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theoretical plates in the cell and n >1 they employed the elution equation as derived from the Plate Theory or one of a similar type i.e,
Xm(n)- xo n]
where the symbols have the meanings previously defined.
For values of , (Xm(n)), where n<1 , however, they developed a separate mathematical argument.
Some examples of the type of curves predicted by the theory of Atwood and Golay are given in figure 6.
Elution Profiles as a Function of Tube Length for Low Aspect
NORMALIZED ELUTED VOLUME V/VT
It is seen that from a short tube, of relatively large diameter, a broad asymmetrical peak is obtained and as the diameter of the tube is reduced (resulting in an increase in the efficiency of the tube in theoretical plates, (n)) the peaks become sharper in the front but with an extended tail. It should also be noted that the tube diameter must be decreased to a point where the efficiency, in theoretical plates, approaches the value of 30
before the elution profile becomes reasonably symmetrical. In practice such a reduction may not be possible as it would reduce the sensitivity of the detector to an unacceptably low level. Fortunately, the peak shapes, illustrated in figure 6, are not usually realized in practice as the tubes leading the mobile phase into the cell and away from it are designed to produce the maximum secondary flow in the cell and thus, reduce dispersion. An example of a typical detector cell design that introduces secondary flow in the cell and reduces dispersion to an acceptable level is shown in figure 7
LC Detector Cell Designed to Introduce Secondary Flow and Reduce Dispersion
It is seen that the entrant and exit tubes are set at an angle which, as the flow direction must be reversed for the mobile phase to flow through the tube, results in a radial flow across the face of the tube window. This not only increases the effective diffusion, and, consequently, reduces dispersion but also has a cleaning action on the face of the tube. The exit tube is also set at an angle to the cell which causes the reverse effect. The mobile phase, passing axially along the cell, must reverse direction In order to leave the cell and, thus, radial flow is again introduced into the cell.
Dispersion of solute bands in cells of different dimensions have also been experimentally measured by Scott and Simpson, (11) but with concentric inlet and outlet tubes, their data, although pertinent to some types of detectors, (for example conductivity detectors) are not applicable to optical detectors where inlet and outlet tubes can not be axially oriented.
Inlet from Column
Optical —-Window /
/ Detector / Cell
In general, it can be said that, often of necessity, the detector cell may be relative large with a low aspect ratio and thus, would theoretically produce serious band dispersion. In practice the predicted dispersion is reduced by deign of the inlet and outlet tubes, as discussed above, to ensure maximum secondary flow in the cell and thus, minimize dispersion. The success of the procedure to reduce detector cell dispersion depends on the type of detector and the principle of detection. For example,it is far easier to design a low dispersion electrical conductivity cell than a low dispersion UV absorption cell.
Effect of Extra Column Dispersion on Column Radius
The total extra column dispersion that takes place in a liquid chromatographic system places a limit on the minimum column radius that can be employed for a given separation. The effect of extra column dispersion on the minimum column radius was examined by Reese and Scott
(13) who derived an equation that allows the minimum column radius to be calculated for any particular separation.
The maximum extra column dispersion, (oe), that can be tolerated, has already been shown to be given by,
The limitation of (oe) to (0.32oc), restricts the increase in variance of the peak eluted from the column to a maximum of 10% and the increase in peak width to 5%.
oe = 0.3 2oc
where oe is the total extra column dispersion, and oc is the column dispersion.
Now, from the Plate Theory, oc = ^n(vo +Kvs)
and, Vr = n(vo +Kvs)
(vo +Kvs) = Vr/n
Substituting ror, ((vo +kvs)), in (iO) from (I i)
oc = Vr/Vn
Now, Vr = Vo+KVs = Vod +k')
Where, Vr, Vo, K, Vs, and k', have the meanings previously ascribed to them.
Thus, oc = Vod +ê')/^ï ....................................... (13)
Now, Vo = otr2l ..................................................... (14)
where, (r) Is the column radius,
(1) is the column length,
(c) is the fraction of the column occupied by the mobile phase
and 1 = nH ........................................................... (15)
Furthermore, if the column is run under optimum conditions and, consequently at the optimum mobile phase velocity, (H) will be at its minimum, i.e.,
H = 2dp ........................................................ (16)
Substituting for (H) in (15) from (16) and for (I) in (14) from (15)