Auxetic behaviour from rotating semi-rigid units

Abstract

Auxetics (i.e. systems with negative Poisson's ratios) exhibit the unexpected feature of becoming fatter when stretched and narrower when compressed. This property is highly desirable as it imparts many beneficial effects on the material's macroscopic properties. Recent research suggests that in an idealised scenario, systems composed of connected ‘rigid squares’ can exhibit auxetic behaviour (Poisson's ratio = –1) due to a mechanism involving relative rotation of the squares. This paper shows through force-field based molecular modelling simulations that although ‘rotating squares’ are responsible for negative Poisson's ratios in various zeolite frameworks, in these real materials, the squares are not rigid and the auxeticity is not as pronounced as in the ‘idealised’ model. In view of this, a new model system made from connected ‘semi-rigid’ squares is proposed and analytical equations for the mechanical properties of this new model system are derived and discussed. It will be shown that the Poisson's ratios in this new model are highly dependent on the extent of rigidity of the squares and the direction of loading. It will also be shown that this new model provides a better description for the behaviour of auxetic zeolite frameworks than the original ‘rotating rigid squares’ model.