Polarity at the nanoscale

Relying on classical electrostatics, we extend the understanding of the electrostatic forces responsible for polarity to nano-objects. We show that while no actual divergence of the electrostatic potential occurs in polar nano-objects, beyond a critical object size, the divergent behavior of the potential differences as a function of size induces polar instability analogous to that at semi-infinite surfaces. We highlight several new and generic properties of polar nano-objects: (1) the dependence of the instability behavior on object dimensionality; (2) the driving role of the smallest structural parameter, not necessarily the thickness; (3) the inhomogeneity of the electrostatic potential within a polar termination and its divergent behavior as a function of the termination size; and (4) the polar character of symmetric stoichiometric objects with a vanishing total dipole moment. We give simple analytical arguments in order to build a generic framework, valid independent of the precise object dimensionality, structure, and ionocovalent characteristics.