Peak skew

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... 

Kirkland, J. J., Yau, W. W., Stoklosa, H. J., and Dilks Jr., C. H., Sampling and extra-column effects in high-performance liquid chromatography influence of peak skew on plate count calculations, /. Chromatogr. Sci., 15, 303, 1977. 

Although a numerical integration is required to compute the peak profile, the moments are calculated directly as fli = tG + XG and o2 = riG + xG and the peak skew as ... 

For EMG peaks, peak skew increases with the ratio xG/oG. Figure 16-32 illustrates the characteristics of such a peak calculated for xG/aG = 1.5. In general, with xG/aG > 1 (peak skew > 0.7), a direct calculation of the moments is required to obtain a good approximation of the true value of N , since other methods give a large error (Yau et al., Modems Size-Exclusion Liquid Chromatography, Wiley, New York, 1979). Alternatively, Eq. (16-165) can be fitted to experimental peaks to determine the optimum values of fG, aG, and xG. 

Mark-Houwink-Sakurada constant Mass transfer coefficient around gel Fractional reduction in diffusivity within gel pores resulting from frictional effects Solute distribution coefficient Solvent viscosity nth central moment Peak skewness nth leading moment Viscosity average molecular weight Number of theoretical plates Dimensionless number... 

Errors in estimation of the retention volumes from the apexes of skewed peaks (peak skewing depends on the flow rate)... 

The CN-column had 8100 theoretical plates and a peak skew of l.k (back/front calculated at 10 % peak height), the N02-column had 2700 plates and peak skew 2.1. 

Figure 2. Graphical depiction of r (exponential tailing component) and a (gaus-sian component) features of an asymmetrical peak (t/a ratio related to peak skew)...

With previous methods, peak skew could not be determined with sufficient precision to be meaningful (3). However, with the tau/sigma method, peak skew is easily calculated to give precise, useful, quantitative information on peak shape. The tau/sigma method for calculating peak skew is preferred over other methods since this approach has a sound theoretical basis and values can be measured with greater precision and accuracy. 

However, using peak skew as a performance criterion does suffer from one drawback it is necessary to have a sophisticated computer to make the calculation. Therefore, most users of HPLC columns will have to use hand-calculated values for peak asymmetry measurement (Figure A). However, these hand-calculated values can be correlated to a first approximation to the computer-generated values of peak skew using the graph shown in Figure 5. 

Graph of first-approximation relationship between peak skew and the peak asymmetry factor... 

In the pH region from 3.5 to 5, the aqueous pH of the mobile phase was close to that of the analyte Ka values, which led to a dramatic change in retention and peak skewing. Working in this pH region would not be recommended because small variations in the mobile-phase pH would lead to undesired changes in retention and selectivity. However, as the aqueous pH was changed from 3 to 2, only minor variations in retention were observed for all the components in the mixture. This also led to the optimal selectivity and resolution of all components in the mixture. 

The computer models described provide a functional simulation of SEC-viscometry-LS analysis of linear polymers. The results for the Flory-Schulz MWD are in qualitative agreement with previous results for the Wesslau MWD. Both models emphasize the importance of determining the correct volume offset between the concentration detector and molecular weight-sensitive detectors. For the Flory-Schulz model, the peak shape, as well as the peak elution volume, can provide information about molecular weight polydispersity. Future work will extend the model to incorporate peak skew and polymer branching. 

Although theory predicts that chromatographic peaks will be symmetrical, peak asymmetry is common, even in the most carefully controlled analytical and preparative separations. The most rigorous definition of peak asymmetry is given by the peak skew (y), which is related to the second (M2) and third moments (M3) of the Gaussian distribution ... 

This classical interpretation is not sufficient, as experimental results clearly indicate that there is peak skewing for this reason, it is useful to study each contribution separately. 

The QIT also shares some advantages with TOF-MS. In particular, ion trap mass spectrometry is known for high sensitivity. Furthermore, sampling is decoupled from scanning, so there is no mass spectral peak skewing in GC-MS and HPLC-MS. 

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