Overlapping of zones

In the analogues of carbon having higher atomic number, the s and p orbitals are more spread out and in consequence overlapping of zones occurs, causing the appearance of metallic properties. Thus there is a gradual transition of the bond type from the metallic to the homopolar. 

In order to obtain sharply resolved zones, the quantity of material applied to the chromatogram should be as small as pOvSSible. RatW large sample volumes are, however, often necessary for the detection (by colour reactions) of substances that are present in low concentration this inevitably results in broadening and overlapping of zones. 

Two-dimensional separations can be represented on a flat bed, by analogy with planar chromatography, with components represented by a series of dots . In fact, zone broadening processes in the two dimensions result in elliptically shaped spots centred on each dot . Overlap of the spots is then possible, but Bertsch (30) also showed how the contributors to the overall resolution, R, along the two axes, and Ry contribute to the final resolution according to the following ... 

A useful tool in the interpretation of SIMCA is the so-called Coomans plot [32]. It is applied to the discrimination of two classes (Fig. 33.18). The distance from the model for class 1 is plotted against that from model 2. On both axes, one indicates the critical distances. In this way, one defines four zones class 1, class 2, overlap of class 1 and 2 and neither class 1 nor class 2. By plotting objects in this plot, their classification is immediately clear. It is also easy to visualize how certain a classification is. In Fig. 33.18, object a is very clearly within class 1, object b is on the border of that class but is not close to class 2 and object c clearly belongs to neither class. 

Inspection of Fig. 15.3 reveals that while for jo 0.1 nAcm , the effectiveness factor is expected to be close to 1, for a faster reaction with Jo 1 p,A cm , it will drop to about 0.2. This is the case of internal diffusion limitation, well known in heterogeneous catalysis, when the reagent concentration at the outer surface of the catalyst grains is equal to its volume concentration, but drops sharply inside the pores of the catalyst. In this context, it should be pointed out that when the pore size is decreased below about 50 nm, the predominant mechanism of mass transport is Knudsen diffusion [Malek and Coppens, 2003], with the diffusion coefficient being less than the Pick diffusion coefficient and dependent on the porosity and pore stmcture. Moreover, the discrete distribution of the catalytic particles in the CL may also affect the measured current owing to overlap of diffusion zones around closely positioned particles [Antoine et ah, 1998]. 

Oros, F.J., Davis, J.M. (1992). Comparison of statistical theories of spot overlap in two-dimensional separations and verification of means for estimating the number of zones. J. Chromatogr. 591, 1-18. 

Figure A. Overlap of depletion zones. The hatched region corresponds to the volume of solvent that is transferred when two particles of radius a and depletion thickness A come into close contact.

The results demonstrate that cadmium can be determined directly the direct determination of copper, manganese, and chromium is also possible, but their application is more limited than cadmium. The lead and nickel determination proved to be the most difficult, since their determination is limited by their low sensitivity and by the overlap of their absorption profiles with the background absorbance generated by seawater matrix. The direct determination of lead and nickel by this technique can be used only for seawater samples taken in coastal or estuarine zones that are quite polluted. 

Nevertheless, we have already noted that the transition of NaAlSijOg from monoclinic to triclinic form may be regarded as the overlap of two high-order transitions, and that high-order transition implies continuity in S, H, and G at the transition point and discontinuity in the Cp function (see section 2.8). The thermodynamic parameters for the two polymorphs on the opposite sides of the transition zone must thus be constrained to fulfill the above requirements. The method followed by Helgeson et al. (1978) is as follows. 

Figure 7.3. Overlap of diffusion zones of cylindrical nuclei growing on a surface. Shaded regions indicate two zones overlapping black region, three zones overlapping.

However, if the samples had a wider MWD, the overlapping of the zones of differing functionality would be much stronger. This overlapping is not connected with the efficiency of the separation system (in our case the column had 4000 theoretical plates). In such a situation it would be more convenient to use a gradient, but in working with OBD problems of detection arise. 

---