Scaling behavior, surface roughness

When one considers a distance scale much smaller than 1 pm, surface roughness also is an issue to observed electrode behavior. The ratio of the microscopic surface area to the projected electrode area is usually designated the roughness factor, and can vary from 1.0 to 5 or so for typical solid electrodes, or much higher for porous electrodes. Capacitance, surface faradaic reactions, adsorption, and electrode kinetics all depend on microscopic area. For example, double-layer capacitance increases with roughness such that the apparent capacitance (C°bs) is larger than the value for a perfectly flat electrode (Cflat) as shown in Equation 10.1 ... 

In the present chapter we will summarize results of two different evaluation procedures for the surface roughness of carbon blacks. In the mono-layer regime we refer to the scaling behavior of the estimated BET-surface area with the size of adsorbed probe molecules (yardstick method). On smooth flat surfaces the BET-area is independent of the adsorbed probe or applied yardstick, while on rough surfaces it decreases with increasing probe (yardstick) size due to the inability of the large molecules to explore smaller cavities. This is shown schematically in Fig. 5. 

These presumptions are based on the results of chanical composition analyses and structural determinations by beam-based analytical methods. To verify the mechanisms involved, it is essential to clarify the frictional and mechanical properties of each layer in the multilayered structure of the tribofilm. Most importantly, with respect to the uppermost surface and the underlying area, which are thought to control the macroscale friction behavior, it is indispensable to determine differences not only in surface roughness, but also in shear strength and frictional behavior relative to depth on a nanometer scale. It is also important to make clear the distribution of the chemical composition relative to the tribofilm depth and to make this chemical distribution consistent with the nanometer-scale frictional and mechanical properties. However, estimating these properties experimentally on a nanometer scale is a difficult task, although several attempts have been made [24-28],... 

The aforementioned nanoprobe and beam-based analyses results made clear the differences in surface roughness, mechanical/frictional properties, surface nanostructure, chemical composition, and surface chemical state on a nanometer scale between the MoDTC/ZDDP and ZDDP tribofilms. These results demonstrated that the nanostructural, nanometer-scale mechanical and chemical properties acted as the controlling factors in the macroscale friction behavior of the tribofilms. From these results, a microstructure model of the tribofilms was developed to explain the mechanism of friction reduction, as shown in fig. 9.20 [3, 34]. 

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