Planar Fraction

The planar fraction is the area covered by the atoms whose centers lie in the plane divided by the area of the plane. Unlike the planar density, which contains the radius of the atoms, the planar fraction is a pure number and is perhaps more meaningful. Planes with the highest planar fraction are the slip planes along which metals deform plastically. The importance of this parameter is discussed in more detail in Chapter 9. 

The planar fraction is just the planar density multiplied by ttR. From Equation 4.17, the planar fraction of the (111) plane in the fee system is 

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The deviation from planarity that is present in a structure such as 1 raises the question of how severely a conjugated system can be distorted from the ideal coplanar alignment of p orbitals and still retain aromaticity. This problem has been analyzed by determining the degree of rehybridization necessary to maximize p orbital overlap in 1. It is found that rehybridization to incorporate fractional amounts of s character can improve orbital alignment substantially. Orbitals with about 6% s character are suggested to be involved... 

These workers used binary solvent systems over a range of mole fractions to determine, for each solute, the constants a and b of equation (8.2). For methyl and phenacyl esters, TLC was used, while overpressured layer chromatography (OPLC) was used for dansyl amino acids. Nurok and co-workers (11) also evaluated how the quality of a simulated separation varies with changing solvent strength by using the inverse distance function (IDF) or planar response function (PRF), as follows ... 

In this scheme, RS and SR represent enantiomers, and so on, and 5 represents some fraction. The following are the possibilities (1) Direct attack by SH on RX gives SR (complete inversion) in a straight Sn2 process. (2) If the intimate ion pair R X is formed, the solvent can attack at this stage. This can lead to total inversion if Reaction A does not take place or to a combination of inversion and racemization if there is competition between A and B. (3) If the solvent-separated ion pair is formed, SH can attack here. The stereochemistry is not maintained as tightly and more racemization (perhaps total) is expected. (4) Finally, if free R" " is formed, it is planar, and attack by SH gives complete racemization. 

In 1995, Mandal et al. [151] described the crystal structure of N,AT-bis-(p-butoxybenzylidene)-a,a -bi-p-toluidine. They found that the two symmetrical fractions of the molecule are almost planar, but the angle between these planes is 63.5°. The molecules are arranged in tilted layers. This tilted layer-like structure is referred as a precursor to the tilted smectic phase. 

FIGURE 11.1 (a) Schematic representation of PLC of Heracleum moellendorfi fruit, crude extract (500-pl 2% solution), system Florisil/AcOEt + B plate preeluted with benzene (b) analytical HPLC of isolated fractions, system ClS/MeOH + HjO (6 4). Abbreviations B — bergaptene, I — imperatorin, Ph — phelopterin, X — xanthotoxin. (For details, see Waksmundzka-FIajnos, M. and Wawrzynowicz, T., 7. Planar Chromatogr., 5, 169-174, 1992.)... 

FIGURE 11.11 (a) Schematic representation of PLC of Heracleum sosnowskyi fruit crude extract, system silanized silica/MeOH + HjO (6 4) (b) rechromatography of fractions I and II from the plate a on Lobar-type column filled with Horisil eluted with 5% MeCN in CHjClj -I- H (7 3) fractions controlled by analytical HPLC in system ClS/MeOH -i- HjO (6 4). For abbreviations, see Figure 11.5. (For details, see Waksmundzka-Hajnos, M. and Wawrzynow-icz, T., /. Planar Chromatogr, 3, 439 141, 1990.)... 

FIGURE 11.30 Densitograms illustrating multiple development of Fumaria officinalis fraction in system silica/2% MeCN and 1% ammonia in PrOH + CH2CI2 (1 9) (a) first, (b) second, (c) third stage of development. (For details, see Jozwiak, G., Wawrzynowicz, T., and Waksmundzka-Hajnos, M., J. Planar Chromatogr, 13, 447-451, 2000.)... 

After the extrachon of total lipids from four different genotypes of flax seed (Linum usitassimum) differing markedly in their acyl composihon, PTLC was used for the isolahon of different lipid classes in the neutral lipid frachon [69]. Application of planar chromatographic methods, including PTLC, in the separahon of food lipids has been reviewed with 40 references by Olsson [70]. The polar lipid fraction of niger seed (Guizotia abyssinica Cass.) collected from different regions of Ethiopia could be separated by PTLC on silica gel [71]. 

Linking TLC with a tandem instrument differs from combining GC or LC with an appropriate spectrometer. Hyphenation of planar chromatographic techniques represents a niche application compared to HPLC-based methods. Due to the nature of the development process in TLC, the combination is often considered as an off-line in situ procedure rather than a truly hyphenated system. True in-line TLC tandem systems are not actually possible, as the TLC separation must be developed before the spots can be monitored. It follows that all TLC tandem instruments operate as either fraction collectors or off-line monitoring devices. Various elaborate plate extraction procedures have been developed. In all cases, TLC serves as a cleanup method. 

Thermolysis of 1-phenyl-3,4-dimethylphosphole in alcoholic solvents in the presence of NiCl2 leads to the synthesis of the racemic biphospholene complex (222).653,654 Upon reaction of the bromo derivative with AgBF4, the meso and racemic diastereomers of (223) are formed, which can be separated by fractional crystallization.655 In both (222) and (223) the coordination sphere is slightly distorted from square planar. 

Square-planar zinc compounds predominate with these ligand types as would be predicted. This is in contrast to the prevalence of tetrahedral or distorted tetrahedral geometries for four-coordinate species that have been discussed thus far. Zinc porphyrin complexes are frequently used as building blocks in the formation of supramolecular structures. Zinc porphyrins can also act as electron donors and antenna in the formation of photoexcited states. Although the coordination of zinc to the porphyrin shows little variation, the properties of the zinc-coordinated compounds are extremely important and form the most extensively structurally characterized multidentate ligand class in the CSD. The examples presented here reflect only a fraction of these compounds but have been selected as recent and representative examples. Expanded ring porphyrins have also... 

The main problem using planar methods is the difficulty in detection and collection of fractions among other less critical problems, such as homogeneous preparation of chromatographic media. However, the detection problem exists also for the coupled-column methods, mainly because of fraction dilution by each stage in a multidimensional separation system. Another aspect is the adjustment of chromatographic time bases between the different dimensions so that first-dimension peaks may be sampled an adequate number of times by the next dimension separation system. This aspect has been recently studied in detail (Murphy et al., 1998), and is covered in detail in Chapters 2 and 6. 

Note that when solving the CFD transport equations, the mean velocity and turbulence state variables can be found independently from the mixture-fraction state variables. Likewise, when validating the CFD model predictions, the velocity and turbulence predictions can be measured in separate experiments (e.g., using particle-image velocimetry [PIV]) from the scalar field (e.g., using planar laser-induced fluorescence [PLIF]). 

Feltz, K.P., D.E. Tillitt, R.W. Gale, and PH. Peterman. 1995. Automated HPLC fractionation of PCDDs and PCDFs and planar and nonplanar PCBs on C18-dispersed PX-21 carbon. Environ. Sci. Technol. 29 709-718. 

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