Adhesion Analysis Considering van der Waals Force in a NanoSized Region Using the Boundary Element Method

Recently, micro- and nanomachines for microelectromechanical systems and the mechanism of bio-adhesive pads have attracted great interest. Nanoscale structures are affected by forces such as the van der Waals force, even though they are neglected in large-scale structures. In this paper, the van der Waals force is introduced to a boundary element method (BEM) program for analyzing adhesion in arbitrarily shaped bodies. The van der Waals force is described by a nonlinear function of the distance between two surfaces in close proximity, and the adhesion and repulsion forces vary greatly within the atom equilibrium distance. Therefore, it is difficult to obtain a solution for the simultaneous equation in the BEM. We propose a method to compute the body deformation and apply it to the adhesion between a cylinder and a flat, rigid substrate. The solution is compared with previously published theoretical results, and the validity of the algorithm for approaching the solution is demonstrated. Further calculations for the adhesive contact of softer and harder cylinders with a rigid substrate are conducted.