Further Conceptual Development

Can the simple roughness factor approach (Eq. (8) be applied if the surface is very much rougher? Many of the surfaces encountered in adhesion technology are very rough indeed. Figure 1 shows a microfibrous oxide on steel and a porous oxide layer on aluminum. Figure 4(a) shows a phosphated steel surface prepared for rubber bonding [53], Fig. (4b) surface treated polytetrafluoroethan (PTFE) [54]. As the scale of roughness becomes finer, the application of a simple roughness factor becomes increasingly unrealistic and unconvincing. It becomes unconvincing not just because of increasing practical difficulty in measuring the ‘‘true’’ area of such surfaces, it becomes conceptually unconvincing. The roughness itself is an essential characteristic of the surfaces. As we approach molecular scale roughness, indeed long before we get there, the energy of the surface molecules is modified as a consequence of the topological configurations they take up. For example, consider a solid-vapor interface. Half of the volume of a sphere centered on a molecule of the solid on a plane surface would comprise solid, half vapor. If, however, the molecule was on the surface of an asperity of a rough surface, less than half of the volume of the sphere would be made up of solid, more than half of vapor, so the energy of this latter molecule would be higher. In terms of the simple ‘‘bond breaking’’ concept, more bonds between molecules of the solid would have been broken to create the environment of the molecule on the rough surface than for that on the smooth. The intrinsic energy of a molecule on a rough surface is higher than that on a smooth surface. It is unjustifiable to regard these surfaces (Figs. 1 and 4) as essentially the same as smooth surfaces which happen to be rough!

Moreover, roughness at an interface may actually develop as a result of bringing the two phases together. They will take up these configurations as a consequence of the molecular interactions at the interface: they are an essential feature of bringing together the two phases 1 and 2. An ideally smooth surface being highly ordered would have low entropy: the development of surface roughness can be seen as an increasing of surface entropy in accordance with the Second Law of Thermodynamics [55-58].

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Figure 4 Examples of rough pretreated substrate surfaces. (a) Phosphated steel prepared for rubber bonding (cf. Ref. 53); (b) PTFE irradiated by argon ions (after Ref. 54).

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