Macroscopic roughness

Detennining the contact area between two rough surfaces is much more difficult than the sphere-on-flat problem and depends upon the moriDhology of the surfaces [9]. One can show, for instance, that for certain distributions of asperity heights the contact can be completely elastic. However, for realistic moriDhologies and macroscopic nonnal forces, the contact region includes areas of both plastic and elastic contact with plastic contact dominating. 

Once it is recognized that particles adhere to a substrate so strongly that cohesive fracture often results upon application of a detachment force and that the contact region is better describable as an interphase [ 18J rather than a sharp demarcation or interface, the concept of treating a particle as an entity that is totally distinct from the substrate vanishes. Rather, one begins to see the substrate-particle structure somewhat as a composite material. To paraphrase this concept, one could, in many instances, treat surface roughness (a.k.a. asperities) as particles appended to the surface of a substrate. These asperities control the adhesion between two macroscopic bodies. 

Although the LD model is clearly a rough approximation, it seems to capture the main physics of polar solvents. This model overcomes the key problems associated with the macroscopic model of eq. (2.18), eliminating the dependence of the results on an ill-defined cavity radius and the need to use a dielectric constant which is not defined properly at a short distance from the solute. The LD model provides an effective estimate of solvation energies of the ionic states and allows one to explore the energetics of chemical reactions in polar solvents. 

Microscopy is one of the most direct physical methods for determining surface roughness. The resolution can go from macroscopic to atomic size, depending on the technique. Thus the order of magnitude of the range of observation is the millimeter for optical microscopy, the micrometer for... 

The strength and extensibility of a noncrystallizable elastomer depend on its viscoelastic properties (28,29), even when the stress remains in equilibrium with the strain until macroscopic fracture occurs. In theory, such elastomers have a time- or rate-independent strength and ultimate elongation, but such threshold quantities apparently have not been measured, though rough estimates have been made (28,30). 

A traditional explanation of solid friction, which is mainly employed in engineering sciences, is based on plastic deformation.12 Typical surfaces are rough on microscopic length scales, as indicated in Figure 3. As a result, intimate mechanical contact between macroscopic solids occurs only at isolated points, typically at a small fraction of the apparent area of contact. 

One important way in which they differ is that currents (either ac or dc) at real interfaces are not uniform across the interface. Therefore, a measured macroscopic dc current density i (A cm" ) will not in general be a microscopic current density i on a small part of the interface (say 1 pm by 1 pm) on a rough or non-uniform electrode. In the formation of each interface it is necessary therefore to ensure that the surface is as smooth as is reasonably practicable. In most cases codes of best practice have been evolved and should generally be followed unless radical improvements are possible. In this way results should at least be comparable from one laboratory to another. 

The obtained PEDOT polymer showed a very good capacity for film formation at a macroscopic level, and very low surface roughness also at a microscopic level, as can be observed in the surface picture of the film obtained by atomic force microscopy (Eig. 7). 

---