Two-dimensional theory of peak overlap

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 

These are most important realizations that will guide the evolution of multiple dimension chromatographic systems and detectors for years to come. The exact quantitative nature of specific predictions is difficult because the implementation details of dimensions higher than 2DLC are largely unknown and may introduce chemical and physical constraints. Liu and Davis (2006) have recently extended the statistical overlap theory in two dimensions to highly saturated separations where more severe overlap is found. This paper also lists most of the papers that have been written on the statistical theory of multidimensional separations. 

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