Theoretical and empirical approaches to express the mobility of small ions in capillary electrophoresis

A discussion is given about the concepts of the ion mobility, the analyte property which governs migration and thus separation selectivity in CE. It deals with small organic and inorganic ions, not with charged polymers or large particles like colloids. The discussion is directed to two main concepts. (i) The first is based on physico-chemistry of ion conductance in solution, and distinguishes three types of mobility. The absolute mobility is the limiting mobility at zero ionic strength; it depends on the solvent and the temperature. It is obtained by extrapolation of the actual mobilities, those of the fully charged particles at finite ion concentration. The observed reduction of the absolute mobility with ionic concentration is related to an ion cloud, and is formulated by the established theories of ion conductance. It explains the actual mobility as function of (beside other factors) the ionic strength, the viscosity and relative permittivity of the solvent, the temperature, the relaxation time of solvent polarisation and the distance of closest approach between ion and counterion. The effective mobility, finally, is the mobility when association and dissociation equilibria play a role. Most important are acid-base reactions, but complexation, ion pairing and homo- and heteroconjugation were considered as well. (ii) The second approach treats mobility data with different mathematical methods, and formulates their dependence on variables like solvent composition with appropriate algorithms. These empirical methods mainly include least squares and neural network-based methods. The least square methods ranges from the simplest model, which uses only the molecular weight of the analyte, to more complicated model requiring three-dimensional structural descriptors of the solutes. Neural networks have been applied to model the mobility using different input variables and various architectures. Work comparing the accuracy of least squares and neural network methods was discussed; the results showed that the neural network method leads to a more accurate mobility calculation. However, the least squares methods could give some information to the factors affecting the mobility of the analytes. The resulting methods allow the prediction of mobilities under different experimental conditions with certain accuracy. It has been shown that using such models, it is possible to predict mobility of analytes after training the models by a minimum number of data to speed up the method development stage.