Observations on "orthogonality" in comprehensive two-dimensional separations

The concept and definition of orthogonality in the context of comprehensive two-dimensional (2D) separations are interesting topics of active discussion. Over the years, several approaches have been taken to quantify the degree of orthogonality, primarily to serve as a metric to optimize (and compare) comprehensive 2D separations. Recently, a mathematical function was reported that is qualitatively instructive for the purpose of providing such a metric. However, the mathematical function has some quantitative shortcomings. Herein, we both explore and partially correct this function. The orthogonality metric, referred to previously and herein as the orthogonality, 0, was mathematically related to the fraction of the 2D separation space occupied by compounds (i.e., fractional coverage) and the peak capacity, P, for one dimension of the 2D separation. The fractional coverage, f, is simply related to the percentage coverage, which is equal to 100%(f). Our main finding was that the values for O as a function of P for a given percentage coverage achieve a constant value at large P but deviate severely to lower O values at small P. For comprehensive 2D separations operated such that the second dimension is at small P, the findings we report have consequences for those who consider applying the O metric. Finally, it is discussed that the percentage coverage may be a better metric to gauge the extent to which the compounds in a given sample mixture have been disseminated in the 2D separation space.