Predicting peak shape in capillary zone electrophoresis: a generic approach to parametrizing peaks using the Haarhoff-Van der Linde (HVL) function

We have found that the Haarhoff−Van der Linde (HVL) peak function provides excellent fitting to the shapes of CZE peaks. Initially designed for overloaded peaks in gas chromatography, this function describes a Gaussian peak when there is no peak distortion, and a triangular peak when there is no diffusional peak broadening. As such, it is ideal for CZE peaks distorted by electromigration dispersion (EMD). Fitting peaks with this function gives four parameters: three of them can be related to the Gaussian peak that would have been obtained in case of no EMD; the last one is a measure of the peak distortion. Using moving boundary theory, this peak distortion parameter may readily be expressed in terms of analyte and background electrolyte mobilities and concentrations, electric field, and sample injection length. The variance of an HVL peak is shown to be described by a universal function, and a master equation is presented. The region where EMD adds less than 10% to the Gaussian variance is shown to be very narrowly spread around the mobility matching condition. Under typical CZE operating conditions with an analyte at 1% of the BGE concentration, significant peak distortion is always present. Because the total peak variance is not an addition of the Gaussian and triangular contributions, the HVL model and the methodology introduced here should always be used to correctly combine variances.