Peak capacity concept

In common with all multidimensional separations, two-dimensional GC has a requirement that target analytes are subjected to two or more mutually independent separation steps and that the components remain separated until completion of the overall procedure. Essentially, the effluent from a primary column is reanalysed by a second column of differing stationary phase selectivity. Since often enhancing the peak capacity of the analytical system is the main goal of the coupling, it is the relationship between the peak capacities of the individual dimensions that is crucial. Giddings (2) outlined the concepts of peak capacity product and it is this function that results in such powerful two-dimensional GC separations. 

It is this ordering that gave the concept a theoretical bent as real separations are not ordered the retention times in most separation techniques appear almost random across a range of separation time. The mathematical definition of peak capacity, nc, for an isocratic separation is given as (Grushka, 1970)... 

The concept of peak capacity is rather universal in instrumental analytical chemistry. For example, one can resolve components in time as in column chromatography or space, similar to the planar separation systems however, the concept transcends chromatography. Mass spectrometry, for example, a powerful detection method, which is often the detector of choice for complex samples after separation by chromatography, is a separation system itself. Mass spectrometry can separate samples in time when the mass filter is scanned, for example, when the mass-to-charge ratio is scanned in a quadrupole detector. The sample can also be separated in time with a time-of-flight (TOF) mass detector so that the arrival time is related to the mass-to-charge ratio. 

This concept assumes that each fraction (peak) collected in the first dimension further separates in the second dimension with regular spacing and that the entire 2D separation space is evenly covered by eluting peaks. More realistically, the peaks would be distributed randomly over the 2D separation space some peaks are likely to coelute, while some area will remain vacant of peaks. Therefore, Equationl2.1 represents an idealized peak capacity estimate although the real number of resolved peaks is lower. Most importantly, the peak capacity proposed by Equation 12.1 is achievable when the chromatographic modes used for separation are completely orthogonal. 

FIGURE 20 Chromatogram illustrating the concept of peak capacity (P) which is the maximum number of peaks that can be accommodated in a chromatogram. 

This chapter provides an overview of essential concepts in HPLC including retention, selectivity, efficiency, and resolution as well as their relationships with key column and mobile phase parameters such as particle size, column length and diameter, mobile phase strength, pH, and flow rate. The significance of several concepts important in pharmaceutical analysis such as peak capacity, gradient time, void volume, and limit of quantitation are discussed. 

In order to talk about fast gradient separations, we need to review the principles involved in measuring the performance of a gradient separation. We can use the concept of peak capacity to measure the separation power of a particular gradient on a given column. The peak capacity (P) is defined as follows ... 

For steady-state zones, where H and N also lack definition, we turned to the peak capacity as a common denominator for different methods. We have learned how to estimate peak capacity for ID separations we now extend this concept to incorporate two axes. For this we must reconsider the matter of spot dimensions when migration occurs along both axes rather than just one. 

Figure 1.10. A hypothetical separation illustrating the concept of peak capacity.

Concepts in gradient analysis (peak capacity, effects of flow rate, gradient time) and method orthogonality... 

The number of theoretical plates N, included in Equation (8), is a measure of column efficiency, which can be individually applied to the two columns of a GCxGC set. But in comprehensive GCxGC, the use of two columns having phases with different characteristics results in the redefinition of peak capacity, a 1 D GC efficiency concept. It also results in the introduction of two new concepts related to the separation behaviour, orthogonality and chromatographic structure, which are specific to GCxGC. These three concepts are discussed in Sections 4.2, 4.3, and 4.4, respectively. 

Figure 3, based in reference [48], shows how the concept of peak capacity in ID GC (gaussian peaks at the top row of the figure, where each cell of the row holds a resolved peak) can be extended to GCxGC. In the scheme, a cell in a row ( D) produces in D a column of cells that can also be occupied by peaks. 

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