Space, separation

The ability of a GC column to theoretically separate a multitude of components is normally defined by the capacity of the column. Component boiling point will be an initial property that determines relative component retention. Superimposed on this primary consideration is then the phase selectivity, which allows solutes of similar boiling point or volatility to be differentiated. In GC X GC, capacity is now defined in terms of the separation space available (11). As shown below, this space is an area determined by (a) the time of the modulation period (defined further below), which corresponds to an elution property on the second column, and (b) the elution time on the first column. In the normal experiment, the fast elution on the second column is conducted almost instantaneously, so will be essentially carried out under isothermal conditions, although the oven is temperature programmed. Thus, compounds will have an approximately constant peak width in the first dimension, but their widths in the second dimension will depend on how long they take to elute on the second column (isothermal conditions mean that later-eluting peaks on 2D are broader). In addition, peaks will have a variance (distribution) in each dimension depending on... 

The peaks are revealed in the 2D separation space as oval-shaped peaks in a contour plot format, reproduced as a schematic diagram in Figure 4.9. The contour-peaks are now completely separated in the 2D space, whereas they were severely overlapping on the first column. 

Figure 4.9 The peaks produced in the second dimension (see Figure 4.8) can be plotted as a contour shape in the retention or separation space, with characteristic retentions in each dimension. It can be seen that such peaks are now well resolved.

The ordering of classes of compounds within the separation space was summarized by Ledford et al. (33), who presented an analogy to the separation by using a mixture of objects of varied shapes, colours and sizes. The experimental dimensions could separate objects based on mechanisms which were sensitive to shape, size or colour, and the choice of two of these for the two-dimensional separation was illustrated. Applications showed a variety of petroleum products on different column sets, as well as a perfume sample. 

Figure 4.13 GC X GC analysis of vetiver essential oil column 1, BPX5 column 2, BPX50 (0.8 m in length). The lower trace presents the pulsed peaks obtained from the modulation process, and shows such peaks in a manner that represents the normal cliromatograpliic result presentation. Tliis nace is many times more sensitive than a normal GC trace. In the upper plot, the 2D separation space shows that the BPX50 column is not very effective in separating components of the oils based on polarity, since all the components are bunched up along the same region of 2D time.

In 1993, Jorgenson s group improved upon then earlier reverse phase HPLC-CZE system. Instead of the six-port valve, they used an eight-port electrically actuated valve that utilized two 10-p.L loops. While the effluent from the HPLC column filled one loop, the contents of the other loop were injected onto the CZE capillary. The entii e effluent from the HPLC column was collected and sampled by CZE, making this too a comprehensive technique, this time with enhanced resolving power. Having the two-loop valve made it possible to overlap the CZE runs. The total CZE run time was 15 s, with peaks occurring between 7.5 and 14.8 s. In order to save separation space, an injection was made into the CZE capillary every 7.5s,... 

For two-electron systems the basic idea of using different orbitals for different electrons goes back to Hylleraas (1929) and to Eckart (1930) who both used it in treating He. The method was thoroughly discussed at the Shelter Island Conference 1951 in treatments of He and H2 (Kotani 1951, Taylor and Parr 1952, Mulliken 1952), but the circumstances are here exceptionally simple because of the possibility of separating space and spin according to Eq. III. 1. 

An interesting special application has been proposed by Schlichthorl and Peter.31,41 It aims at deconvolution of electrochemical impedance data to separate space charge and surface capacitance contributions. The method relies on detection of the conductivity change in the semiconductor associated with the depletion of majority carriers in the space charge region via potential-modulated microwave reflectivity measurements. The electrode samples were n-Si(lll) in contact with fluoride solution. 

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. 

The idea here was to examine which pair of techniques and individual columns could lead to the best separations in 2DLC. This is achievable by using ID separations and then comparing how the retention of each component varies across the separation space. Another innovation here was the use of IT-derived metrics such as information entropy, informational similarity, and the synentropy. As stated in this paper, The informational similarity of 2D chromatographic systems, H is a measure of global... 

Davis and coworkers (1991, 1993) examined the ramifications of random zones placed in two-dimensional separation spaces. This work discovered that the peak capacity was not as efficiently utilized in two dimensions as opposed to onedimensional separations. Davis (1991) said... 

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. 

Davis (1993) extended the statistical overlap theory to generalized -dimensional separations with the consistent result that the separations get much better, but as dimensionality increases the efficiency of using that separation space decreases. For -dimensional separations, Davis says... 

Column Selection The selection of the two types of columns to be used is perhaps the most important consideration in 2DLC method development. This is driven by the need to have orthogonal dimensions for the solutes under investigation, otherwise the solutes will elute along the diagonal of the separation space, as discussed in Chapter 2. We have observed a number of 2DLC applications in the literature,... 

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. 

The description of the degree of retention data correlation is more complicated than it appears. For example, the 2D retention maps cannot be characterized by a simple correlation coefficient (Slonecker et al., 1996) since it fails to describe the datasets with apparent clustering (Fig. 12.2f). Several mathematical approaches have been developed to define the data spread in 2D separation space (Gray et al., 2002 Liu et al., 1995 Slonecker et al., 1996), but they are nonintuitive, complex, and use multiple descriptors to define the degree of orthogonality. 

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... 

Similar mathematical solution can be derived from a Poisson distribution of random events in 2D space. The probability that 2D separation space will be covered by peaks in ideally orthogonal separation is analogical to an example where balls are randomly thrown in 2D space divided into uniform bins. The general relationship between the number of events K (number of balls, peaks, etc.) and the number of bins occupied F (bins containing one or more balls, peaks, etc.) is described by Equation 12.3, where N is the number of available bins (peak capacity in 2DLC). 

Using Equation 12.5 one can describe the orthogonality of different 2DLC data shown in Fig. 12.2 with quantitative values. The data points of 196 tryptic peptides were projected in the normalized space divided into 14 x 14 bins (196 bins in total). Please note that regardless of the number of bins in the normalized separation space,... 

Total theoretical peak capacity for the ID and 2D LC/MS analyses of the yeast ribosomal protein sample was calculated as 240 and 700, respectively. Individual separation peak capacities were calculated by dividing the total separation time by the average peak width at baseline, and the 2D peak capacity determined as the product of the peak capacity of the two dimensions. These theoretical calculations rely on optimal use of the two-dimensional separation space, which in turn is dependent upon the lack of correlation between the component retention times in the two separation modes. Thus, the maximum use of the theoretical peak capacity is not only dependent on the selection of chromatographic modes based on different physicochemical... 

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