Can nanotubes display auxetic behaviour?

Fully generalised analytical expressions for Iongitudinal Poisson's ratio are developed for armchair and zigzag Single-Walled Nanotubes (SWNTs) using an energy equivalent approach. Deformation is assumed due to simultaneous bond stretching and bond angle variation in response to an applied axial load. A parametric study Is then perfonned to explore under what circumstances SWNTs may exhibit auxetic (negative Poisson's ratio) response. In principle, auxetic behaviour can be achieved by modifying the hexagonal cell shape to adopt a re-entrant geometry for the case of bond angle variation being the dominant deformation mechanism. Alternatively, altering the length of the characteristic bond oriented in an off-axis direction to below a critical value or modifying the force constants governing the deformation modes so that bond stretching dominates for the conventional hexagonal cell shape can also lead to auxetic behaviour.