Surfaces from Profile Data

The values for the peak heights shown on the abscissa of Fig, 12-10 are with respect to an arbitrary datum, which from the scale of the profilometric trace is obviously well below the deepest valley seen in the trace. It is also obvious, from the direction in which the scale runs, that the ordinate shows in inverse fashion the cumulative per- 

Note that Fig. 12-10 illustrates only a way of counting the number 

Whitehouse and Archard [10] used a more generalized statistical formulation and applied it to the ground surface whose profilometric trace 

3 B - B Probability density curve for the Gaussian distribution of ordinates where y = (i/tf. Data by Whitehouse and Archard [10]. 

TABLE 12-4. CUMULATIVE DISTRIBUTION OF ORDINATE HEIGHTS AND PEAK HEIGHTS OF THE PROFILE SHOWN IN FIGURE 12-11. 

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DBCP. The predictions suggest that DBCP is volatile and diffuses rapidly into the atmosphere and that it is also readily leached into the soil profile. In the model soil, its volatilization half-life was only 1.2 days when it was assumed to be evenly distributed into the top 10 cm of soil. However, DBCP could be leached as much as 50 cm deep by only 25 cm of water, and at this depth diffusion to the surface would be slow. From the literature study of transformation processes, we found no clear evidence for rapid oxidation or hydrolysis. Photolysis would not occur below the soil surface. No useable data for estimating biodegradation rates were found although Castro and Belser (28) showed that biodegradation did occur. The rate was assumed to be slow because all halogenated hydrocarbons degrade slowly. DBCP was therefore assumed to be persistent. 

Fig. 3.11. Positive-ion SRM ion current profiles for 1 (m/z 443—415 black trace), 2 (mJz 443 - 415, red trace), and 3 (m/z 345-285, blue trace) obtained during development lane scans of replicate development lanes of the RP C2 TLC separation of a mixture (50 ng each) of rhodamines 6G (1), B (2), and 123 (3) at surface scan rates of (a) 19, (b) 44, and (c) 190 jum/s using a DESI solvent (methanol) flow rate of 0.5 //Emin. Dwell time was 100 ms for each transition. Signal levels were normalized to the signal in panel (c). Chromatographic resolution, R, calculated from the data is shown in each respective panel. Reprinted with permission from G. J. Van Berkel et al. [89].

Petersen 87, 120) discusses the use of profile data to understand better the mechanism of the carbon-carbon dioxide reaction. He reacted diameter rod samples in an apparatus previously described 85). Profile data were determined on the reacted rods as follows A 3 -in. hole was drilled through the center of the rod prior to placing it on an ordinary screwcutting engine lathe. Following incremental cuts of approximately 0.25 mm. from the exterior surface, the rod was removed from the lathe and weighed, and its diameter was determined by a micrometer caliper. For each cut, the apparent density of the material removed was calculated from the weight loss and volume of carbon removed. 

The Sn2 reaction in solution. We saw above the application of microsolvation to Sn2 reactions ([14, 15]). Let us now look at the chloride ion-chloromethane Sn2 reaction in water, as studied by a continuum method. Figure 8.2 shows a calculated reaction profile (potential energy surface) from a continuum solvent study of the Sn2 attack of chloride ion on chloromethane (methyl chloride) in water. Calculations were by the author using B3LYP/6-31+G (plus or diffuse functions in the basis set are considered to be very important where anions are involved Section 5.3.3) with the continuum solvent method SM8 [22] as implemented in Spartan [31] some of the data for Fig. 8.2 are given in Table 8.1. Using as the reaction coordinate r the deviation from the transition state C-Cl... 

Water Column DMS Profiles. Nguyen et al. (441 was the first to report DMS water column profiles. One profile had a maximum at 10 m, while the second profile maximum was at 30-32 m. The third profile showed a continual decrease in DMS with depth (0-130 m). They concluded from the data that DMS maximum could move vertically and might account for locally high surface DMS concentrations. 

Profiles of Rn, "Ra, and temperature in the surface waters of the subarctic Pacific Ocean. Open symbols are Rn data from profiles taken on different days filled squares represent Ra data. From Emerson etal. (1991). 

Stations and Inglesia [44] simulated for comparison the ordered surface of a crystal obtained by cutting the bulk material, the unrelaxed cut-off amorphous surface, as well as the latter relaxed. The last case was the random structure created by the Monte Carlo sphere packing method. They calculated the adsorption potential surface for some weakly bound adsorbates (N2, Ar, CH4) with the aim of judging the fidelity of the surface models by comparison with the available experimental data on the heats of adsorption and surface diffusivity. The adsorption energy profile in Fig. 5.12 gives an interesting look of the surface from the point of view of the problems discussed in this book the concrete data will be called for an analysis in later sections. 

In all these cases a system of non-linear equations is obtained, the numerical solution of which yields the concentration profile near a solid surface. From that concentration profile the (excess) adsorption isotherm is calculated next. Thus, although more accurate, this theoretical treatment does not lead to simple compact expressions which are so much preferred in practical interpretation of experimental data. 

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