Detailed modeling of the adhesion force between an AFM tip and a smooth flat surface under different humidity levels

Adhesion forces between a probe tip and a flat surface under humid conditions are usually evaluated using the geometric model of the water bridge profile. However, the force equilibrium of the water/air film must exist since the film is in a stationary state and thermodynamic equilibrium. In the present study, a sophisticated numerical model, which is based on both geometry constraints and the force equilibrium of the water/air film, is proposed to compute adhesion forces. The results obtained are in good agreement with the experimental results by pull-off tests presented in the literature. The maximum separation distance can be evaluated using the present model. When the contact angle of the tip equals that of the flat surface, the tip radius, rather than the humidity level, dominates the adhesion force. The capillary pressure force was found to be a major component of the adhesion force at low humidity levels. The surface tension force significantly increased when the relative humidity was increased.