Exploratory analysis in chromatography

There are different ways in which LC or GC analysis can lead to three-way data. These were already briefly described in the introduction. If chromatographic measurements are performed on different stationary phases, at different mobile phase compositions for different solutes (chemicals), then a three-way array of retention factors (or of peak-widths, asymmetry factors etc.) is generated. Such arrays can be studied to explore the differences and similarities between stationary phases and/or solutes. 

An example will be given on the use of three-way models to explore chromatographic data. The data have the structure of stationary phases x mobile phases x solutes and the purpose of the analysis is to understand the differences between different stationary phases and 

This resulted in a three-way array X (6 x 6 x 8) of retention factors with mode one holding the stationary phase, mode two the mobile phase and mode three the solutes. The purpose of the analysis was two-fold (i) to investigate the differences between the types of stationary-phase material and (ii) to develop a calibration model for transfer of retention factors from one stationary phase to another one. Only the first part of the investigations will be discussed. 

There is a priori knowledge about this data set. The main source of variation between the stationary phases is due to differences in hydrophobicity. The C18 phase is the most hydrophobic one whereas the CN and phenyl phases are the least hydrophobic. The C6 and C8 phases are slightly less hydrophobic than the C18 phase and the Cl phase takes an intermediate position between C18 and CN. There may also be differences in selectivity2 between the types of stationary phases. Chemically, C6 and C8 are similar, but C6 and CN are quite different and may show a different selectivity. The column packings may also differ in efficiency, i.e. yield different peak widths, but this is not reflected in a retention factor. Hence, two sources of variation are expected between the stationary phases. 

For reasons to be explained below, all retention factors k were transformed logarithmically to In k. Due to the design used, it is possible to check for nonlinear mixing behavior of the mobile phase, i.e. nonlinear variation of In k with composition. Such behavior is indeed present the mean In k of toluene on Cl at mobile phase wml and wal is 1.38, corresponding to a k value of 3.98. The In k value of toluene on Cl at mobile phase ami (the 0.5 0.5 mixture of wml and wal) is 1.10, corresponding to a k value of 3.01. This is a clear difference, which indicates that nonlinearities are present. Hence, there are at least three sources of variation in the mobile-phase mode the relative amounts of the two organic modifiers and nonlinear mixing behavior. 

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