Peaks, shape asymmetry

In a real chromatogram the peaks often have profiles that are non-Gaussian. There are several reasons for this. Besides the accepted approximations, such as invariance of the distribution coefficient K with concentration, there are irregularities of concentration in the injection zone at the head of the column. Furthermore, the speed of the mobile phase is zero at the walls and maximum at the centre of the column. The asymmetry observed in the peak shape is measured by a parameter called the skewing factor, which is calculated at 10% of the peak height (Fig. 1.4) ... 

All peaks (certainly all peaks that need to be measured) should be symmetric, with an asymmetry factor A/B in Figure 23-13 in the range 0.9-1.5. Asymmetric peak shapes should be corrected as described at the end of Section 25-1 before optimizing a separation. 

The asymmetry of peak shape is preserved in anthraxolite heated to 1200°C. showing that turbostratic disorder persists in spite of a general enhancement of ordering. The band is also sharper and narrower. This may be interpreted to mean either that fewer class intervals are represented in the crystallite size distribution or that increased ordering of aromatic lamellae has reached the point where graphite (hid) planes are more common. Diffraction peaks of both (100) and (101) fall with the 2-A. band. 

In ideal situations, all peak shapes are Gaussian. However, in certain cases, many eluted components do not show true Gaussian behavior. A measure of this nonideal behavior is the asymmetry factor, (b/a). This factor can be determined by drawing a line from the peak maxima perpendicular to the baseline and then measuring the widths (b and a) at one-tenth peak height (see Fig. 9.2.5). Values of —1.0 for b/a are recommended higher values indicate considerable skewing of the eluted component. 

Peak shape is usually expressed by the peak asymmetry (AJ. In Fig. 3, the peak asymmetry factor for substance B is given by... 

Asymmetry factor, Ai The plate number, N, assumes that the peak shape is Gaussian, but in practice this is rare. It is more hkely that the peak is asymmetrical, i.e. it tails . This is quantified using the asymmetry factor. As, calculated as shown in Fig. 31.7. 

The simplest form of an HPLC SST involves comparison of the chromatogram with a standard one, allowing comparison of the peak shape and the peak width baseline resolution. Additional parameters that can be experimentally calculated to provide quantitative SST report include the number of theoretical plates, separation factor, resolution, tailing or peak asymmetry factor, accuracy, and precision (RSD of six measurements). Resolution may also be combined with a selectivity test to check the resolution of the analytes from components present in the sample matrix. If matrix components interfere with a method, a matrix blank may be included in the SST. Peak shape and asymmetry, or tailing factor, can... 

Since as5mimetry cannot be completely eliminated, it should be addressed in the profile fitting procedure. Generally, there are three ways of treating the asymmetry of Bragg peaks, all achieved by various modifications of the selected peak shape function ... 

In Eq. 2.61 a is a free variable, i.e. the asymmetry parameter, which is refined during profile fitting and z,- is the distance fi om the maximum of the symmetric peak to the corresponding point of the peak profile, i.e. z,-= 20yfc - 20 . This modification is applied separately to every individual Bragg peak, including Kaj and Ka2 components. Since Eq. 2.61 is a simple intensity multiplier, it may be easily incorporated into any of the peak shape functions considered above. Additionally, in the case of the Pearson-VII function, asymmetry may be treated differently. It works nearly identical to Eq. 2.61 and all variables have the same meaning as in this equation but the expression itself is different ... 

Peak shape parameters, which include full width at half maximum H), asymmetry (a), and exponent (P) for Pearson-VII or mixing parameter (ti) for pseudo-Voigt functions. All peak shape parameters are typically refined for Kai reflections. The corresponding Ktt2 components are assumed to have H, a, P (or p) identical to Ka In some applications, peak shape parameters may be fixed at certain commonly observed values, or they may only be adjusted manually. 

---