Static Capillary Force

We describe here the capillary force resulting from a liquid meniscus bridging two solid surfaces. We make the following assumptions  

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In the previous section we described static capillary forces. Viscous forces may also bring an additional contribution that will be readily measured with AFM dynamical modes. Therefore, in the framework of AFM studies, it is of interest to evaluate the effect of the liquid viscosity. We distinguish two cases corresponding to different configurations discussed in the next section of this chapter. We first evaluate the viscous force compared to the capillary one and then the effect of the boundary condition. 

For the case of a static liquid bridge of contact angle 0, surface tension induces an attractive capillary force Fcap between the two particles... 

Static Mode in Liquids In liquids, the capillary force is not present allowing a more straightforward interpretation of the results. Furthermore, the contact area is as small as a single-atom contact. Special cantilevers have to be used for the operation in liquid. When reused, those cantilevers must be carefully cleaned and are best kept wet until employed again. 

The ultimate equilibrium would be that of a drop or film of liquid that spreads until it thins to a monomolecular layer. Actually, a quasi-static equilibrium will be reached when the viscous forces exceed the gravitational and surface tension forces and the thinning of the film becomes imperceptibly slow. However, as discussed below, there are surface chemical and capillary forces acting at the three phase boundary that cause liquids to diffuse from the edge of a drop or a film. There is a school of thought and some experimental evidence that when a liquid film becomes very thin its chemical characteristics become different than that of the bulk liquid because of orientation effects induced by the solid substrate. Derjaguin strong advocate... 

Figure 6.2 Examples of static self-assembly, (a) Crystal structure of a ribosome, (b) Self-assembled peptide-amphiphile nanofibers, (c) An array of millimeter-sized polymeric plates assembled at a water/perfluorodecalin interface by capillary interactions, (d) Thin film of a nematic liquid crystal on an isotropic substrate, (e) Micrometer-sized metallic polyhedral folded from planar substrates, (f) A 3-D aggregate of micrometer plates assembled by capillary forces.

If there is a contamination layer, there is a third possibility the tip may be held in contact with the surface by the capillary forces, even when the force on the cantilever is attractive. This causes confusion, since attractive force on the cantilever can be taken to mean non-contact mode, but here high resolution is possible because the tip is in contact with the surface. A true non-contact mode with a static probe is difficult to maintain in a stable manner, as the soft lever is near instability. 

Here, all forces have been made dimensionless with respect to a measure of the capillary force, or Ttya. Note that the bridge strength consists of two components. Fcap is the strength of a static capillary bridge, and is a function of curvature of... 

To evaluate the importance of the capillary forces, the boundary conditions on the free boundary must be introduced with the surface tension elfect, then the kinematic condition (5a) is retained, while the static condition at the resin front (neglecting the air influence) can be written as [58] ... 

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