An Atomistic-Based Nonlinear Plate Theory for Hexagonal Boron Nitride.

Through the continuity of the DREIDING force field, we propose, for the first time, the finite-deformation plate theory for the single-layer hexagonal boron nitride (h-BN) to clarify the atomic source of the structure against deformations. Divergent from the classical Föppl-von Karman plate theory, our new theory shows that h-BN's two in-plane mechanical parameters are independent of two out-of-plane mechanical parameters. The new theory reveals the relationships between the h-BN's elastic rigidities and the atomic force field: (1) two in-plane elastic rigidities come from the bond stretching and the bond angle bending; (2) the bending rigidity comes from the inversion angle and the dihedral angle torsion; (3) the Gaussian rigidity only comes from the dihedral angle torsion. Mechanical parameters obtained by our theory align with atomic calculations. The new theory proves that two four-body terms in the DREIDING force field are necessary to model the h-BN's mechanical properties. Overall, our theory establishes a foundation to apply the classical plate theory on the h-BN, and the approach in this paper is heuristic in modelling the mechanical properties of the other two-dimensional nanostructures.

Curvature-based interaction potential between a micro/nano curved surface body and a particle on the surface of the body.

The interaction potential between a curved surface body and a particle located on the surface of the body is studied in this paper. Based on the negative exponential pair potential (1/R(n)) between particles, the interaction potential is proved to be of the curvature-based form, i.e., it can be written as a function of curvatures of the surface. Idealized numerical experiments are designed to test the accuracy of curvature-based potential. Based on the curvature-based potential, propositions below are confirmed: a highly curved surface body will induce driving forces on the particle located on the surface, and curvatures and the gradients of curvatures are essential factors forming the driving forces. In addition, the tangent driving force acting on the particle from the curved surface body is studied. Based on duality, the following rule is proved: for a convex or concave curved body sharing the same curved surface, the curvature-based interaction potential between them and a particle on the surface can make up the potential of a particle in the whole space.