Asymmetry factors

Elution volume, exclusion chromatography Flow rate, column Gas/liquid volume ratio Inner column volume Interstitial (outer) volume Kovats retention indices Matrix volume Net retention volume Obstruction factor Packing uniformity factor Particle diameter Partition coefficient Partition ratio Peak asymmetry factor Peak resolution Plate height Plate number Porosity, column Pressure, column inlet Presure, column outlet Pressure drop... 

Band Asymmetry. The peak asymmetry factor AF is often defined as the ratio of peak half-widths at 10% of peak height, that is, the ratio b/a, as shown in Fig. 11.2. When the asymmetry ratio lies outside the range 0.95-1.15 for a peak of k =2, the effective plate number should be calculated from the expression... 

In practice, the calculation of peak skew for highly tailing peaks is rendered difficult by basehne errors in the calculation of third moments. The peak asymmetry factor, A, = b/a, at 10 percent of peak height (see Fig. 16-32) is thus frequently used. An approximate relationship between peak skew and A, for taihng peaks, based on data in Yau et al. is Peak skew= [0.51 -t- 0.19/(A, — 1)] . Values of A, < 1.25... 

FIG. 16-32 Exponentially modified Gaussian peak with Xq/Gq = 1.5. The graph also shows the definition of the peak asymmetry factor at 10 percent of peak height. 

Occasionally, samples are run that adsorb onto the packing material. Generally, if one of the performance characteristics of the column changes by 10% or more, it is prudent to clean the column. These performance characteristics are (1) asymmetry factor, retention time, resolution, and theoretical plates. 

The peak measured for a plate number determination contains additional information about the packing quality of a column. The same peak may also be used to quantify information about the shape as well. The peak width on both sides of the perpendicular through the peak maximum is measured at a height of 10% of the maximum height (see Fig. 14.2). The quotient of the back by the front part of the peak is defined as the asymmetry factor (AF) ... 

Most manufacturers do not specify the asymmetry factor. Therefore this parameter can serve only for the observation of the column performance during its use. For interpretation, see the remarks about discarding a column. 

In the elucidation of retention mechanisms, an advantage of using enantiomers as templates is that nonspecific binding, which affects both enantiomers equally, cancels out. Therefore the separation factor (a) uniquely reflects the contribution to binding from the enantioselectively imprinted sites. As an additional comparison the retention on the imprinted phase is compared with the retention on a nonimprinted reference phase. The efficiency of the separations is routinely characterized by estimating a number of theoretical plates (N), a resolution factor (R ) and a peak asymmetry factor (A ) [19]. These quantities are affected by the quality of the packing and mass transfer limitations, as well as of the amount and distribution of the binding sites. 

Fig. 6-7. Asymmetry factor (AJ of the L-enantiomer versus sample load (A) and versus flow rate (B) on L-PA-imprinted polymers. Flow rate 1.0 ml min . Mobile phase MeCN/[potassium phosphate 0.05 M, pH 7] (7/3, v/v).

The PECD measurement clearly takes the form of a cosine function with an amplitude given entirely in terms of the single chiral parameter, b. It therefore provides exactly the same information content as the y asymmetry factor dehned above [Eq. (8)]. Experimental advantages of examining the PECD rather than the single angular distribution /p(0) are likely to include some cancellation of purely instrumental asymmetries (e.g., varying detection efficiency in the forward-backward directions) and consequent improvements in sensitivity. 

Figure 2. Photoelectron chiral asymmetry factor, y, obtained as a function of electron kinetic energy at hv = 21.2 eV for the (R)- and (S)- enantiomers of glycidol. Also included is a moderate resolution photoelectron spectrum recorded under identical conditions. Data from Refs. [37, 38].

On an undulator beamline, 54 would normally only be non-zero as a consequence of some defect or optical pollution from some source. The dichroism and asymmetry factor, y, will scale with 3 so that the ideal for PECO measurements would be to have i3 1 and 4 0. 

