## Basic Theory and Configurations

Giddings' treatment of the peak capacity for a single mode leads to the expression:

N1/2

m where m = 4 implies unit resolution (4o separation), N is the plate number, and kn is the retention factor for the last member of a series of peaks numbered from zero (nonretained) through to n (last peak out). A sequence of independent modes, each having a peak capacity ¿i, should exhibit a multiplicative separation effect with an overall result given by:

With a conventional single-column approach the peak capacity increases with dwindling returns. To increase the peak capacity by a factor of 10, a 100-fold increase in column length would be necessary. In coupled chromatography however the effect is, theoretically, multiplicative and leads to an exponential increase with the number of columns within the configuration with different retention mechanisms.

Not all column types are compatible: typical examples of compatible systems with sufficiently different retention mechanisms are size exclusion and normal-phase chromatography, reversed-phase and ion exchange chromatography, ion exchange and rever-sed-phase chromatography and polar bonded phase and normal-phase chromatography. The columns employed can have the same or different lengths: even a very short column, like a guard column, is used as the first column for some applications.

When one discrete zone is collected from the firstdimension column and reinjected into the second dimension, the resulting data are two individual one-dimension data sets. In linear coupled-column systems, the peak capacities of the individual columns can be summed, not multiplied. In so-called comprehensive automated system, the resulting data are a matrix, usually represented as a contour plot with each chromatographic separation along an axis.

The multidimensional resolution (Rs) for comprehensive multidimensional chromatography was suggested to be equal to the Euclidean norm of the resolution in each dimension. Schure et al. showed that this definition, under a certain set of assumptions, could be utilized to produce an experimentally simple method for 2-D resolution estimation:

Figure 1 Schematic diagram of the two-dimensional resolution measurement using a 2-D contour (bottom) and the corresponding slice for resolution determination. (Reproduced with permission from Murphy RE, Schure MR and Foley JP (1998) Analytical Chemistry 70: 1585-1594. Copyright 1998 American Chemical Society.)

Figure 1 Schematic diagram of the two-dimensional resolution measurement using a 2-D contour (bottom) and the corresponding slice for resolution determination. (Reproduced with permission from Murphy RE, Schure MR and Foley JP (1998) Analytical Chemistry 70: 1585-1594. Copyright 1998 American Chemical Society.)

R"

be constructed but attention must be given to the [3] effects of the injection volume and flow rates on the performance of the coupled system.

where P is the ratio of the difference between the amplitude at the valley and average peak maximum (f) and the average maximum peak (g) of the resulting one-dimensional chromatogram at the peak maxima in the contour plot, as shown in Figure 1 (t1>x and t2,x are the retention times of the peak maxima for peaks 1 and 2 in the x separation axis. The peak maxima in the y dimension are similarly denoted as t1,y and t2,y).

A host of methods exist for coupling the various separation systems. In order to set up a switching network, the separation problem must be analysed and a valve configuration selected according to the solution. A review of commonly used switching networks is given by Ramsteiner (see Further Reading). These techniques only require minor modifications to existing equipment and, of equal importance, enable the sample preparation procedures to be completely automated.

For multidimensional chromatography a standard high pressure liquid chromatograph is used with the addition of one or more switching valves. These valves may be simple, manually operated six-, eight-or 10-port valves or may be automatically controlled. An eight-port valve with matching sample loops is typically used when the comprehensive mode of operation is utilized. When coupling two or more separation techniques online, not only has an interface to

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