Gap junctions in freeze-fractured membranes of the arachnoid mater

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Measuring the order in ordered porous arrays: can bees outperform humans?

A method that explains how to quantify the amount of order in “ordered” and “highly ordered” porous arrays is derived. Ordered arrays from bee honeycomb and several from the general field of nanoscience are compared. Accurate measures of the order in porous arrays are made using the discrete radial distribution function (RDF). Nanoporous anodized aluminum oxide (AAO), hexagonal arrays from functional materials, hexagonal arrays from nanosphere lithography, and square arrays defined by interference lithography (all taken from the literature) are compared to two-dimensional model systems. These arrays have a range of pore diameters from ∼60 to 180 nm. An order parameter, OP ₃ , is defined to evaluate the total order in a given array such that an ideal network has the value of 1. When we compare RDFs of man-made arrays with that of our honeycomb (pore diameter ∼5.89 mm), a locally grown version made by Apis mellifera without the use of foundation comb, we find OP ₃ =0.399 for the honeycomb and OP ₃ =0.572 for man’s best hexagonal array. The nearest neighbor peaks range from 4.65 for the honeycomb to 5.77 for man’s best hexagonal array, while the ideal hexagonal array has an average of 5.93 nearest neighbors. Ordered arrays are now becoming quite common in nanostructured science, while bee honeycombs were studied for millennia. This paper describes the first method to quantify the order found in these arrays with a simple yet elegant procedure that provides a precise measurement of the order in one array compared to other arrays.