Self-organization of a mesoscale bristle into ordered hierarchical helical assemblies

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A well known phenomenon is the clumping of wet hair. Wet hair.jpg

This can be explained by studying the elasticity of each hair strand and the adhesion among the neighboring hair strands. When the hair strands are immersed in water, and the water is allowed to evaporate, capillary forces between the strands cause them to deform, adhere to each other, and form clumps.

This paper demonstrates that this elastocapillary force can be used to self-assemble stiff and upright nano-pillars to helical clusters and even coiled large-area structures. The fundamental theory involves the following parameters:

<math>r</math>: circular radius of the nano-pillars

<math>L</math>: length of nano-pillars

<math>d</math>: distance between adjacent nano-pillars

<math>E</math>: Yong's modulus

<math>B\sim Er^4</math>: bending stiffness of the nano-pillars

<math>J</math>: adhesive energy per unit area

<math>\gamma</math>: interfacial tension of the evaporating liquid


Example.jpg

<math>\tau=\pi</math>