A nonlinear electrophoretic model for PeakMaster: I. Mathematical model

Abstract

We extended the linearized model of electromigration, which is used by PeakMaster, by calculation of nonlinear dispersion and diffusion of zones. The model results in the continuity equation for the shape function φ{symbol}(x,t) of the zone: φ{symbol}t = -(v0 + vEMDφ{symbol})φ{symbol}x + δφ{symbol}xx that contains linear (v0) and nonlinear migration (vEMD), diffusion (δ), and subscripts x and t stand for partial derivatives. It is valid for both analyte and system zones, and we present equations how to calculate characteristic zone parameters. We solved the continuity equation by Hopf-Cole transformation and applied it for two different initial conditions-the Dirac function resulting in the Haarhoff-van der Linde (HVL) function and the rectangular pulse function, which resulted in a function that we denote as the HVLR function. The nonlinear model was implemented in PeakMaster 5.3, which uses the HVLR function to predict the electropherogram for a given background electrolyte and a composition of the sample. HVLR function also enables to draw electropherograms with significantly wide injection zones, which was not possible before. The nonlinear model was tested by a comparison with a simulation by Simul 5, which solves the complete nonlinear model of electromigration numerically. © 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.