Filtration Properties of Auxetics with Rotating Rigid Units

Auxetic structures and materials expand laterally when stretched. It has been argued that this property could be applied in the design of smart filters with tunable sieving properties. This work analyses the filtration properties of a class of auxetic structures which achieve their auxeticity through a rotating rigid unit mechanism, an archetypal mechanism known to be responsible for this behavior in a number of crystalline materials. In particular, mathematical expressions are derived for the space coverage of networks constructed from a variety of quadrilaterals, as well as the pore radius. The latter is indicative of the particle size that can pass through when the particle dimension is comparable to the pore size, whereas the space coverage is indicative of the rate of flow when the particles are of a much smaller dimension than the pore size. The expressions suggest that these systems offer a wide range of pore sizes and space coverages, both of which can be controlled through the way that the units are connected to each other, their shape and the angle between them.