Fractional overlap

Fig. 9. Influence of local temperature T and varying catalyst structure on the CO oxidation effectiveness factor . Each Pt/y-Al203 catalyst was reconstructed by packing of y-Al203 particles of two different sizes with small-to-large particles number 16. Small particles size d = 1 pm was kept constant, while large particles size <72 and particles fractional overlap (level of sintering) were varied. Gas concentrations the same as in Fig. 8 (Koci et al., 2007a).

As a reference value for Sn, Haddon suggested the p7t,p7t overlap integral SB between nearest neighbours in benzene (R = 1.3964 A, S = 0.246) and to define the fractional overlap rj = SJSB. The fractional overlap reflects the degree of p7t,p7t overlap that has developed for a given bond. A 7t-bond is fully developed for values of r close to 1, while... 

Fractions of three groups of substances used in beer production are extracted from hops using supercritical C02. The first fraction, the so-called oil essence, was obtained via extraction with C02 at a density of 0.30 g mL 1 and a temperature of 50°C. Bitter substances were collected as the second fraction at a C02 density of 0.70 gmL 1 (50°C) that fraction overlapped only slightly the third and last fraction of neutral fats, extracted at a C02 density of 0.90gmL 1 (50°C). 

An obvious criterion by which to judge the extent of separation of chromatographic peaks, especially for the optimization of a quantitative analysis, is the fraction of the peak that is free of overlap from adjacent peaks. The definition for this so-called fractional overlap criterion is illustrated in figure 4.3. An equation to describe the fractional overlap is... 

Figure 4.3 Illustration of the definition of the fractional overlap (FO) as a criterion for the separation of a pair of adjacent peaks in a chromatogram.

A comparison of various elemental criteria has been reported by Knoll and Midgett [412] and by Debets et al. [413]. Figure 4.4 shows the variation of some of the criteria for the separation of pairs of chromatographic peaks as a function of the time difference between the peak tops (At = t2 — t,). By definition, Rs (and hence S) varies linearly with At. The peak-valley ratios (P) and the fractional overlap both increase rapidly with increasing At at first, but level off towards At 4 ct to reach the limiting value of 1. At high values of At, Rs and S will keep increasing, while the other criteria will not. 

Figure 4.5 shows the variation of the fractional overlap criterion with At for three different values of the ratio of peak heights (A). These data were calculated for Gaussian peaks. It is clear that FO will be lower for peak ratios different from unity. Similar... 

Figure 4.5 Variation of the fractional overlap criterion (FO) and the resolution (RJ as a function of the difference in retention times between the two solutes. FO data calculated for Gaussian peaks of varying peak height ratios (A = h2/hl). Courtesy of Anton Drouen [405].

Spindle Add. fract symm. uniq. captured Fract. symm. uniques not recorded Fractional overlap with previous spindles ... 

In (a) the gel applied for separation has an unsuitable, too narrow pore size distribution and the largest macromolecules are already excluded from the gel pores, while the retention volumes of the lowest polymer fractions overlap the peaks of admixtures, impurities, air, etc. In (b) the gel has optimal pore size distribution. The chromatogram can be processed in the following manner ... 

The basic assumption is that water is decomposed by radiation into eaq, OH, and H30+, which are formed inhomogeneously in spurs. In these spurs, which are spherical, with a diameter of 10-40 A., several pairs of these radicals are initially formed where their initial concentration is very high (0.1-1M). The distance between spurs depends on the LET of the radiation. For y-, x-rays, or fast electrons most of the spurs are isolated, and only a small fraction overlaps and forms blobs or short tracks (56). At high LET radiation, the overlapping of the spurs produces cylindrical tracks. 

FIGURE 9.16 Calculated fractional overlap between the ion cloud and an 800 pm-diameter laser beam as a function of of the stored ions. The solid circle ( ) at g j=0.68 corresponds to the value at which a dip is observed in the measured fluorescence signal (see Figure 9.17d). 

It is well known that the quantity of sample that can be processed by TLC is subject to an upper limit. The reason for the limit is that, as the weight of the sample is increased, so the area occupied by each fraction on the chromatogram increases. Ultimately, the resolution becomes unacceptable because contiguous fractions overlap. Purdy and Truter [21] have described several methods of quantifying TLC and these are discussed next under separate headings. Further experimental details are given in this chapter on TLC are discussed in Chapter 4, Section 3. 

The simplified fractionator includes a delumper model to convert the 21 kinetic lumps into >80 pure- and pseudo-components, which are then divided into user-specified boiling fractions. A non-linear distribution function generates ideal distillation curves with realistic fraction-to-fraction overlap. The fractionator can inter-convert distillation methods, so a user can calculate D-86, D-1160, D-2887, and/or TBP curves for gasoline and LCO. 

Figure 7 displays the calculated results of the degree of polymerization at exactly the gel point P. = 200). It can be seen that many linear polymers k = 0) still exist even at the gel point. Also, each fraction overlaps with others heavily, and the distribution will not show a skewed shape. With improvements in modem analytical techniques, skewed distributions and sometimes bimodal distributions are occasionally reported [40, 41], Such skewed distribution cannot be formed in the genre of Flory s ideal dendritic model however, it becomes important in a real system with nonideal parameters such as stmctural dependence of the crosslinking reaction (including cyclization) and degree of polymerization. 

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