Eigenmobilities in background electrolytes for capillary zone electrophoresis. I. System eigenpeaks and resonance in...

A background electrolyte system for capillary zone electrophoresis which is composed of three strong univalent ionic constituents is investigated. The ion 1 is considered as a counter-ion and two ions, 2 and 3, are considered as co-ions in relation to the analyte ion 4. We investigate the linearized model of electromigration in such a system and calculate the eigenvalues of a corresponding matrix. The model is formulated in such a way that the eigenvalues of the system are certain mobilities, which we call eigenmobilites, which characterize specific features of the electtrophoretic migration. One of the eigenmobilities is the system eigenmobility u(s) causing the rise of the system peak, called here the system eigenpeak. A situation when the analyte has the same mobility as the system eigenmobility, u(4) = u(s), is analyzed in detail. We show that it leads to the resonance-the mutual jump in the concentration profile of both co-ions, 2 and 3, has a shape of the spatial derivation of the originally sampled analyte profile and, moreover, it grows linearly with time. After a sufficiently long time it can be "amplified" to any value. The resonance has then a great impact on signals of indirect detection methods, like indirect UV detection or conductivity detection. In the framework of the linearized model the relative velocity slope S(x), a measure of electromigration dispersion, is expressed as S(x) = F(u(1) + u(4))(u(2) - u(4))(u(3) - u(4))/[u(4)(u(s) - u(4))], where u(i) is the mobility of the ith ion and F is the Faraday constant. As in practice the concentration of the analyte is not infinitely small and has a certain finite value, the analyte will be at the resonance severely dispersed to a much broader spatial interval. When a specific detector is used, the signal of such an analyte can apparently be missed without any notice.