Static measurement of forces

In this section we report on force measurements performed in contact mode. Since the tip velocity is small, it is generally considered that the meniscus is always at equilibrium dynamic effects are therefore not considered. We present two examples emphasizing the role of boundary conditions and constraints in the capillary force. 

1 Capillary adhesion forces influence of relative humidity 

The influence of RH on the magnitude of adhesion force between a tip and a surface is an important issue in AFM. The commonly observed behavior is that the capillary force exhibits a maximum for a certain humidity value, which varies from experiment to experiment. Recently, Kober et al. investigated the influence of tip sizes and aspect ratios (characterized by scanning electron microscopy [SEM]) on the pull-off force. The experimental results show that for tips with a large radius (typically above 15 nm), a 

The precise dependence of the meniscus shape on RH values can be derived from an energetic approach by considering the grand canonical potential that contains bulk and surface contributions. The meniscus shape is obtained by a minimization procedure, whereas the force is obtained as the derivative of the potential with respect to the tip-surface separation. The results reported in Fig. 9.5 give the overall evolution of the adhesion force for different 

An interpretation of the origin of these behaviors can be obtained by a geometrical approach. If one considers the so-called toroidal approximation for which the meniscus profile is assumed circular and if one neglects the tension force, the capillary force can simply be written as a Laplace term  

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The Z factor in Fig. 6.1 is simply the change of elevation between two points, in feet. Z may also be expressed as an energy term as footpounds per pound of mass. Note that here it is pounds of mass rather than of moving fluid, since this is a static measure of force. 

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