**8. Effect of RMS roughness on adhesion**

In the study of surfaces, related applications to adherence are extremely important. The surface morphology plays a significant effect on adherence. In this section we will discuss the effects that surface roughness plays on adherence.

Adherence is a chemical-physical phenomenon responsible for the union of two surfaces when they come into contact. This union has force of high magnitude in conditions where there is a chemical bond with sharing of electrons, or Coulomb attraction. In some cases the bond strength has relatively low magnitude to occurring by attractive forces of VdW type. The origin of the adhesion force is the same fundamental force of nature responsible for the binding of atoms and molecules.

This phenomenon of interest is multidisciplinary, for example, the effect of adherence on civil engineering projects, cell adhesion in different microorganisms, adhesion of bacteria on the surface of dental enamel, adhesion of polymeric membranes in separation processes for solutes, adhesion of nanoparticles, among others (Bowen et al., 1998).

When contact occurs between two solid bodies, adhesion is not observed. This is due to the fact that much of the surface has a roughness at the microscale. This roughness decreases the area of active interaction between two solid bodies, as only regions with peaks come into contact, thus reducing adhesion.

Liu, D. -L. et al (2007) conducted a study concerning the effect of RMS roughness on the adhesion using AFM. This study provided a better understanding of the effect of roughness on the adhesion when working in the nanoscale. On this scale the effects of adhesion are significant in applications of microelectromechanical systems.

The total adhesion force in this case, the contribution of all molecules involved in the process can be described by the equation (Bowen et al., 1998).

$$F = 2\,\text{moR} \left[ \frac{\text{R}\_{\text{q}}}{\text{R} + \text{R}\_{\text{q}}} + \left( \frac{\text{h}\_{\text{c}}}{\text{h}\_{\text{c}} + \text{R}\_{\text{q}}} \right)^{2} \right] \tag{13}$$

Where: R = tip radius; Rq= RMS of roughness; hc = distance separating the tip/sample, and 2πωR represents the strength of the AFM system. The total force is normalized by the surface energy so that ω is the work of adhesion force.

The adhesion force falls with increasing surface roughness and also with increasing radius of the tip used in AFM.
