First-principles derived force field for h-BN monolayer nanostructures: Applications to sheets, nanotubes and nanotori

Abstract

In this work, we present an empirical force field for hexagonal boron nitride (hBN) monolayers, derived via a bottom-up strategy from first principles calculations. We aim to deliver a simple analytical force field for boron nitride which is efficient and applicable to large-scale simulations, without compromising its accuracy. The force field is developed with the goal to analytically reproducing the potential energy contributions arising from planar bond-stretching and bond-angle-bending deformations, as well as from out-of-plane torsional deformations, as obtained from periodic density functional theory calculations. Analytical anharmonic potential energy functions were employed to describe and parameterize the force field through a fitting process. The potential is applied for estimating in-plane (stiffness matrix and elastic constants) and out-of-plane (bending and Gaussian rigidity) mechanical properties of monolayer hBNs using both molecular mechanics calculations and analytical formulas. Additionally, we determined the elastic properties of more complex nanostructures, including hBN nanotubes and nanotori. By combining a continuum model for bent hollow beams with the definition of bending rigidity, we validate the model predictions against an analytical expression for the bending rigidity of large-diameter hBN nanotubes, expressed as a function of their radius and the in-plane Young modulus.