Dispersion, detector extra column

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. 

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. 

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... 

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. 

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. 

If the total extra-column dispersion is shared equally between the sample volume and the detector,... 

The system dead volume must be reduced to an absolute minimum, particularly when using very efficient narrow-bore SEC columns. Extra column dispersion becomes a greater consideration as the column volume is reduced, and dead volume should be minimized in all parts of the system, including injection valves, connecting tubing, and detectors, if the column performance is to be realized. 

Dispersion can be produced outside the column by dead volume in the injector, the detector or the plumbing. The combined effect of all these is called extra-column dispersion. Fig. 2.3c shows an example of this, in which different dead volumes are connected between the column and the detector, and Fig. 5.3b shows dispersion produced by dead volume at the top of the column. You can see from these that dead volume effects can cause a serious loss of performance. 

Post-column on-line derivatisation is carried out in a reactor located between the column and the detector. With this technique, the derivatisation reaction does not need to go to completion, provided it can be done reproducibly, and the reaction does not produce any chromatographic interferences. The reaction needs to take place in a fairly short time at moderate temperatures, and the reagent should not be detectable under the same conditions at which the derivative is detected. The mobile phase may not be the best medium in which to carry out the reaction, and the presence of the reactor after the column will increase the extra-column dispersion. 

Fig. 2.4p shows three types of post-column reactor. In the open tubular reactor, after the solutes have been separated on the column, reagent is pumped into the column effluent via a suitable mixing tee. The reactor, which may be a coil of stainless steel or ptfe tube, provides the desired holdup time for the reaction. Finally, the combined streams are passed through the detector. This type of reactor is commonly used in cases where the derivatisation reaction is fairly fast. For slower reactions, segmented stream tubular reactors can be used. With this type, gas bubbles are introduced into the stream at fixed time intervals. The object of this is to reduce axial diffusion of solute zones, and thus to reduce extra-column dispersion. For intermediate reactions, packed bed reactors have been used, in which the reactor may be a column packed with small glass beads. 

In terms of volume, V0 is a measure of the system dead volume from the injector to the detector. For a well designed system with low extra-column dispersion, V0 will be roughly equal to the dead volume of the column, that is, the volume of the column not occupied by the packing particles. 

The Van Deemter equation remained the established equation for describing the peak dispersion that took place in a packed column until about 1961. However, when experimental data that was measured at high linear mobile phase velocities was fitted to the Van Deemter equation it was found that there was often very poor agreement. In retrospect, this poor agreement between theory and experiment was probably due more to the presence of experimental artifacts, such as those caused by extra column dispersion, large detector sensor and detector electronic time constants etc. than the inadequacies of th Van Deemter equation. Nevertheless, it was this poor agreement between theory and experiment, that provoked a number of workers in the field to develop alternative HETP equations in the hope that a more exact relationship between HETP and linear mobile phase velocity could be obtained that would be compatible with experimental data. 

Equation (24) allows the minimum column radius to be calculated from its length, the particle diameter of its packing and the extra column dispersion of the chromatographic system. Unfortunately, the extra column dispersion is rarely known and very few manufacturers even provide data on the overall dispersion of the detector. When values are given for the detector dispersion, it is often for the sensing cell alone and does not include internal connecting tubes and, as a consequence, can be very misleading. 

The total extra column dispersion can be easily measured by removing the column and connecting the tube from the sample valve directly to the tube leading to the detector. A very small sample ( 0.2jil or less) is then injected into the system and the dispersion calculated as follows,... 

As a finite mass of solute is placed on the column, any increase in peak volume necessary to compensate for high extra column dispersion will dilute the solute concentration as sensed by the detector. Consequently, as the sensitivity, or minimum detectable concentration of the detector, has a limit, increasing the column diameter will result in a reduced mass sensitivity. 

The importance of the extra column dispersion now becomes apparent, as equation (26) shows that the minimum detectable mass increases linearly with the extra column dispersion. It is also becomes obvious that it is of little use designing a detector for increased sensitivity (Xd) if this is achieved (as is often the case) at the expense of increased extra column dispersion (oe). Conversely, if the chromatographic system is designed to have very low extra column dispersion, a proportional reduction in the minimum detectable mass will be achieved even if the... 

Another extremely important instrument specification is the total dispersion that takes place in the sample valves, connecting tubes and detector cell of the chromatograph. The subject of extra column dispersion has already been discussed in the previous chapter. 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. 

It is seen that the optimum column radius for an open tubular column varies widely with inlet pressure arid the difficulty of the separation. Considering a separation of some difficulty, for example ( a = 1.02), it is seen that at an inlet pressure of lOOOp.s.f, the optimum column diameter would be about 4 micron whereas, at an inlet pressure of only 1 psi, it would be about 43 micron. The former would be quite difficult to coat with stationary phase and would demand detectors and injection systems of almost impossibly low dispersion A column of 43 micron in diameter, on the other hand, would be piactical from the point of view of both ease of coating and an acceptable system extra column dispersion. However, the lengths of such columns arid the resulting analysis times remains to be determined and may preclude their- use. 

The stochastic model applies to processes involving the stationary phase. To analyze the chromatogram, we need to subtract contributions to peak broadening from dispersion in the mobile phase and extra-column effects such as finite injection width and finite detector volume. These effects account for the width of the unretained peak. To subtract the unwanted effects, we write... 

The detector flow-cell, the contribution of which to ctv is approximately equal to its volume [707], represents a considerable and recognizable contribution to the extra-column band broadening. Typical conventional flow-cells have a volume of 8 pi, which is quite substantial compared with the maximum allowable extra-column dispersion. 

Table 7.3a lists the maximum allowable extra-column dispersion for the first three columns listed in table 7.1, using three different internal diameters. It is seen that the contribution from the detector flow-cell (as well as other contributions) will have to be reduced considerably if short columns packed with 3 pm particles are to be used. An even larger reduction in the extra-column dispersion is required for the use of columns with a reduced inner diameter. 

Instrument dispersion can be reduced by optimizing injector and detector systems and reducing diameter of connection capillaries. The individual sources of volumetric extra-column broadening specified in equation (17-26)... 

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