Force adhesive

The thermodynamic adsorption theory (dominant in many adhesion practices) is based on the secondary forces (van der Waals and acid-base ones/hydrogen bonding). The importance of these forces is discussed in this section. 

Adhesive forces between macroscopic surfaces can be strong even when just van der Waals (dispersion) forces are present (as seen also in Chapter 2). This is because such forces between macroscopic particles or surfaces are much longer-range than between molecules, as Ulustrated below for some characteristic cases of practical significance  

In Ec uations 6.9-6.11, H is the distance, R is the sphere radius, / is the surface tension and A is the so-called Hamaker constant (see Chapter 2 and also later in Chapter 11). 

The value for the surface tension in Equations 6.9-6.11 depends on the situation it is the solid surface tension for a solid in vacuum or the solid-vqiour surface tension if the solid is in a vapour environment or the solid-liquid interfacial tension, if the solid is immersed in a liquid. 

The last parts of Equations 6.9-6.11 are based on one of the most widely used expression for the Hamaker constant. A, as a function of distance and surface tension  

As mentioned in the introduction, in addition to assuming a spherical particle and a smooth surface, we shall assume that electric charges are not present in the problem, and the effects of gravity will be ignored as well. 

The adhesive force between a neutral particulate contaminant and the wafer is expected to be due to the attractive Van der Waal s interaction between molecules.This is a macroscopic force found by averaging over the force between all the molecules of a particle and the neighboring surface. For a spherical particle sitting on a flat wafer, it is known that surface roughness will cause the mean distance of separation between the particle and the wafer to be nonzero. The attractive force between these two entities acts along the normal between the sphere and the wafer, and is given by  

The force due to the shear in the vdscous sublayer on a particle lying on a surface, is analogous to the formula for Stoke s drag  

One sees immediately from this equation that when U 1000 cm/s, the shear force will exceed the adhesive force for r = 1 micron. This puts movement of the particle due to the shear force in the realm of reality. 

In general, for the particles to move, F must be greater than the force of friction iy which is given by the following equation  

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Fig. VI-6. The force between two crossed cylinders coated with mica and carrying adsorbed bilayers of phosphatidylcholine lipids at 22°C. The solid symbols are for 1.2 mM salt while the open circles are for 10.9 roM salt. The solid curves are the DLVO theoretical calculations. The inset shows the effect of the van der Waals force at small separations the Hamaker constant is estimated from this to be 7 1 x 10 erg. In the absence of salt there is no double-layer force and the adhesive force is -1.0 mN/m. (From Ref. 66.)...

The interfacial free energy per unit area is given by the adhesion force Fo/lrR", estimate the Hamaker constant responsible for the adhesion force in the crossed-cylinder geometry illustrated in the inset to Fig. VI-6. 

The flotation of mica has been correlated to the adhesion force measured from surface force (SFA—see Section VI-4) experiments although, to these authors, it is clear that dynamic effects prevent an absolute comparison [69, 70],... 

Thundat T, Zheng X-Y, Chen G Y, Sharp S L, Warmack R J and Schowalter L J 1993 Characterization of atomic force microscope tips by adhesion force measurements App/. Phys. Lett. 63 2150... 

Florin E-L, Moy V T and Gaub FI E 1994 Adhesion forces between individual ligand-receptor pairs Science 264 415... 

The separation of two surfaces in contact is resisted by adhesive forces. As the nonnal force is decreased, the contact regions pass from conditions of compressive to tensile stress. As revealed by JKR theory, surface tension alone is sufficient to ensure that there is a finite contact area between the two at zero nonnal force. One contribution to adhesion is the work that must be done to increase surface area during separation. If the surfaces have undergone plastic defonnation, the contact area will be even greater at zero nonnal force than predicted by JKR theory. In reality, continued plastic defonnation can occur during separation and also contributes to adhesive work. 

The avidin-biotin complex, known for its extremely high affinity (Green, 1975), has been studied experimentally more extensively than most other protein-ligand systems. The adhesion forces between avidin and biotin have been measured directly by AFM experiments (Florin et al., 1994 Moy et al., 1994b Moy et al., 1994a). SMD simulations were performed on the entire tetramer of avidin with four biotins bound to investigate the microscopic detail of nnbinding of biotin from avidin (Izrailev et al., 1997). 

M2irrink et al., 1998] Marrink, S.-J., Berger, O., Tieleman, R, and Jahnig, F. Adhesion forces of lipids in a phospholipid membrane studied by molecular dynamics dimulations. Biophys. J. 74 (1998) 931-943... 

E.-L. Florin, V. T. Moy, and H. E. Gaub. Adhesion forces between individual ligand-receptor pairs. Science, 264 415-417, Apr. 15 1994. 

In the pendular state, shown in Figure la, particles ate held together by discrete lens-shaped rings at the points of contact or near-contact. For two uniformly sized spherical particles, the adhesive force in the pendular state for a wetting Hquid (contact angle zero degree) can be calculated (19,23) and substituted for H. in equation 1 to yield the foUowing, where y is the Hquid surface tension in N/m. 

