Increasing chromatographic resolution of analytical signals using derivative enhancement approach

A few decades ago, Giddings made a bleak statistical prediction stating that when using a chromatographic column with a peak capacity of n, one "has no real hope" of separating n compounds because of peak overlap. This statement holds true for today's far more complex separations including chiral, achiral or isotopic separations. Co-eluting chiral and isotopically labeled positional isomers pose a mass spectrometric challenge as isobaric analytes. Several advanced mathematical approaches exist to resolve and extract areas from overlapping data, such as Fourier self-deconvolution, wavelets, multivariate curve resolution, and iterative curve fitting. In this work, we develop a very straightforward approach to mathematically enhance signal resolution using the properties of derivatives while conserving peak area and its position. This technique is based on the fact that the area under a derivative of a distribution is equal to zero. Consequently, by alternately subtracting and adding multiples of even-derivatives (second, fourth, sixth, and so on) from the original peak, the area under a peak is conserved, and the bandwidth is reduced. Unlike multivariate curve resolution and iterative curve fitting approaches, this protocol does not require prior knowledge of the number of peaks. The concept is theoretically discussed for Gaussian and Lorentzian peaks. Several challenging chromatographic applications using deuterated benzenes, chiral separations, and biological applications are shown using twin-column recycling and conventional chromatography. The proposed protocol for a pair of overlapping peaks is currently limited to a R_s of 0.7 or greater with error < 1% under ideal conditions. Furthermore, tuning of peak shape by the first derivative is also described which can remove the exponential convolution of tailing peaks.