Peak, asymmetry

The three dispersion mechanisms of peak broadening described by the van Deemter theory do not in themselves 

There are two commonly used measures of asymmetry of chromatographic peaks (Dolan 2002). The peak asymmetry factor Aj is given by  

There are a number of causes of peak asymmetry in both gas and liquid chromatography, including heat of adsorption, high activity sites on the support or absorbent, and nonlinear adsorption isotherms. Assuming that good quality supports and adsorbents are used, and the column is well thermostatted, the major factor causing peak asymmetry appears to result from nonlinear adsorption isotherms. 

The equation for the retention volume of a solute, that was derived by differentiating the elution curve equation, can be used to obtain an equation for the retention time of a solute (tr) by dividing by the flowrate (Q), thus, 

the velocity of a solute band along the column (Z) is obtained by dividing the column length (L) by the retention time, (tr)j consequently. 

Thus the band velocity (Z) is inversely proportional to (Vm + KVs), and for a significantly retained solute, Vm KVs, consequently. 

It is seen from the above equation that the band velocity is inversely proportional to the distribution coefficient with respect to the stationary phase. It follows that any changes in the distribution coefficient (K) will result directly in changes in the band velocity (Z). Consequently, if the isotherm is linear, then all concentrations will travel at the same velocity and the peak will be symmetrical. 

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  

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 

In analytical applications of liquid chromatography the most common causes of peak asymmetry are mixed mechanisms of retention, incompatibility of the sample with the chromatographic mobile phase, or development of excessive void volume at the head of the column. In preparative applications of liquid chromatography and related techniques, column overload can also contribute to peak asymmetry. The causes of severe peak asymmetry in analytical applications should be identified and corrected because they are frequently accompanied by concentration-dependent retention, non-linear calibration curves and poor precision. In addition, peak asymmetry can significantly compromise column efficiency leading, in turn, to reduced resolution and lower peak capacity (see sections 2.5 and 2.6). 

A proper configuration of the instrument and its alignment can substantially reduce peak asymmetry but unfortunately, they cannot eliminate it completely. The major asymmetry contribution, which is caused by the axial divergence of the beam, can be successfully controlled by Soller slits especially when they are used on both the incident and diffracted beam s sides. The length of the Soller slits is critical in handling both the axial divergence and asymmetry however, the reduction of the axial divergence is usually accomplished at a sizeable loss of intensity. 

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  

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  

In some advanced implementations of the modified pseudo-Voigt function, an asymmetric peak can be constructed as a convolution of a symmetric peak shape and a certain asymmetrization function, which can be either empirical or based on the real instrumental parameters. For example, as described in section 2.9.1, and using the Simpson s multi-term integration rule this convolution can be approximated using a sum of several (usually 3 or 5) symmetric Bragg peak profiles  

Consider the isotherms depicted in figure (3). Each curve represents a different isotherm relating the concentration of the solute in the stationary phase (Xs) to that of the mobile phase (Xm). 

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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. 

Figure 4. The Effect of Peak Asymmetry on the Apparent Composition of Closely Eluting Solutes...

The major cause of peak asymmetry in GC is sample overload and this occurs mostly in preparative and semi-preparative separations. There are two forms of sample overload, volume overload and mass overload. 

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 ... 

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. 

However, the major contribution to peak asymmetry is usually a result of column overload and the two effects that can occur are depicted in figure 9. 

Peak Asymmetry Resulting from Column Overload... 

In analytical LC there are two primary reasons why chemical derivatization of the sample constituents would be necessary, and they are 1) to enhance the separation and 2) to increase the sensitivity of detection. Under certain circumstances, derivatization can also be used to reduce peak asymmetry, i.e. to reduce tailing, or to improve the stability of labile components so that they do not re-arrange or decompose during the chromatographic process. However, sensitivity enhancement is the most common goal of derivatization. For example, aliphatic alcohols that contain no UV chromaphore can be reacted with benzoyl chloride to form a benzoic ester. 

It would seem that, in practice, the inequality defined in (3) can frequently occur but the converse does not appear to be true. Thus, peak asymmetry (in part or whole) resulting from inequality in mass transfer between the two phases manifests itself in the form shown in figure 1. 

Alternatively, peak asymmetry could arise from thermal effects. During the passage of a solute along the column the heats of adsorption and desorption that are evolved and adsorbed as the solute distributes itself between the phases. At the front of the peak, where the solute is being continually adsorbed, the heat of adsorption will be evolved and thus the front of the peak will be at a temperature above its surroundings. Conversely, at the rear of the peak, where there will be a net desorption of solute, heat will be adsorbed and the temperature or the rear of the peak will fall below its surroundings. 

In practice, it is probable that both of the effects discussed contribute to the overall peak asymmetry. Unfortunately, peak asymmetry varies in extent from the very obvious to the barely noticeable and because of this, peak asymmetry is often dismissed as the normal shape of a single solute peak. Such an assumption can cause serious errors in both qualitative and quantitative analysis. 

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... 

If the test solutes show reasonable peak asymmetry with lower than average plate count values for well retained solutes (k > 2) the column is most probably poorly packed. The number of theoretical plates, normalized to one meter column length by... 

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