Parabolic-Lorentzian modified Gaussian model for describing and deconvolving chromatographic peaks

A new mathematical model for characterising skewed chromatographic peaks, which improves the previously reported polynomially modified Gaussian (PMG) model, is proposed. The model is a Gaussian based equation whose variance is a combined parabolic-Lorentzian function. The parabola accounts for the non-Gaussian shaped peak, whereas the Lorentzian function cancels the variance growth out of the elution region, which gives rise to a problematic baseline increase in the PMG model. The proposed parabolic-Lorentzian modified Gaussian (PLMG) model makes a correct description of peaks showing a wide range of asymmetry with positive and/or negative skewness. The new model is shown to give better fittings than other models as the Li, log-normal or Pap-Pápai models, which have a different mathematical basis. The model parameters are also related to peak properties as the skewness and kurtosis. The PLMG model is applied to the deconvolution of peaks in binary mixtures of structurally related compounds that are highly overlapped (retention times in min): oxytetracycline (9.00)--tetracycline (10.20), sulfathiazole (3.67)--sulfachloropyridazine (3.93), and sulfisoxazole (5.14)--sulfapyridine (5.24). The use of non-linear least-squares calibration in combination with the PLMG model gave superior results than the classical multiple linear least-squares and partial least-squares regressions. The proposed method takes into account run to run changes in retention time that occur along the injection of standards and samples, and the possible interactions that exist between the coeluting compounds. This decreases significantly the quantitation errors.