Electrical adhesion force

Ikazaki, F. and M. Kamamura, Electric Adhesion Force of a Single Particle and of a Powder at Room Temperature and Above Ambient Temperature and its Application to a Fluidized Bed, Particle Sci. Tech., 2, 3, 1984, pp. 271-283. Inculet, I. I., N. H. Malak, and J. A. Young, Corona Charging of Immobilized Spherical Particles, in Electrostatics 1983, Ed. S. Singh, Conf. Ser., 66, Inst. Phys, 1983. pp. 98-105. 

Calculation of electrical adhesion force In order to calculate the electrical adhesion force, the charge distribution at the interface must be determined. This requires the solution of Poisson s equation in one dimension as... 

Inserting Eq. 2-12 into Eq. 2-11, one obtains the electrical adhesion force per unit area, pressure, as... 

For solid surfaces interacting in air, the adhesion forces mainly result from van der Waals interaction and capillary force, but the effects of electrostatic forces due to the formation of an electrical double-layer have to be included for analyzing adhesion in solutions. Besides, adhesion has to be studied as a dynamic process in which the approach and separation of two surfaces are always accompanied by unstable motions, jump in and out, attributing to the instability of sliding system. 

Force-distance microscopy measures repulsive, attractive, and adhesion forces between the time and surface during approach, contact, and separation. This technique combines electrical with adhesion or physical property as a means to study sample surfaces. 

Much more important are adhesion forces which are due to electrical double layers. This phenomenon can develop if the particles touch each other and is permanent. According to Krupp the attraction pressure due to electrical double layers between two semi-infinite bodies is in the order of Pei = 1 to lO N/m (10 to lO dyn/cm ). In comparison, the van der Waals attraction pressure between two semi-infinite bodies is Pvdw = 2xl0 to 3xl0 N/m (2 X 10 to 3 X 10 dyn/cm ). 

Schmidlin (56) has pointed out that the commonly observed broad range of van der Waals forces between toner and carrier particles causes xerographic development to require much higher electric fields for toner release than those required to establish a sharp threshold. In fact, he argues that if the adhesive forces between these surfaces could be made sufficiently small and uniform ("noise-free"), it should be possible to reduce electrostatic charge density required for a given... 

Adhesive force Act between the adherend surfaces and the adhesive layer molecules and are mainly based on electrical interactions (dipoles). 

Polarity Differences in electric charges in molecules. In adhesive molecules in particular responsible for the development of adhesive forces. See dipole. 

As mentioned several times before, the natural adhesion forces (see Section 5.1.1), caused, for example, by molecular (e.g. van-der-Waals) or electrical forces (e.g. due to asymmetric molecular structures), may become much larger than the separation forces which are mass and shape related. Therefore, if collisions or, generally speaking, contact between ultrafine particles occur, a rather strong bond will develop. This phenomenon is also responsible for the fact that most nano-sized particles do not exist as individuals but as assemblies of many particles (Fig. 10.41) this might be a problem in those applications where ultrafine particles must be deposited individually or in monolayers (see Chapter 12). For the effective separation of such particles from gases, however, agglomeration is desired and must be promoted. 

While the adsorption theory is the most accepted one, mechanical interlocking comes into play in case of substrates with a special kind of roughness such as galvannealed steel where the liquid can spread into cavities and thereby interlock with the substrate. The diffusion theory does not play an important role for polymer-metal interfaces. The contribution of the electrostatic theory is not easy to estimate. However, the electrical component of the adhesive force between the planar surfaces of solids becomes important if the charge exchange density corresponds to 10 electronic charges, meaning about 1% of the surface atoms [71]. 

At a critical voltage, the small polymer beads jumped across to the other electrode in the cell. This occurred because the electrostatic force applied to each sphere overcame the van der Waals adhesion force. The theory shows that there are three forces acting on the particles in this experiment first, there is the molecular adhesion force due to van der Waals force, inWDjA, where D is the diameter of the small spheres and W is the work of adhesion second, there is the electrostatic charge on the particle which pulls it onto the surface of the plastic film, giving a force Jta O /4e , where a is the charge density on the particles and () is the permittivity of free space and third, there is the applied electric field V which acts to make the particles jump across the gap of thickness Di, These three forces are drawn schematically in Fig. 13.16 and balanced in the equation below... 

The existence of an electrical double layer at the interface between a metal and a polymer adhering to it has been satisfactorily demonstrated. Undoubtedly, the electrostatic forces developed from this interaction could contribute to the total adhesive bond strength. However, the theories that have been advanced are less than rigorous and have been subject to severe criticism. Nevertheless, there are some phenomena that cannot be explained without recourse to this explanation in some form (see Electrical adhesion). 

When the vibration technique is used, simultaneous measurements can be made of the electric charges produced upon detachment of the particles, this information being needed to calculate the electrical component of adhesive force (see Section 15). For this purpose we can use a unit described in [82], which differs from previously used units of the electrometric type [11,14] in that the new unit uses electronic and loop oscillographs. This obviates the dependence on visual observation, giving instead a photographic record of the electrical processes taking place in the contact zone between the dust particles and the sub-... 

Fig. 111.8. Apparatus for determination of adhesive force in various gases and vapors (1) dust-covered surface (2) striker arm (3) bell jar (4) heating coil (5) dropping funnel (6) electrical supply (7) electromagnet.

Contact between a particle and a painted surface may be regarded as contact between two semiconductors, one of which is in contact with the metal substrate (Fig. IV. 1. c). At the boundary between the particle and the painted surface, a contact potential difference develops. It may be supposed that the value of ( c depends on the way in which the conduction band bends and that this in turn is related to the thickness of the paint layer. If the particle was uncharged before contact, then, in order to eliminate the electric component of the force of adhesion, it would be necessary to have Pc = 0, i.e., no bending of the conduction band. Experiment shows, however, that particles are always charged hence, in order to eliminate the electrical component of the adhesive force, we must have... 

We see from these data that the electrical charges increase as the particle size diminishes, so that the electrical component of the adhesive forces also becomes greater. The same trend, but with a change in the size of the charge, was found when aluminum oxide particles were detached under the same conditions [28]. 

The magnitude of the electrical component of adhesive force can be calculated from the formula... 

---