Standard Test Method for Adhesion Between Steel Tire Cords and Rubber. Steel cords are vulcanised into a block of mbber and the force necessary to pull the cords linearly out of the mbber is measured as adhesive force. ASTM method D2229-93a can be used for evaluating mbber compound performance with respect to adhesion to steel cord. The property measured by this test method indicates whether the adhesion of the steel cord to the mbber is greater than the cohesion of the mbber, ie, complete mbber coverage of the steel cord or less than the cohesion of mbber (lack of mbber coverage). 

Fig. 13. Two-component development involving competition between electrostatic and adhesive forces, where + outside and beneath the large circles represents the positively charged toner and the large circles containing negative signs represent carrier beads.

The electrostatic adhesive force is proportional to whereas the dispersion force F does not depend on the charge on the toner, and for a given set... 

Bradley [29,30] and, independently, Derjaguin [31] were the first to recognize that a particle, under the influence of adhesion forces, could act like a Hertzian... 

As indicated, an implicit assumption of the JKR theory is that there are no interactions outside the contact radius. More specifically, the energy arguments used in the development of the JKR theory do not allow specific locations of the adhesion forces to be determined except that they must be associated with the contact line where the two surfaces of the particle and substrate become joined. Adhesion-induced stresses act at the surface and not a result of action-at-a-distance interatomic forces. This results in a stress singularity at the circumference of the contact radius [41]. The validity of this assumption was first questioned by Derjaguin et al. [42], who proposed an alternative model of adhesion (commonly referred to as the DMT theory ). Needless to say, the predictions of the JKR and DMT models are vastly different, as discussed by Tabor [41]. 

Numerous AFM imaging techniques have been developed and commercialized to monitor topography, friction, mechanical response, capacitance, magnetic properties, etc. However, adhesion measurements require the tip to come into, and out of, contact to measure attractive and adhesion forces. Therefore, other than to select an analysis region, most imaging techniques are not useful for adhesion studies. Instead, measurements are necessarily based on force-displacement curve approaches. 

Hertzian mechanics alone cannot be used to evaluate the force-distance curves, since adhesive contributions to the contact are not considered. Several theories, namely the JKR [4] model and the Derjaguin, Muller and Torporov (DMT) model [20], can be used to describe adhesion between a sphere and a flat. Briefly, the JKR model balances the elastic Hertzian pressure with attractive forces acting only within the contact area in the DMT theory attractive interactions are assumed to act outside the contact area. In both theories, the adhesive force is predicted to be a linear function of probe radius, R, and the work of adhesion, VFa, and is given by Eqs. 1 and 2 below. 

Fig. 2. Maps (2x2 pm) of. sample topography (height variation) and pull-off adhesive force for a Langmuir-Blodgett film on mica consisting of a I I mixture of palmitic (Cl6) and lignoceric (C24) fatty acids [46].

An example of interaction stiffness and force curves for a Si surface with a native oxide at 60% relative humidity (RH) is shown in Fig. 12 [104]. The stiffness and force data show an adhesive interaction between the tip and substrate. The hysteresis on retraction is due to a real change in contact area from surface oxide deformation and is not an experimental artifact. The adhesive force observed during retraction was consistent with capillary condensation and the surface energy measured from the adhesive force was close to that of water. 

Part of adhesive composition responsible for adhesive forces. 

Even the void fraction together with particle size distribution does not provide all of the necessary information on the kind of flow. The mutual forces between distinct particles depend not only on the distance between the particles but also on the surface properties of the particles. The strength of the attractive forces between particles depends on conditions. For instance, the moisture content of the solid is essential for determining the attractiv c forces between particles, especially for hydroscopic materials such as wood. Airflow between particles usually tends to separate particles, whereas the surface forces, adhesion forces, tend to bring them together. 

Adhesion of particles Small particles experience adhesion forces, allowing them to attach to surfaces. These forces may be made up from surface tension of liquid films, or London (Van der Waals) forces. 

Principles The process consists of tumbling the metal to be coated with a powder of the coating metal. It is considered that a form of welding is involved, but the type of conditions conducive to successful deposition indicates that the deposit adheres by mechanical keying (A/, must therefore be relatively soft) and adhesive forces. Thus pretreatments such as abrading or pickling enhance the keying effect, and the use of a soft metal... 

When corrosion develops on painted steel the question is often raised as to whether corrosion was a result of paint failure or the paint failure was caused by corrosion. Several studies have shown that adhesion forces are reduced greatly after water soaking or even at very high humidity -and it has been argued that film detachment by water usually precedes underfilm corrosion . Against this view others have claimed that those paints known to have reduced wet adhesion, e.g. those based on alkyd resins, are not uniquely, or even especially, subject to underfilm corrosion Several factors should be considered in this discussion ... 

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