A general, accurate procedure for calculating molecular interaction force

The determination of molecular interaction forces, e.g., van der Waals force, between macroscopic bodies is of fundamental importance for understanding sintering, adhesion and fracture processes. In this paper, we develop an accurate, general procedure for van der Waals force calculation.This approach extends a surface formulation that converts a six-dimensional (6D) volume integral into a 4D surface integral for the force calculation. It uses non-uniform rational B-spline (NURBS) surfaces to represent object surfaces. Surface integrals are then done on the parametric domain of the NURBS surfaces. It has combined advantages of NURBS surface representation and surface formulation, including (1) molecular interactions between arbitrary-shaped objects can be represented and evaluated by the NURBS model further common geometries such as spheres, cones, planes can be represented exactly and interaction forces are thus calculated accurately; (2) calculation efficiency is improved by converting the volume integral to the surface integral.This approach is implemented and validated via its comparison with analytical solutions for simple geometries. Calculation of van der Waals force between complex geometries with surface roughness is also demonstrated. A tutorial on the NURBS approach is given in Appendix A.

Graphical abstractNURBS based surface formulation for calculating van der Waals force: (a) NURBS representation of a sphere; (b) subdivided NURBS patches; (c) analytical solution and the numerical results; (d) relative error.Figure optionsDownload full-size imageDownload as PowerPoint slide