2D retention maps

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. 

The previously mentioned methods for determining retention indices in the second GCxGC column (see Section 3.1.2) are based in the assignation of RI values to points in the two-dimensional retention map, and can be used in an inverse design to predict the peak coordinates of compounds of known retention indices in the 2D separation space, using experimental retention data for n-alkanes as references for the mapping process, or estimating these values from ID GC data. 

Moreover, the two procedures display different and complementary properties so that each of them is the method of choice to obtain specific information on the 2D separations. The SMO procedure is an unique tool to quantitatively estimate the degree of peak overlapping present in a map as well as to predict the influence of different experimental conditions on peak overlapping. The strength of the 2D autocovariance function method lies in its ability to simply single out ordered retention pattern hidden in the complex separation, which can be related to information on the chemical composition of the complex mixture. 

To study the influence of polymer structure, molar mass, and end groups on the performance of these polyesters, 2D LACCC-SEC separations were carried out. The contour map that is most useful for quantitative analysis and interpretation is reproduced in Plate 2. The ordinate is proportional to the LACCC retention of the polyester. Specific end groups of polyester model compounds are also shown as a guideline. These model compounds with various end group and polymer structure characteristics were run under identical conditions... 

In GCxGC, retention indices can be used as retention parameters derived from the retention times for both first and second dimensions CRI and RI) since two values instead of one are used for characterising the retention, their usefulness for qualitative purposes is markedly enhanced. In this case, the 2D separation space defined by and 1r is mapped by instead using LRI in the first dimension and RI in the second dimension. 

In both cases, the mapping of the 2D space using the n-alkanes allows an easy calculation of RI values for a compound. Figure 2 shows the position in the 2D space of a compound x (black circle), having and tRx as retention times, which elutes between the Cig and C17 curves. If isovolatility curves have been obtained by a mathematical fitting process, the equations involved can be used to estimate and at RI calculation from Equation (3) only requires, besides these values, the holdup time (see Section 3.3) in order to obtain the adjusted retention times. 

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