Practical peak capacity

But Equation (7) defines a maximum theoretical peak capacity. "Practical" peak capacity values, related to the experimental separation of components in a mixture, are lower for several reasons. 

To minimize the multiple path and mass transfer contributions to plate height (equations 12.23 and 12.26), the packing material should be of as small a diameter as is practical and loaded with a thin film of stationary phase (equation 12.25). Compared with capillary columns, which are discussed in the next section, packed columns can handle larger amounts of sample. Samples of 0.1-10 )J,L are routinely analyzed with a packed column. Column efficiencies are typically several hundred to 2000 plates/m, providing columns with 3000-10,000 theoretical plates. Assuming Wiax/Wiin is approximately 50, a packed column with 10,000 theoretical plates has a peak capacity (equation 12.18) of... 

However, with practical samples the way the (k ) values of the individual components for any given complex solute mixture are distributed is not predictable, and will vary very significantly from mixture to mixture, depending on the nature of the sample. Nevertheless, although the values for the theoretical peak capacity of a column given by equation (26) can be used as a reasonable practical guide for comparing different columns, the theoretical values that are obtained will always be in excess of the peak capacities that are actually realized in practice. 

Although the ability to generate separation systems with significantly enhanced peak capacities is the most obvious practical usage of two-dimensional GC, there are several ancillary benefits which are often also achieved when analysis is performed using this approach. 

A practical method for enhancing the peak capacity, and thus the resolution of analytes in multicomponent complex mixtures, can be achieved by changing the mode of the separation during the chromatographic analysis, employing a column switching system in order to optimize a separation. 

A theoretical model whereby maximum peak capacity could be achieved by the use of 3-D planar chromatographic separation was proposed by Guiochon and coworkers (23-27). Unfortunately, until now, because of technical problems, this idea could not be realized in practice. Very recently, however, a special stationary phase, namely Empore silica TLC sheets, has now become available for realization of 3-D PC. This stationary phase, developed as a new separation medium for planar chromatography, contains silica entrapped in an inert matrix of polytetrafluoroethy-lene (PTFE) microfibrils. It has been established that the separating power is only ca. 60% of that of conventional TLC (28) this has been attributed to the very slow solvent migration velocity resulting from capillary action. 

When John Phillips, in 1991, presented the practical possibility of acquiring a real comprehensive two-dimensional gas chromatographic separation (33), the analytical chemists in the oil industry were quick to pounce upon this technique. Venkatramani and Phillips (34) subsequently indicated that GC X GC is a very powerful technique, which offers a very high peak capacity, and is therefore eminently suitable for analysing complex oil samples. These authors were able to count over 10 000 peaks in a GC X GC chromatogram of a kerosine. Blomberg, Beens and co-workers... 

Liu, Z., Patterson, D.G., Lee, M.L. (1995). Geometric approach to factor analysis for the estimation of orthogonality and practical peak capacity in comprehensive two-dimensional separations. Anal. Chem. 67, 3840-3845. 

This chapter examines another measure of the space used by 2D separations subject to correlation. Some researchers use the words, peak capacity, to express the maximum number of zones separable under specific experimental conditions, regardless of what fraction of the space is used. By definition, however, the peak capacity is the maximum number of separable zones in the entire space. No substantive reason exists to change this definition. The ability to use the space, however, depends on correlation. In deference to previous researchers (Liu et al., 1995 Gilar et al., 2005b), the author adopts the term, practical peak capacity, to describe the used space. The practical peak capacity is the peak capacity, when the separation mechanisms are orthogonal, but is less than the peak capacity when they are not. The subsequent discussion is based on practical peak capacity. 

The practical peak capacity of these spaces can be characterized by 2D statistical-overlap theory. Consider a relatively simple problem of probability. If, on average, m circles of diameter d() are distributed randomly in a large area A, then the average number p of clusters of isolated and overlapping circles approaches (Roach, 1968)... 

It is important to realize that statistical-overlap theory is not constrained by the contour of area A, which does not have to be rectangular as in earlier studies (in addition to previous references, see Davis, 1991 Martin, 1991,1992). In other words, Equations 3.2 and 3.3 should apply to the spaces WEG, FAN, and PAR. In this chapter, the number of clusters of randomly distributed circles in such areas is compared to the predictions of Equations 3.2 and 3.3a to assess the relationship between nP and practical peak capacity. Similarly, the number of peak maxima formed by randomly distributed bi-Gaussians in such areas is compared to the predictions of Equations 3.2 and 3.3b, and to Fig. 3.2, to make another assessment. 

The agreement provides the answer to the question posed earlier in the chapter a measure of practical peak capacity, as assessed by statistical-overlap theory, is nv... 

The author anticipates that many readers will find the results reported here to be commonplace. If so, then why do we so often report the individual peak capacities of the two dimensions and their product as the 2D peak capacity One answer—the conservative one—is that the latter is indeed the maximum number of peaks that can be separated, in agreement with the definition. A more realistic answer is that it is easy to do and appears more impressive than it really is—especially to those who fund our work. In fact, as a practical metric it is often nonsense. Because orthogonality is so difficult to achieve, especially in 2DLC, the peak capacity is a measure of only instrumental potential, not of separation potential, and consideration of... 

The aim of this chapter is to evaluate the orthogonality of selected 2DLC systems for the separation of peptides. The orthogonality of different chromatographic modes was quantitatively characterized using a novel geometric approach. Practical peak capacity was calculated from the theoretical peak capacity and the knowledge of... 

TABLE 12.2 Theoretical Peak Capacity, Orthogonality, and Practical Peak Capacity of Investigated 2DLC Setups. Second Dimension was in All Cases Carried Ont Using Cig Column and Typical LCMS Compatible Elution Conditions... 

As discussed above, in a typical proteomic experiment with a limited number of fractions collected, the practical peak capacity of 2DLC is well below 1000. This resolution is dramatically lower than the values considered in literature. 

The proposed estimate has several limitations. When taking into account the limited orthogonality of investigated 2DLC modes, the practical peak capacity is reduced approximately to half. It needs to be also emphasized that a full separation power of the first LC dimension is realized only when the number of collected fractions exceeds its peak capacity (Murphy et al., 1998). If the number of fractions analyzed is low, the achievable chromatographic peak capacity suffers. 

A comparison of theoretical and practical peak capacity values, summarized in Table 12.2, leads to a conclusion that even the most promising 2DLC setups do not provide for the peak capacity needed to fully resolve a complex proteomic sample. As a result, the eluent entering the MS source typically contains multiple coeluting peptides. 

MS maximum peak capacity, MS practical peak capacity, Number of MS/MS spectra Number of identified peptides (one precursor per second) (25% success rate, 63%... 

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