The second row in Fig. 15 shows examples at the three selected photon energies of the C=0 15 difference spectra obtained for both enantiomers. After normalization by the mean spectrum the asymmetry factor F(54.7°) is plotted along the bottom row. After correction for the cos(54.7°) term arising from the specific experimental geometry the net forward-backward asymmetry, y, can be estimated to reach a peak 15% in the hv = 298.7-eV photoionization. 

Figure 15. Circular dichroism of the C=0 C li peak (BE = 292.7 eV) in fenchone at three different photon energies, indicated, (a) Photoelectron spectrum of the carbonyl peak of the (1S,4R) enantiomer, recorded with right (solid line) and left (broken line) circularly polarized radiation at the magic angle, 54.7° to the beam direction, (b) The circular dichroism signal for fenchone for (1R,4A)-fenchone (x) and the (lS,41 )-fenchone (+) plotted as the raw difference / p — /rep of the 54.7° spectra, for example, as in the row above, (c) The asymmetry factor, F, obtained by normalizing the raw difference. In the lower rows, error bars are included, but are often comparable to size of plotting symbol (l/ ,4S)-fenchone (x), (lS,4R)-fenchone (+). Data are taken from Ref. [38],...

The experimental dichroism is seen to have its greatest magnitude some 5 eV above threshold, where 0.10. This corresponds to an asymmetry factor in the forward-backward scattering of y 20%. Such a pronounced PECD asymmetry from a randomly oriented sample looks to comprehensively better the amazingly high 10% chiral asymmetry recorded with highly ordered nanocrystals of tyrosine enantiomer [25] or the spectacular 12.5% asymmetry reported from an oriented single crystal of a cobalt complex [28]. 

Because the sense, or sign, of chiral asymmetry in the forward-backward electron scattering asymmetry depends on the helicity of the photon and of the molecule, it is essential that these variables are properly specified in any study to permit meaningful comparisons to be made. Discussing and comparing quantitative asymmetry factors, y [Eq. (8)] and dichroism [Eq. (9)] likewise requires agreement on the convention adopted in the definition of these terms. 

Circular dichroism convention. In this chapter, dichroism and asymmetry factors are defined as /icp hep or / =... 

Having chosen the test mixture and mobile diase composition, the chromatogram is run, usually at a fairly fast chart speed to reduce errors associated with the measurement of peak widths, etc.. Figure 4.10. The parameters calculated from the chromatogram are the retention volume and capacity factor of each component, the plate count for the unretained peak and at least one of the retained peaks, the peak asymmetry factor for each component, and the separation factor for at least one pair of solutes. The pressure drop for the column at the optimum test flow rate should also be noted. This data is then used to determine two types of performance criteria. These are kinetic parameters, which indicate how well the column is physically packed, and thermodynamic parameters, which indicate whether the column packing material meets the manufacturer s specifications. Examples of such thermodynamic parameters are whether the percentage oi bonded... 

Test solute k Asymmetry factor n/m Separation Factor... 

The peak asymmetry factor should be scrutinized first. In this discussion we refer to the peak asymmetry factor measured at 10% of the peak height (see section 1.5). Some column supply companies use the baseline measurement to specify peak asymmetry, leading to larger limiting values than those given here. Peak asymmetry, especially of unretained or weakly retained peaks (k < 3), is typical of poorly packed columns (if instrumental contributions can be excluded). If only the unretalned peak (k < 1) is asymmetric and/or there is a significant difference (> 15%)... 

Plate number N (as for Gaussian peaks) Resolution factor Rs Asymmetry factor As... 

The frequency of fluid oscillation at which levitation takes place is plotted in Fig. 40 against the corresponding amplitude A of oscillation, the asymmetry factor ka or ratio of the duration of the downstroke to that of the upstroke, and the resin particle diameter d. From these experimental data, the three parameters of the equation were correlated to the particle diameter ... 

Peak asymmetry factor AF Ratio of peak half-widths at 10% peak height... 

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