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

Surface Energy of Curved Surface Based on Lennard-Jones Potential

Although various phenomena have confirmed that surface geometry has an impact on surface energy at micro/nano scales, determining the surface energy on micro/nano curved surfaces remains a challenge. In this paper, based on Lennard-Jones (L-J) pair potential, we study the geometrical effect on surface energy with the homogenization hypothesis. The surface energy is expressed as a function of local principle curvatures. The accuracy of curvature-based surface energy is confirmed by comparing surface energy on flat surface with experimental results. Furthermore, the surface energy for spherical geometry is investigated and verified by the numerical experiment with errors within 5%. The results show that (i) the surface energy will decrease on a convex surface and increase on a concave surface with the increasing of scales, and tend to the value on flat surface; (ii) the effect of curvatures will be obvious and exceed 5% when spherical radius becomes smaller than 5 nm; (iii) the surface energy varies with curvatures on sinusoidal surfaces, and the normalized surface energy relates with the ratio of wave height to wavelength. The curvature-based surface energy offers new insights into the geometrical and scales effect at micro/nano scales, which provides a theoretical direction for designing NEMS/MEMS.

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.