A new measure of orthogonality for multi-dimensional chromatography

Multi-dimensional chromatographic techniques, such as (comprehensive) two-dimensional liquid chromatography and (comprehensive) two-dimensional gas chromatography, are increasingly popular for the analysis of complex samples, such as protein digests or mineral oils. The reason behind the popularity of these techniques is the superior performance, in terms of peak-production rate (peak capacity per unit time), that multi-dimensional separations offer compared to their one-dimensional counterparts. However, to fully utilize the potential of multi-dimensional chromatography it is essential that the separation mechanisms used in each dimension be independent of each other. In other words, the two separation mechanisms need to be orthogonal. A number of algorithms have been proposed in the literature for measuring chromatographic orthogonality. However, these methods have their limitations, such as reliance on the division of the separation space into bins, need for specialist software or requirement of advanced programming skills. In addition, some of the existing methods for measuring orthogonality include regions of the separation space that do not feature peaks. In this paper we introduce a number of equations which provides information on the spread of the peaks within the separation space in addition to measuring orthogonality, without the need for complex computations or division of the separation space into bins.