Theory of Zone Sampling

Unlike the continuous zone development mechanism utilized in a planar separation experiment, comprehensive MDLC is a sequential operation in which finite volumes of eluant are injected into the next dimension column. Because of this finite volume aspect, the mechanism and consequences of sampling eluant from one column with subsequent injection into the next column must be understood. Undersampling would lead to a loss in two-dimensional resolution and oversampling would lead to excessively long run times as the second dimension column would be used in a very inefficient way. 

FIGURE 2.6 Segmenting the concentration signal over a Gaussian zone with 1,3,10, and 20 samples taken in phase to the main peak. The area under these segmented curves is equal. This figure is taken from Murphy (1998). Reprinted with permission from the American Chemical Society. 

Toward this goal we write the average concentration of solute in the sample loop, (C), accumulated over a time interval ts which is between tt and tt i as 

Finally, we obtain Cs as the sample loop concentration by summing up the individual loop solute concentrations across all time segments as 

In Equation 2.16, u(t) is the unit function such that u(t) = 0 when t 0 and u(t) = 1 when t 0 and N is the number of samples across a peak. Equation 2.16 is then substituted into Equation 2.13 to get os in Equation 2.13, given a in Equation 2.15. 

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As discussed below, if the two media used for separation in 2DLC are correlated with respect to the retention mechanism, the peak capacity will be lower than expected from the product approximation. The dependence of the peak capacity product on the correlation between retention mechanisms is covered in Chapter 3. Furthermore, as pointed out by Carr and coworkers (Stoll et al., 2006), if the second dimension sampling of the first dimension is undersampled, the potential peak capacity will not be able to be utilized. This is discussed in the theory of zone sampling section below. Further implications of peak capacity limitations due to sampling have been recently given by Tanaka and coworkers (Horie et al., 2007). 

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