Roughness factor, definition

There is no clear definition of what magnitude of enhancement entitles a system to be classified as a SERS-active system. In this review we will arbitrarily set the demarcation line for SERS at a 100-fold enhancement level. Any enhancement higher than that will be considered as SERS, while lower enhancements will be ignored. The reason for this limit is that it is within simple surface coverage effects (roughness factor) and trivial enhancements resulting from reflectivity of metal surfaces and possible orientation effects. " ... 

Compared with one-dimensional diffusion in a plane sheet, for the same a value (such as a = 0.5), the fraction of mass loss is much larger for the solid sphere (T=0.9484) than for the planar slab (7=0.5622). To reach the same degree of mass loss (such as 50%), a smaller value is needed for the sphere (a = 0.0305) than for the thin slab = 0.1963). The difference in terms of is a factor of 6.4. Because the definition of is jD(f)df/a, by comparing with Equation 5-67b, we see that is proportional to 1/G. The difference in the value of for the same degree of mass loss for spherical and plane sheet shapes roughly explains the difference between G values (55/8.65 = 6.4) for spherical and plane sheet shapes. 

In unimolecular reactions, where complex molecules are involved, a fraction only of the activated molecules react, and this fraction is determined by specific factors. Thus a rigid parallelism between the heats of activation and the temperatures at which different reactions attain some assigned rate cannot be expected. Nevertheless in any expression containing an exponential term that term tends to play a predominant role, and a definite, if rough, parallelism still exists, showing that even in the case of more complex reactions the value of E is perhaps the most important factor in determining the rate of reaction. 

The work of Fox and Gex [Eqs. (17) and (24)] does represent a systematic approach to the problem, and their definition of mixedness (time when the last wisp of red color disappeared) is probably a conservative one. If the rash assumption is made that the results of different workers can be compared, the data of van de Vusse indicate that the results of Fox and Gex with propeller mixers would probably predict results for other agitator types within about a fourfold factor. While they are far from precise in a general way, these relations should be useful for rough estimates of mixing time. 

If we subtract 1 and multiply by 1000 on both sides, the left side of the equation is equal to the definition of of O2 with respect to the standard SMOW, and the right side is +20%o. This value is lower than the measured value of 23.5%o because roughly half of the oxygen production by photos5mthesis occurs on land and about half in the ocean. O2 from terrestrial photosynthesis is 4%o-8%o heavier than SMOW because evaporation exceeds precipitation in the water of leaves, where most of the photosynthesis of the terrestrial biosphere occurs. The mean 8 0 from oceanic and terrestrial photosynthesis is thus +22%o to +24%o. If one assumes that the partitioning of photosynthesis between the land and ocean remained the same and fractionation factors did not change in the past, then the sole reason for changes in the 8 0-02 of the atmosphere trapped in bubbles of the ice is due to the variation in the isotope ratio of seawater. 

A minimum roughness of the support surface is also required to produce defect-free membrane layers. In the present context, surface roughness is defined as the average perpendicular (to the surface) distance between peaks and dips in the support surface. As discussed in Chapter 6, several other definitions of roughness can be given and used. The roughness of the support may limit the minimum achievable layer thickness. From a fracture mechanics point of view, surface roughness determines the maximum size and sharpness of flaws which can act as crack initiators (via the stress intensity factor). 

When steady-state conduction occurs within and outside solids, or between two contacting solids, it is frequently handled by means of conduction shape factors and thermal contact conductances (or contact resistances), respectively. This chapter covers the basic equations, definitions, and relationships that define shape factors and the thermal contact, gap, and joint conductances for conforming, rough surfaces, and nonconforming, smooth surfaces. 

Gruesbeck and Collins (39) evaluated the effect of increasing brine viscosity (by addition of a polymer) on the critical velocity for permeability damage. They observed a roughly proportional decrease in the critical velocity when the viscosity was increased by a factor of 10. However, they were unable to draw definitive conclusions regarding the quantitative effect of fluid viscosity because of a very limited amount of data being available. 

---