Extra-column dispersion

The Golay equation [9] for open tubular columns has been discussed in the previous chapter. It differs from the other equations by the absence of a multi-path term that can only be present in packed columns. The Golay equation can also be used to examine the dispersion that takes place in connecting tubes, detector cells and other sources of extra-column dispersion. Extra-column dispersion will be considered in another chapter but the use of the Golay equation for this purpose will be briefly considered here. Reiterating the Golay equation from the previous chapter. 

Figure 10.10. An example of peak broadening caused by instrument dispersion (extra-column band-broadening), which affects the early eluting peaks more severely. Figure courtesy of Academy Savant.

Having established that a finite volume of sample causes peak dispersion and that it is highly desirable to limit that dispersion to a level that does not impair the performance of the column, the maximum sample volume that can be tolerated can be evaluated by employing the principle of the summation of variances. Let a volume (Vi) be injected onto a column. This sample volume (Vi) will be dispersed on the front of the column in the form of a rectangular distribution. The eluted peak will have an overall variance that consists of that produced by the column and other parts of the mobile phase conduit system plus that due to the dispersion from the finite sample volume. For convenience, the dispersion contributed by parts of the mobile phase system, other than the column (except for that from the finite sample volume), will be considered negligible. In most well-designed chromatographic systems, this will be true, particularly for well-packed GC and LC columns. However, for open tubular columns in GC, and possibly microbore columns in LC, where peak volumes can be extremely small, this may not necessarily be true, and other extra-column dispersion sources may need to be taken into account. It is now possible to apply the principle of the summation of variances to the effect of sample volume. 

A number of HETP equations were developed other than that of Van Deemter. Giddings developed an alternative form that eliminated the condition predicted by the Van Deemter equation that there was a finite dispersion at zero velocity. However, the Giddings equation reduced to the Van Deemter equation at velocities approaching the optimum velocity. Due to extra-column dispersion, the magnitude of which was originally unknown, experimental data were found not to fit the Van Deemter... 

To reiterate the definition of chromatographic resolution a separation is achieved in a chromatographic system by moving the peaks apart and by constraining the peak dispersion so that the individual peaks can be eluted discretely. Thus, even if the column succeeds in meeting this criterion, the separation can still be destroyed if the peaks are dispersed in parts of the apparatus other than the column. It follows that extra-column dispersion must be controlled and minimized to ensure that the full performance of the column is realized. 

There are four major sources of extra-column dispersion which can be theoretically examined and/or experimentally measured in terms of their variance contribution to the total extra-column variance. They are as follows ... 

The sum of the variances will give the overall variance for the extra-column dispersion (og). Thus,... 

Equation (1) shows how the extra-column dispersion is made up and according to Klinkenberg [1] must not exceed 10% of the column variance (Oj.) if the resolution... 

To realistically evaluate the effect of extra-column dispersion on column performance, it is necessary to evaluate the maximum extra-column dispersion that can be tolerated by different types of columns. Such data will indicate the level to which dispersion in the detector and its associated conduits must be constrained to avoid abrogating the chromatographic resolution. 

Equations (2) and (4) allow the permissible extra-column dispersion to be calculated for a range of capillary and packed columns. To allow comparison, data was included for a GC column, in addition to LC columns. The results are shown in Table 1. 

Table 1. The Permissible Extra-column Dispersion for a Range of Different Types of Column...

The standard deviation of the extra-column dispersion is given as opposed to the variance because, as it represents one-quarter of the peak width, it is easier to visualize from a practical point of view. It is seen the values vary widely with the type of column that is used, (ag) 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. 

Extra-column dispersion can arise in the sample valve, unions, frits, connecting tubing, and the sensor cell of the detector. The maximum sample volume, i.e., that volume that contributes less than 10% to the column variance, is determined by the type of column, dimensions of the column and the chromatographic characteristics of the solute. In practice, the majority of the permitted extra-column dispersion should... 

A low volume (0.2 pi) Valeo sample valve was employed with one end of the open tube connected directly to the valve and the other connected directly to the sensor cell of the detector. The UV detector was the LC 85B manufactured by Perkin Elmer, and specially designed to provide low dispersion with a sensor volume of about 1.4 pi. The total variance due to extra-column dispersion was maintained at... 

Another critical instrument specification is the total extra-column dispersion. The subject of extra-column dispersion has already been discussed in chapter 9. It has been shown that the extra-column dispersion determines the minimum column radius and, thus, both the solvent consumption per analysis and the mass sensitivity of the overall chromatographic system. The overall extra-column variance, therefore, must be known and quantitatively specified. 

Unfortunately, some of the data that are required to calculate the specifications and operating conditions of the optimum column involve instrument specifications which are often not available from the instrument manufacturer. In particular, the total dispersion of the detector and its internal connecting tubes is rarely given. In a similar manner, a value for the dispersion that takes place in a sample valve is rarely provided by the manufactures. The valve, as discussed in a previous chapter, can make a significant contribution to the extra-column dispersion of the chromatographic system, which, as has also been shown, will determine the magnitude of the column radius. Sadly, it is often left to the analyst to experimentally determine these data. 

The maximum value for the extra-column dispersion that is acceptable, (oe), is given by (chapter 9)... 

As has been previously discussed, the limitation of (oe) to (0.32oc), allows the variance of the peak eluted from the column to be increased by a maximum of 10% by any extra-column dispersion and, consequently, the width of the peak by a maximum of 5%. 

Maximum Sample Volume and Maximum Extra-Column Dispersion... 

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