Capillary image force

The first term in the right-hand side of Equation 4.168 expresses the gravity force pushing the particle to slide down over the inclined meniscus on the wall the second term originates from the pressure difference across the meniscus on the wall the third term expresses the so-called capillary image force, that is, the particle is repelled by its mirror image with respect to the wall surface [37,344]. 

Figure 3.12 Capillary image force between the floating particle and its image [19]. (a) Fixed contact angle at the wall (6 = tv2) (b) Fixed contact line at the wall (0)=0).

Ihe above two cases are rare and special in reality, which are simply described by Capillary Image Force [19]. The above method cannot be directly used for general and realistic conditions where the contact angle is not fixed just to 90° but can be any angle over a wide range and the contact line is positioned to an arbitrary elevation. 

In Eqns. (3.91) and (3.104), the first term comes from the capillary image force the second one originates from the buoyancy force and the last term is the pressure jump across the interface and is typically small for small particles [Pg.101]

The value of the pull-off force can he reduced significantly hy imaging under liquids, because of elimination of capillary condensation forces, which pull the tip towards the sample. 

One central concern with routine AFM on polymers is the presence of shear forces that occur in CM. These forces are a result of friction between AFM probe tip and the polymer sample and may deform and plastically modify the polymer surface. This has been observed even for glassy materials, such as PS, when imaged at ambient conditions (see Sect. 3.2.3 in Chap. 3 Fig. 3.16). In addition to sample damage, the tip may be affected by adhering particulates or, even worse, by wear. These phenomena limit the resolution dramatically and may result in unwanted artefacts (excessive tip imaging). Thus, minimized imaging forces are essential, and this may require the operation under a suitable liquid to eliminate capillary forces. 

For the operation of contact mode AFM under liquid there are only few details that differ from operation in air. The imaging forces can often be controlled much more precisely if the adhesion is lower due to the absence of capillary forces. Hence the adjustment of the setpoint requires more attention and can be done with much more precision. The adjustment can be based on acquired force-displacement curves (see below, Fig. 3.39). Setpoint deflection values close to the out of contact deflection yield minimized normal forces [82-84],... 

For particle adhesion, the total forcesUOS) consist of Lifshitz-van der Waals forces the electrostatic induced image forces the capillary force F, the chemical forces ch (such as the acid-base interaction), and the double layer force F ... 

The resolution of contact mode AFM is, as is typical for AFM in general, limited by the tip size, tip shape, and deformation in the tip-sample contact area. The range and strength of the interatomic and intermolecular forces between tip and sample may become significant, if the imaging force is very small. For operation in air, however, capillary condensation may occur in the tip-sample contact [12], which results in significant attractive forces that cannot be counteracted in a stable manner. Imaging in liquid (e.g., water or ethanol) can... 

Fig. 10. Analysis of the atomic lattice images of the lead compound entering CNTs by capillary forces (a)detailed view of the high resolution image of the filling material, (b)tetragonal PbO atomic arrangement, note the layered structure and (c)tetragonal PbO observed in the [111] direction, note that the distribution of lead atoms follows the contrast pattern observable in (a), (d)bidimensional projection of the deduced PbO filling orientation inside CNTs as viewed in the tube axis direction, note that PbO layers are parallel to the cylindrical CNT cavity.

Figure 1.8 Schematic diagram of a capillary (one of hundreds) within the printing head of a bubble-jet printer. The resistor heats a small portion of solution, which boils thereby increasing the pressure. Bubbles form within 5 (rs of resistance heating after 10 xs the micro-bubbles coalesce to force liquid from the aperture and a bubble is ejected a further 10 xs later. The ejected bubble impinges on the paper moments afterwards to form a written image. Reproduced by permission of Avecia...

Recently, Razumovskid441 studied the shape of drops, and satellite droplets formed by forced capillary breakup of a liquid jet. On the basis of an instability analysis, Teng et al.[442] derived a simple equation for the prediction of droplet size from the breakup of cylindrical liquid jets at low-velocities. The equation correlates droplet size to a modified Ohnesorge number, and is applicable to both liquid-in-liquid, and liquid-in-gas jets of Newtonian or non-Newtonian fluids. Yamane et al.[439] measured Sauter mean diameter, and air-entrainment characteristics of non-evaporating unsteady dense sprays by means of an image analysis technique which uses an instantaneous shadow picture of the spray and amount of injected fuel. Influences of injection pressure and ambient gas density on the Sauter mean diameter and air entrainment were investigated parametrically. An empirical equation for the Sauter mean diameter was proposed based on a dimensionless analysis of the experimental results. It was indicated that the Sauter mean diameter decreases with an increase in injection pressure and a decrease in ambient gas density. It was also shown that the air-entrainment characteristics can be predicted from the quasi-steady jet theory. 

In the non-contact mode (Fig. 6b), AFM acquires the topographic images from measurements of attractive forces in close proximity of the surface, as the tip does not touch the sample and the cantilever oscillates close to the sample surface [12]. This mode is difficult to work with in ambient conditions due to the interference of the capillary forces. Very stiff cantilevers are needed so that the attraction does not overcome the spring constant of the cantilever. However, the lack of contact with the sample means that this mode should be the least invasive and hence cause the least disruption. The disadvantage of this method is that the tip may jump into contact with the surface due to attractive forces. 

The various surface forces are seen to be responsible for capillary rise. The lower the surface tension, the lower the height of the column in the capillary. The magnitude of y is determined from the measured value h for a fluid with known pL. The magnitude of h can be measured directly by using a suitable device (e.g., a photograph image). 

Fig. 19 SEM images of ID pattern recorded holographically by two beam interference in SU-8 and developed using a water rinse to minimize the capillary force of drainage [77]...

Note, that the surface and deformation forces are of the same order of magnitude. Therefore, surface forces should be as small as possible to minimise damaging and indentation of soft polymer samples. For example, sharp probes have a lower capillary attraction and adhesion forces, and therefore enable more gentle probing of a soft polymer than a blunt tip. A sharp tip can also be moved in and out of the contamination layer more readily than a blunt tip. This is particularly important for non-contact intermittent contact imaging described in Sect. 2.2.1. 

Similar to all scanning microscopies, the resolution in SFM depends on the effective size of the probe and its modifications which arise from sample-probe interactions. Theoretically, the effective size is determined by the probe geometry and the force-distance dependence between the tip and sample. In addition, the aperture increases because of the tip-sample deformation, surface roughness, capillary forces, and various sources of noise. Experimentally, the resolution is limited by the sensitivity of the force detection system, the image noise, and the scanner precision. 

As discussed in Sect. 2.2.2, FMM images can lose the material contrast when the sample stiffness exceeds the stiffness of the cantilever. In addition, the net signal contains friction effects because of the cantilever bending and the sample indentation. Furthermore, in liquid samples, capillary forces dominate the response at low frequencies [ 127]. These drawbacks can be overcome by operating the microscope above the contact resonance frequencies. In the so-called con-tact-mode scanning local-acceleration microscope the cantilever oscillates at very low amplitudes of ca. 0.1 nm which still provides strong enough contrast with respect to the mechanical properties [122]. Since the response of the canti-... 

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