Unified model for adhesive contact between solid surfaces at micro/nano-scale

Abstract

Because of the huge specific surface area at the micro/nano scale, inter-surface adhesion and surface effects play a critical role in the behavior of solid-to-solid contact. The inter-surface adhesion originates from the intermolecular traction between two surfaces, while the surface effects, including residual surface stress and surface elasticity, result from the physical discrepancy between the surface atoms and their bulk counterparts. Despite the importance of both effects, theoretically modeling them together is still a challenging open issue because of the nonlinear coupling nature in between. This study is dedicated to the development of a unified theoretical framework with consideration of both inter-surface adhesion and surface effects based on the Gurtin–Murdoch surface elasticity theory. The two effects are integrated into a self-consistent equation concerning surface gaps and interactions, and a novel regularization method is proposed to address the oscillation and singularity of the equation. It is demonstrated that an adhesive contact problem with surface effects can be decomposed into two fundamental issues. One addresses the classical problem without considering residual surface stress or surface elasticity, and the other focuses solely on residual surface stress. Theoretical predictions show that the surface effects suppress or even eliminate the surface deformation and jumping instability during contact, effectively stiffening the solid surfaces. Three types of pull-off force transitions with surface effects are obtained, forming continuous bridges among the rigid (Bradley), soft (JKR), and liquid-like (Young–Dupre) limits. The adhesion transitions considering surface effects in this work are universal, and the existing limits or transitions can be regarded as special cases of this work. Our study provides a further understanding of the adhesive contact between micro/nano solids and may be instructive for practical applications where inter-surface adhesion and surface effects are dominant, such as nanoindentation, micro-electro-mechanical systems, and microelectronics.