Measure of peak asymmetry

More practical measures of peak asymmetry ( 4 ) involve the comparison of the width of the tail, bf, of the peak to its front, Of (Figure 2.2)... 

Should one wish, these variables can easily be converted back to their expanded form through the definitions given in Equations 7 -9. Our measure of peak asymmetry is the ratio of half widths,... 

The area of a peak is the integration of the peak height (concentration) with respect to time (volume flow of mobile phase) and thus is proportional to the total mass of solute eluted. Measurement of peak area accommodates peak asymmetry and even peak tailing without compromising the simple relationship between peak area and mass. Consequently, peak area measurements give more accurate results under conditions where the chromatography is not perfect and the peak profiles not truly Gaussian or Poisson. 

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... 

The splitting in Figure 25 shows that both orientations of 180=C=160 are present in the crystal. The separation of the peaks is a measure of the asymmetry of the environment, while the shift of their average from the value expected from unlabeled C02 is probably related to the average strength of the intermolecular force constants. 

If the peak to be quantified is asymmetric, a calculation of the asymmetry would also be useful in controlling or characterizing the chromatographic system [52]. Peak asymmetry arises from a number of factors. The increase in the peak asymmetry is responsible for a decrease in chromatographic resolution, detection limits, and precision. Measurement of peaks on solvent tails should be avoided. 

Figure 7.9 Effect of peak asymmetry on manual measurements. (Reprinted from Ref. 14 with permission.)...

The tailing factor, 7 , a measure of peak symmetry, is unity for perfectly symmetrical peaks, and its value increases as tailing becomes more pronounced. In some cases, values less than unity may be observed. As peak asymmetry increases, integration, and hence precision, becomes less reliable. The calculation is expressed by the equation... 

Recommendations for the position at which should be measured vary. One of the most rigorous treatments of peak asymmetry is that of Foley and Dorsey (1983) who have described tailing in terms of an exponentially... 

Fig. 2 (A) Measurement of peak tailing using USP tailing factor and peak asymmetry factor. (B) Peak resolution. (From Merck...

Efficiency (or number of theoretical plates) (N) A measure of peak band spreading determined by various methods, some of which are sensitive to peak asymmetry. In practice, a higher N gives more efficient chromatographic conditions. 

The assumption for the measurement of peak widths in Eqs. (8)—(10) is that the peak is Gaussian. Unfortunately, few peaks are truly Gaussian and, in general, for asymmetrical peaks, N, calculated by a Gaussian-based equation, increases the higher up on the peak the width is measured. Figure 3 shows the error in plate-count determinations for asymmetrical peaks as a function of the peak height at which the width is measured. A more accurate approach to efficiency measurement has been presented by Foley and Dorsey (7), which takes into account the peak asymmetry. 

If baseline drift has occurred then the peak height is measured from the mid point on the line joining start and end points of the peak and peak width at half height by drawing the horizontal vector to the line drawn at Aq.s parallel to the base line (Figure 8.4). Measurement of peak data assumes symmetrical peaks. Data from asymmetric peaks with an asymmetry ratio of greater than 1.2 will be less accurate. 

There are several measures of peak tailing. A common one is the ratio of the width of the tail of the peak to the width of the front of the peak at either 5 or 10% of the height of the peak (see Fig. 2.3 for an illustration of the measurement of the various asymmetry factors) ... 

Figure 1.5 Measurement of the asymmetry of a chromatographic peak, where h is the peak height and a and b are measured at 10% of h.

Figure 13.18c shows in an oversimplified way how the shape of the curve affects the value of a. For this illustration we assume that the position of the right side of the curve is determined solely by the electric potential at the electrode, whereas the left side of the curve is determined solely by chemical factors that are unaffected by the potential of the electrode, and assume also that the two sides of the curve meet at a cusp. When the electric potential is increased by an amount

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Peak asymmetry or skewing is a well-documented (4,6,7) characteristic of chromatographic peaks and is measured easily by ratioing the peak half widths at 10% height as shown ... 

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%)... 

Moment analysis is one of the simplest types of analysis and is useful for measuring the performance of the chromatography. Moments can be used to measure the same things that are measured in ID chromatographic systems these include the first, second, and third moments, which are more accurate than the related peak maximum, peak width, and peak asymmetry. In 2D, however, these values each have a component in each dimension and this can be easily determined in software-based measurement systems. 

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