Maria C. García-Alvarez-Coque Ernesto F. Simó-Alfonso José M. Sanchis-Mallols Juan J. Baeza-Baeza Department of Analytical Chemistry, University of Valencia, Burjassot, Spain A new mathematical function for describing electrophoretic peaks A new model is proposed for characterizing skewed electrophoretic peaks, which is a combination of leading and trailing edge functions, empirically modified to get a rapid recovery of the baseline. The peak model is a sum of square roots and is called thereby “combined square roots (CSR) model”. The flexibility of the model was checked on theoretical and experimental peaks with asymmetries in the range of 0–10 (expressed as the ratio of the distance between the center and the trailing edge, and the center and the leading edge of the chromatographic peak, measured at 10% of peak height). Excellent fits were found in all cases. The new model was compared with other three models that have shown good performance in modelling chromatographic peaks: the empirically transformed Gaussian, the parabolic Lorentzian-modified Gaussian, and the Haarhoff-van der Linde function. The latter model was proposed recently to describe electrophoretic peaks. The CSR model offered the highest flexibility to describe electrophoretic peak profiles, even those extremely asymmetrical with long tails. The new function has the advantage of using measurable parameters that allow the direct estimation of peak areas, which is useful for quantitative purposes. Keywords: Capillary electrophoresis / Electrophoretic peaks / Peak modelling DOI 10.1002/elps.200410370 1 Introduction 1.1 General aspects Tailing peaks, sometimes extremely deformed, are not rare in liquid chromatography and capillary electrophore- sis [1, 2]. In liquid chromatography, the observed asym- metry is produced by several factors, such as slow kinet- ics that gives rise to nonequilibrium interactions, the het- erogeneity of the stationary phase, column overload, and extra-column effects. In capillary electrophoresis, peak profiles depend on the physical-chemical processes inside the capillary, the heterogeneity of the capillary sur- face, capillary overload, solute mobility, and instrumental effects. The proposal of a flexible mathematical function to fit properly the peak shape is very convenient. The fitted curve should be useful for a quick acquisition of electro- phoretic information, noise filtering, deconvolution, and correction of baseline drift. The reliability of predictions of peak resolution depends also often in a good description of peak shape. The proposal of a single equation able to describe the electrophoretic signal is, however, not easy. Several mathematical functions that describe chromato- graphic peak shapes have been reported [2–12]. Most of them are, however, unable to fit elongated tailing peaks commonly observed in capillary electrophoresis. In this work, a flexible function able to cope with almost every peak asymmetry found in capillary electrophoresis is proposed. The function is a combination of square roots that describe the ascending and descending part of the peak. The flexibility of the model was evaluated on theoretical and experimental peaks with asymmetries in a wide range. The new model was compared with other three models that have shown good performance in the fitting of chromatographic and/or electrophoretic peaks: the empirically transformed Gaussian (ETG) [2], the para- bolic Lorentzian-modified Gaussian (PLMG) [11], and the Haarhoff-van der Linde (HVL) function [9, 12]. 1.2 Theory In the peak models described below, some common symbols are used in order to allow comparison between the different functions, as follows: time (t), signal height at time t (h), and several parameters related to peak position Correspondence: Prof. Juan J. Baeza-Baeza, Department of Analytical Chemistry, University of Valencia, c/Dr. Moliner SO, E-46100 Burjassot, Spain E-mail: Juan.Baeza@uv.es Fax: 134-96-354-4436 Abbreviations: CSR, combined square roots; ETG, empirically transformed Gaussian; HVL, Haarhoff-van der Linde; PLMG, parabolic Lorentzian-modified Gaussian; RE, relative fitting error 2076 Electrophoresis 2005, 26, 2076–2085  2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim