Our results show that buckling-induced reconfiguration in these rationally designed architectures offers a unique system with a range of materials advantages: (i) it can be designed at various length-scale; (ii) the reconfiguration can occur upon application of different stimuli; (iii) the transformation can be made fully reversible; and (iv) the system can be controlled to yield either uniform achiral or chiral configurations with user-defined handedness. The unique capability of direct visualization of both the nucleation and propagation of the pattern provides a rich platform to study the processes of symmetry breaking and chiral amplification, which play a crucial role both in living and non-living systems. From a practical perspective, the full control over the chiral outcome in combination with the capability of using a wide range of length scales, materials, stimuli, and geometrical designs provides a new class of reversibly transformable architectures with a broad field of applications ranging from tunable mechanical metamaterials to switchable optics.

Publications:

• S.H. Kang*, S. Shan*, W.L. Noorduin*, M. Khan, J. Aizenberg$, and K. Bertoldi$ (\$corresponding author, * equal contribution). Buckling-induced reversible symmetry breaking and amplification of chirality in supported cellular structures. Advanced Materials, 2013.