Column efficiency Theoretical efficiency (number of theoretical plates)

Column efficiency
Theoretical efficiency (number of theoretical plates)

As the analyte migrates through column, it occupies a continually expanding zone (Figure 1.6). This linear dispersion measured by the variance
increases with the distance of migration. When this distance becomes L, the total column length, the variance will be:

Reminding the plate theory model this approach also leads to the value of the
height equivalent to one theoretical plate H and to the number N, of theoretical plates N =L/H.
Therefore (Figure 1.7), any chromatogram that shows an elution peak with the temporal variance permits the determination of the theoretical efficiency N for the compound under investigation (1.8), and by deduction, of the value of H knowing that H =L/N;
If these two parameters are accessible from the elution peak of the compound, just because t
R
and  are in the same ratio as that of L to
. On the chromatogram,  represents the half-width of the peak at 60.6 per
cent of its height and t
R
the retention time of the compound. t
L
and  should be measured in the same units (time, distances or eluted volumes if the flow is constant). If  is expressed in units of volume (using the flow), then 4 corresponds to the ‘volume of the peak’, that contains around 95 per cent of the injected compound. By consequence of the properties of the Gaussian curve (w= 4 and w
=235), Equation 1.9 results. However, because of the distortion of most peaks at their base, expression 1.9 is rarely used and finally Equation 1.10 is preferred.
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N is a relative parameter, since it depends upon both the solute chosen and the operational conditions adopted. Generally a constituent is selected which appears towards the end of the chromatogram in order to get a reference value, for lack of advance knowledge of whether the column will successfully achieve a given separation.