Extracolumn Dispersion

Extracolumn dispersion is that contribution to the total band dispersion that arises from spreading processes taking place outside the column and for convenience will be taken as.  

Now the maximum increase in band width that can be tolerated before loss of resolution becomes unacceptable was determined by Klinkenberg [9] to be 10% of the column variance thus, 

In practice equation (7) is usually applied to the dead volume peak as all peaks have equal importance and the dead volume peak is the most narrow and thus tolerates the least extracolumn dispersion. 

As an example of the use of equation (8) in detector design, let us calculate the standard deviation of the extracolumn dispersion that can be tolerated by an LC column 10 cm long 4.6 mm I.D packed with particles 10 p in diameter. 

the height of the theoretical plate (HETP) of a column packed with particles having a diameter (dp) will be approximately (2dp), and thus the efficiency (n) for a column of length (1) will be 

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The packed GC column has a value for (og) of about 55 pi, whereas the high efficiency microbore LC column only 0.23 pi. It is clear that problems of extracolumn dispersion with packed GC columns are not very severe. However, shorter GC capillary columns with small diameters will have a very poor tolerance to extracolumn dispersion. In the same way, short microbore LC columns packed with small... 

The chromatography literature contains a vast amount of dispersion data for all types of chromatography and, in particular, much of the data pertains directly to GC and LC. Unfortunately, almost all the data is unsuitable for validating one particular dispersion equation as opposed to another. There are a number of reasons for this firstly, the necessary supporting data (e.g., diffusivity data for the solutes in the solvents employed as the mobile phase, accurate distribution and/or capacity factor constants (k")) are not available secondly, the accuracy and precision of much of the data are inadequate, largely due to the use of inappropriate apparatus with high extracolumn dispersion. 

In a packed column the HETP depends on the particle diameter and is not related to the column radius. As a result, an expression for the optimum particle diameter is independently derived, and then the column radius determined from the extracolumn dispersion. This is not true for the open tubular column, as the HETP is determined by the column radius. It follows that a converse procedure must be employed. Firstly the optimum column radius is determined and then the maximum extra-column dispersion that the column can tolerate calculated. Thus, with open tubular columns, the chromatographic system, in particular the detector dispersion and the maximum sample volume, is dictated by the column design which, in turn, is governed by the nature of the separation. 

Extracolumn dispersion is a major problem for the packed fused silica capillary columns with internal diameters less than 0.35 mm. Peak standeunl deviations will be in the submicroliter range and extensive equipment modification is required for operation under optimum conditions. A reasonable compromise is to esploy injection voluMs of a few hundred nanoliters or less with detector volumes of a similar or preferably smaller size. This demands considerable ingenuity on behalf of the analyst since, as... 

The extra-column dispersion governs the dimensions of the column that we use. In the calculation above, the dispersion is increased by about 8% by the extra-column effects. If we want the dispersion to be increased by no more than this, then should not be any smaller than the value calculated above. This in turn limits the retention volume, and thus the volume of the column itself. The minimum column volume we can use will depend on the amount of extracolumn dispersion and on what we consider to be an acceptable increase in peak width that is produced by extra-column effects. In practice, this acceptable increase is taken as 10%, based on an unretained solute, and if we take 50 (i as a typical figure for extracolumn dispersion then the minimum column diameter works out at about 4.5 mm for a column 25 cm long. 

Narrow-bore columns of between 1.0 and 2.5 mm ID are available for use in specially designed liquid chromatographs having an extremely low extracolumn dispersion. For a concentration-sensitive detector such as the absorbance detector, the signal is proportional to the instantaneous concentration of the analytes in the flow cell. Peaks elute from narrow-bore columns in much smaller volumes compared to those from standard-bore columns. Consequently, because of the higher analyte concentrations in the flow cell, the use of narrow-bore columns enhances detector sensitivity. The minimum detectable mass is directly proportional to the square of the column radius (107) therefore, in theory, a 2.1-mm-ID column will provide a mass sensitivity about five times greater than that of a 4.6-mm-ID column of the same length. 

The speed of a chromatographic separation is fixed by the particle size, the stationary phase characteristics, the available pressure, the solvent viscosity, the solute diffusivity, the a values of the critical pair, and extracolumn dispersion. One way to achieve faster separations is to reduce the particle size of the stationary phase. However, if material of smaller diameter is packed into a conventional size column, the backpressure will become prohibitively high. Thus, in a compromise between speed and optimum performance, narrow (<2 mm) columns packed with small 3-5 ju.m diameter particles have been developed. 

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. 

To maximize the peak response, it is important to use the longest cell path length possible without introducing extracolumn dispersion. With... 

It is particularly important to minimize extracolumn dispersion when using small-bore columns because the peak volumes are sufficiently small that extracolumn dispersion can degenerate the separation significantly. There are four major sources of extracolumn dispersion ... 

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... 

It is seen that the maximum value for the standard deviation of all the processes that contribute the extracolumn dispersion must be less than 4.5 microliters and gives an indication of the difficulties involved in designing detectors that can function well with microbore columns. It is also seen that equation (8) can be extremely useful in detector design and provides the necessary data that would allow a detecting system to be constructed to suit a particular range of column sizes. It is obvious that, although the maximum value for (a ) is now known, it will be necessary to examine quantitatively the contribution of the various extracolumn dispersion processes to the overall value of (Og). These details will be discussed later in this book. 

Thus (m ), the mass sensitivity of the chromatographic system depends on the detector sensitivity, column dimensions, column efficiency and the capacity factor of the eluted solute. However, irrespective of the column properties, the mass sensitivity is still directly related to the detector sensitivity. It will also be seen that the column radius will depend on the extracolumn dispersion, much of which arises from the detector connecting tubes and sensor. It follows that the design of the detector and its sensitivity has a major influence on the mass sensitivity of the overall chromatographic system. 

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.. 

It is of considerable interest to calculate the maximum extracolumn dispersion that can be tolerated for different types of columns. This will indicate the level to which dispersion in the detector and its associated conduits must be contained to avoid abrogating the chromatographic resolution. 

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. 

Table 4 The Permissible Extracolumn Dispersion for a Range of Different Types of Column...

The problem was solved by the development of multifunctional detectors, where more than one property of the solute is concurrently measured while it is situated in a single sensor cell. This arrangement reduces both the cost of the detector and also the extracolumn dispersion as only one cell is employed and only the normal column detector connection is necessary. The first multifunctional detector was developed by DuPont and was a bifunctional detector that simultaneously measured UV absorption and solute fluorescence. 

I where the subscripts extr, dif. Joule, cone, and ads indi- cate the contributions from extracolumn dispersion, longitudinal diffusion. Joule self-heating, concentration... 

The open-tubular column is, by far, the most popular type of GC column in use today. As a result of its small internal cross section, however, extracolumn dispersion can become a serious problem. This means that open-tubular columns must be used with special types of injector and reduced volume connectors, and certain detectors must have specially designed sensor cells to avoid impairing column performance. 

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