Flexoelectric-like radial polarization of single-walled nanotubes from first-principles

Abstract

Abstract Flexoelectricity is the polar response of an insulator to strain gradients such as bending. While the size dependence makes it weak in bulk systems in comparison to piezoelectricity, it can play a bigger role in nanoscale systems such as thin films and nanotubes (NTs). In this paper we demonstrate using first-principles calculations that the walls of carbon nanotubes (CNTs) and transition metal dichalcogenide nanotubes (TMD NTs) are polarized in the radial direction, the strength of the polarization increasing as the size of the NT decreases. This is reminiscent of a flexoelectric response in bulk insulators, the strain gradient being achieved by bending the 2D monolayers into NTs. For CNTs and TMD NTs with chiral indices (n, m), the radial polarization of the walls P R diverges below C ( n , m ) / a = n 2 + n m + m 2 ∼ 10 , where C(n, m) is the circumference and a is the monolayer lattice constant. For CNTs, P R drops to zero above this value but for TMD NTs there is a non-zero polarization, which is ionic rather than electronic. The size dependence of P R in the TMD NTs is interesting: it increases gradually and reaches a maximum of P R ∼ 100  C  cm−2 at C(n, m)/a ∼ 15, then decreases until C(n, m)/a ∼ 10 where it starts to diverge. Measurements of the radial strain on the bonds with respect to the monolayers shows that this polarization is the result of a larger strain on the outer bonds than the inner bonds, but did not explain the peculiar size dependence. These results suggest that while the walls of smaller CNTs and TMD NTs are polarized, the walls of larger TMD NTs are also polarized due to a difference in strain on the inner and outer bonds.