Origin of order in bionanostructures
Nanoscale nipple arrays covering the corneal surface of many insects provide antireflection properties and have inspired industrial applications. Based on visual inspection, the dense packing of these nanostructures was initially described to adopt a regular hexagonal order. However, Fourier analysis revealed lack of order over larger distances of the lens cornea, with only patches of hexagonally organized nanostructures. Here we developed a formal mathematical analysis of nippled nanocoatings read by atomic-force microscopy (AFM). This analysis permits automatic assessment of the degree of order in nanostructural packings and its correlation with various characteristics of the nanoscale objects. We applied this analysis to corneae of 17 insect species from 6 orders. We find no correlation between the degree of order and the overall size of the lens. Instead, a strong correlation of the order and the density of the nipple packing exists. Surprisingly, we also see that order correlates with the height of the nanostructures. We discuss these findings in the context of the origin of order in the bio-nanoworld, where order may result largely from the dense packing of the nanostructures, rather than from specialized patterning mechanisms. Our findings uncover mechanisms of order formation, which may also apply to micro- and macro-structures.