A hybrid of exponential and gaussian functions as a simple model of asymmetric chromatographic peaks

Abstract

A hybrid of exponential and Gaussian functions is developed as a model of asymmetric peak profiles. This exponential-Gaussian hybrid function (EGH) is mathematically simple, numerically stable, and its parameters are readily determined by making graphical measurements and applying simple equations. Furthermore, the statistical moments of the EGH function can be accurately approximated (within±0.15% error) at any level of asymmetry using formulae that are easily programmed into a computer. These features of the EGH make it very easy to implement by most chromatographers. The EGH serves as a useful alternative to the exponentially modified Gaussian (EMG) for modeling slightly asymmetric peaks since the two models produce nearly the same profile at relatively low asymmetries. The EGH also serves as an addition to the extensive list of alternative models that are sometimes better than the EMG at describing highly asymmetric peaks. A comparison between EMG and EGH curves at various asymmetries is made by analysis of toluene, phenylalanine, and pyridine on a reversed-phase liquid chromatographic system.