Extracolumn variance

E. Extracolumn Band Broadening or Variance To maximize the effective number of theoretical plates, the contribution of the entire chromatographic system to band broadening (system variance, o-2ys) must be minimized. The system variance may be broken down into contributions from the column variance, a 01, as described above, and extracolumn diffusion and mixing processes, cr2x. As with the case of the column variance, extracolumn variance is an additive property and may be broken down into the major components ... 

Experimentally there are two methods of determining the ] extracolumn band broadening of a chromatographic instrument. The linear extrapolation method, discussed above, is relatively straightforward to perform and interpret but rests on the validity.. of equation (5.1) and (5.3). The assu itlon that the individual contributions to the extracolumn variance are independent, may not be true in practice, and it may be necessary to couple some of the individual contributions to obtain the most accurate values for the extracolumn variance [20]. It is assumed in equation (5.3) ... 

There are four major sources of extracolumn dispersion (i) dispersion due to the injection volume, (ii) dispersion due to the volume of the detector cell, (iii) dispersion due to the detector response time, and (iv) dispersion resulting from the volume in the connecting tubing between the injector and the column and also between the column and the detector. Thus, extracolumn dispersion takes place between the injector and the detector, only, and the system volume contributed by the solvent delivery system does not contribute to dispersion. The total permitted extracolumn dispersion (variance) is shared, albeit unequally, between those dispersion sources. A commonly accepted criterion for the instrumental contribution to zone broadening, suggested by Klinkenberg,17 is that it should not exceed 10% of the column variance. 

The above equation is the algebraic description of the principle of the summation of variances and is fundamentally important. If the individual dispersion processes that are taking place in a column can be identified, and the variance that results from each dispersion determined, then the variance of the final band can be calculated from the sum of all the individual variances. An example of the use of this principle is afforded by the calculation of the maximum extracolumn dispersion that can be tolerated for a particular column. This... 

There are four major sources of extracolumn dispersion which are measured in terms of their variance. 

The sum of the variances will give the overall variance for the extracolumn dispersion. Thus... 

Equation (12) shows how the extracolumn dispersion is made up and according to Klinkenberg [9] must not exceed 10% of the column variance if the resolution of the column is to be maintained, i.e.. 

Equations (13) and (15) allow the permissible extracolumn dispersion to be calculated for a range of capillary columns and packed columns. The results are shown in table 4. The standard deviation of the extracolumn dispersion is given as opposed to the variance, because it is easier to visualize from a practical point of view. The values for (a ) represents half the width (in volume flow of mobile phase) at 0.607 of the height of the peak that would have been caused by extracolumn dispersion alone. It is seen the values vary widely with the type of column that is used. (Og) values for GC capillary columns range from about 12 pi for a relatively short, wide, macrobore column to 1.1 pi for a long, narrow, high efficiency column. 

How is the efficiency influenced by the BGE Peak I broadening is the result of different processes in CZE I occurring during migration [in addition, extracolumn effects contribute to peak width (e.g., that stemming from the width and shape of the injection zone, or the -f. aperture of the detector cell)]. If the system behaves I linearly, the individual peak variances (the second mo-9 ments), o j, are additive according to a... 

There are two general experimental methods for estimating the extracolumn band broadening of a chromatographic instrament. The linear extrapolation method is relatively straightforward to perform and interpret but rests on the validity of Eq. (1.34) and the model used to calculate the contribution for the column variance. A plot of a T against tR, Vr or (1 + k) for a series of homologous compounds will be linear. The true column efficiency can be obtained from the slope of the line and o ext from the intercept on the vertical axis [162,167,168]. The assumption that the individual... 

What we would like to know is the influence of the extracolumn effects relative to those inside the column. Let us first calculate the peak width and the variance of a peak inside the column ... 

To get a handle on the relative contributions of the different contributions to extracolumn band spreading, we need to make some estimates of the individual variances. Let us first estimate the contribution of the injection... 

Note What is behind this statement is the law of the additivity of variances. It is a basic law of statistics. It states, in simple terms, that if multiple random events contribute to an observed distribution, then the variances of the distribution of the individual events sum up to form the variance of the overall distribution, provided that the individual events are independent of each other. We will encounter this law in various disguises in chromatography. The most obvious form of it is the additivity of the variances of extracolumn and intracolumn effects discussed in the next chapter.)... 

The influence of large injection volumes can be treated like any other extracolumn band-spreading effects. The band spreading inside the column is independent of the band spreading outside the column. Thus we can simply add the variance of the injection volume to the variance of the band contributed by the column ... 

Although ideally the observed variance is equal to the column variance, most HPLC systems detract from the column efficiency. Equation (22) can be used to calculate the importance of extracolumn effects ... 

According to a recent study, the commercially available LC systems can be classifled in three groups (1) optimized systems for fast separation with very low dispersion (crv,ext < 0 P-L ) (2) hybrid LC systems recommended for both fast and conventional separations ((Tv,ext = 10-30 p-L ) and (3) conventional LC systems with an extra-column variance over 50 pL (Figure 5.5). These major differences in extracolumn peak variance have a significant impact on measured column performance and achievable analysis time (63). Further improvements in instrument design (smaller dispersion) are necessary to take the full advantage of the most recent very efficient small columns. Today it is not always possible to utilize the potential of these small columns. The loss in efficiency can reach 30%-55% with commercially available optimized UHPLC systems (63). 

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