Particle Adhesive force

Zhang, R, Busnaina, A. A., Reng, J., and Rury, M. A., Particle Adhesion Force in CMP and Subsequent Cleaning Processes," Proceedings, 4th International Chemical-Mechanical Planarization for ULSI Multilevel Interconnection Conference, Santa Clara, CA, Reb. 11-12,1999, pp. 61-64. 

Modifications to the Geldart (1973) fluidization diagram have been proposed by Molerus (1982) and Zenz (1984), but are not considered here as they require some knowledge or measurement of particle adhesion forces and bulk surface tension, respectively. That is, detailed investigations into evaluating and/or developing such fluidization diagrams are beyond the present scope of work. 

Micromechanical force measurement apparatus (Taylor, 2006 Taylor et al., 2007) Particle adhesive forces Yes Adhesive forces vs. time (min) 15 psi >5 pm Adhesive forces between hydrate—hydrate particles, hydrate particle-surface... 

The frictional and adhesion forces between the abrasive particles and wafer surfaces were experimentally measured using alumina and silica slurries with and without citric acid. Although citric acid did not affect the zeta potential of the silica particles, it resulted in a more negative zeta potential of the alumina particles due to the adsorption of the negatively charged citrate ions onto the alumina surfaces. The highest particle adhesion force was measured in an alumina slurry without the addition of citric acid. However, the alumina slurry with the addition of citric acid had the lowest particle adhesion force due to the adsorption of citrate ions onto the alumina surfaces. Although citrate ions could easily adsorb onto alumina particles, the silica particles did not appear to benefit in terms of reduced frictional force when in citric acid solutions. 

For particle adhesion, forces caused by liquid bridges are most important and. 

Also shown in Fig. III.3 is the dependence of the experimental accuracy on the nonuniformity of particle diameter in the dust fractions (curve 1). With Ad/d v = 0.05, the error of the method is 15%. Hence, the tilt-plate method will give accurate results only if the particles are monodisperse. If the particle size varies significantly within the fraction, the method is less accurate, becoming unsuitable in practice for the determination of particle adhesive force for example, with d = 40-60 /rm, we find that Adld y = 0.2 and B = 60%. 

For more concentrated solutions (0.1 and 1 mol/liter) with the same detaching force, almost all of the particles remain on the dust-covered substrate. Hence, with solution concentrations above 0.1 mol/liter, it is impossible to determine the relationship between particle adhesive force and the nature of the electrolyte by use of the inclined-surface technique. 

Changes in Adhesion to Paint and Varnish Coatings because of Electrical Forces. By changing the electrical component of adhesive force, considerable reductions can be achieved in the adhesion of dust to surfaces, in some cases even complete elimination of dust accumulation. Previously (see Section 15) we examined the possibilities of changing the electrical component of particle adhesive force by modifying the properties of the surface. Adhesive forces can... 

Fig. VI11.4. Integral curves for particle adhesive force distribution on oily painted surfaces (oil amount 0.1 mg/cm ), for spherical glass particles with following diameters (in Mm) (1) 60 (2) 120 (3) 160 (4) 200 (5) 250.

As in the case of air, the particle adhesive force tends to increase at first as the amount of oil contamination is increased since the particles sink into the oil film and are held more strongly on the specimen surface as the oil film thickness is increased still further, however, the particle adhesive force drops off since the particles are now removed together with the oil layer. The maximum adhesion is observed at an oil-contamination level of 0.25-1 mg/cm. ... 

L.J. Jallo, Y. Chen, J. Bowen, E Etzler, R. Dave, Prediction of inter-particle adhesion force from surface energy and surface roughness. Journal of Adhesion Science and Technology, 25,367-384, 2011. 

Y. Kato, M. Ohkuma, Y. Shimada, H. Sunada, Evaluation of the flowability of surface-modified preparations by the measurement of the inter-particle adhesive force. Journal of Drug Delivery Science and Technology, 15, 217-221, 2005... 

The manner in which particle-adhesion forces vary with particle diameter [i.e., the function yp(dp)] for various flow velocities is indicated in Fig. VI.9. An analogous relationship between the adhesion number and particle size is obtained for various vibrational forces (10, 15, and 20 g units). 

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. 

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... 

This expression relates the action-at-a-distance forces between atoms to the macroscopic deformations and dominated adhesion theoiy for the next several decades. The advent of quantum mechanics allowed the interatomic interactions giving rise to particle adhesion to be understood in greater depth. 

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]. 

Whereas the JKR model approached the topic of particle adhesion from a contact mechanics viewpoint, the DMT theory simply assumes that the adhesion-induced contact has the same shape as a Hertzian indentor. The normal pressure distribution Ph(p) for the Hertzian indentor is related to the repulsive force and the distance from the center of the contact circle to the point represented by r according to the relationship [49]... 

It is clear that the presence of electrostatic charges, whether due to contact charging, fractoemissions, or some other mechanism, will affect particle adhesion. However, to date there has been no satisfactory attempt made at properly integrating electrostatic forces into partiele adhesion theory. 

As previously mentioned, electrodynamic interactions, such as those arising from London forces, can also contribute to the adhesion of particles. These forces are dominated by dipole interactions and are broadly lumped into the classification known as van der Waals interactions. A more detailed description of van der Waals interactions than can be presented in this article is given in books by Israelachvili [95] and by Rimai and Quesnel [96]. 

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. 

Vakarelski et al. [88] also investigated the adhesive forces between a colloid particle and a flat surface in solution. In their case they investigated a sihca sphere and a mica surface in chloride solutions of monovalent cations CsCl, KCl, NaCl, and LiCl. The pH was kept at 5.6 for all the experiments. To obtain the adhesive force in the presence of an electrostatic interaction, they summed the repulsive force and the pull-off force (coined foe by the authors ) to obtain a value for the adhesive force that is independent of the electrostatic component. 

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