Peak capacity separation number

Since in TLC it appears more appropriate to define separation in space rather than in time as is usual in HPLC, the term separation number (peak capacity) SN was introduced (5,6). SN is defined as the number of fractions that can be accommodated over the available separation distance under the assumption that all fractions are regularly spaced and there is one available for each position. 

In their seminal work from 1983, Davis and Giddings used a statistical theory to define the number of peaks observable in 1DLC separation upon the injection of a sample of different complexity on a column of a given peak capacity (Davis and Giddings, 1983). The theory was later extended into 2D separation space (Davis, 2005 Shi and Davis, 1993), also discussed in Chapter 2 of this book. The theory implies that when the 1D or 2D separation space is randomly covered with the number of peaks equal to the separation space peak capacity (area), the normalized surface coverage is... 

A reduced peak capacity in one domain may be counterbalanced by an increased peak capacity in another domain. If we know the average peak width of a chromatographic separation and the gradient duration, we can calculate the maximum number of peaks that can be separated. (Note peak capacity does not mean that this number of compounds in a sample will be separated they may still co-elute). That means we can operate between two limits (1) a peak capacity of zero representing a flow injection analysis and (2) a minimal required peak capacity that defines the peak capacity to separate all compounds in a given mixture. Unfortunately, especially in the early stages of drug... 

A relatively new analytical separation technique known as Ultra Performance HPLC or Ultra Performance Liquid Chromatography (UPLC ) is similar in principle to HPLC except that it uses smaller particle sizes (<2.5 pm) and higher flow rates to increase the speed of separation and peak capacity, or number of peaks resolved per unit time in gradient separations (Swartz, 2005). UPLC was used to separate and quantify six major polyphenolic compounds in cocoa with a 50 mm by 2.1 mm column with a 1.7 pm particles size and a run time of only... 

Figure 2.26 Simulated chromatograms, generated with random numbers, representing a separation at peak capacity 41 and a sample with ten compounds.

The peak capacity of a column has been defined as the number of peaks that can be fitted into a chromatogram between the dead point and the last peak, with each peak being separated from its neighbor by 4a. The last peak of chromatogram is rather a... 

Giddings pointed out (32) that separated compounds must remain resolved throughout the whole process. This situation is illustrated in Figure 1.5, where two secondary columns are coupled to a primary column, and each secondary column is fed a fraction of duration Ar from the eluent from the first column. The peak capacity of the coupled system then depends on the plate number of each individual separation and on At. The primary column eliminates sample components that would otherwise interfere with the resolution of the components of interest in the secondary columns. An efficient primary separation may be wasted, however, if At is greater than the average peak width produced by the primary column, because of the recombination of resolved peaks after transfer into a secondary column. As At increases, the system approaches that of a tandem arrangement, and the resolution gained in one column may be nullified by the elution order in a subsequent column. 

LC-LC coupling systems are also employed to perform separations requiring very large plate numbers. However, it has been demonstrated (see equation (5.20) that for coupled columns peak capacity increases linearly with the square root of n... 

Figure 8.4 Schematic diagram of the peak capacity (n ) of a 2-D planar chromatograpliic system (i) the number of squares represents the number of compounds wliich can theoretically be separated.

Figure 8.14 Schematic diagram of the peak capacity of a 3-D r ) planar chromatograpMc system employing mobile phases of different composition the number of cubes represents the number of compounds which can theoretically be separated.

Another approach to defining the separation capacity of a column is by its peak capacity (the number of peaks than can be resolved at any specific resolution, usually R, i, in a given separation time). For SEC the pe2dc capacity, PCgc, is given approximately by... 

The separating power of a column can Ise expressed as its peak capacity defined as the number of peaks that can be resolved, at any specified resolution level, in a given separation time. For the general case it can be calculated using equation (1.49)... 

Therefore, a 4a separation (R = 1), in which peak retention times differ by four times the width at half-height, corresponds to a 2% area overlap between peaks.1 The maximum number of peaks that could be separated in a given time period assuming a given value of R, is defined as the peak capacity.1 The peak capacity must be greater — usually much greater — than the number of components in the mixture for a separation to succeed. The resolution of two compounds can also be written in terms of the number of plates of a column, N, the selectivity, a, and the capacity factors, k, and k j, as12... 

Resolution in capillary gel electrophoresis of DNA sequencing was shown to be directly proportional to the product of the number of bases and the relative peak distance, i.e., to the mean separation of peaks.43 Reformulation of the treatment of the capacity factor has been used to simplify and clarify the interpretation of the separation factor in electrophoresis.44 Peak... 

General applications While capillary separation methods produce peak capacities, n, numbered in hundreds, many real-world mixtures (e.g. in the petroleum industry) require values of 104. This can only... 

The challenge in effectively utilizing the multidimensional peak capacity is to find different types of columns that can uniformly spread the component peaks across the separation space. This challenge means that the separation mechanism of the two columns should be as dissimilar as possible or uncorrelated. A number of experimental studies have been undertaken to examine this effect (Liu et al., 1995 Slonecker et al., 1996 Gray et al., 2002). Chapter 3 examines the effect of correlation on peak capacity in detail using simulation techniques. 

Certainly two-dimensional techniques have far greater peak capacity than onedimensional techniques. However, the two-dimensional techniques don t utilize the separation space as efficiently as one-dimensional techniques do. These theories and simulations utilized circles as the basis function for a two-dimensional zone. This was later relaxed to an elliptical zone shape for a more realistic zone shape (Davis, 2005) with better understanding of the surrounding boundary effects. In addition, Oros and Davis (1992) showed how to use the two-dimensional statistical theory of spot overlap to estimate the number of component zones in a complex two-dimensional chromatogram. 

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 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... 

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