Frans_M_Everaerts_Isotachophoresis_378342.pdf

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MATHEMATICAL MODEL FOR ISOTACHOPHORESIS
Fig.4.1. The original situation for the separation of anionic species. A mixture of anionic and
cationic species has been introduced between a leading electrolyte and a terminating electrolyte.
AL, leading anionic species; A, . . Ir sample anionic species; AT, terminating anionic species; BL,
buffering counter ionic species of the leading electrolyte; B, . . ,., counter ionic species of the sample;
BT, counter ionic species of the terminating electrolyte.
This regulating function prescribed that at any point the sum of concentrations divided
by the mobilities must be constant for all ionic species. In practice, all theoretical models,
which have been described in several papers, are essentially based on this principle,
although the situation is complicated by the use of different names and approaches. Also,
often no clear distinction has been made between the different performances of the
electrophoretic separations.
In this chapter, a theoretical model is described for isotachophoretic separations and
a number of experiments are described with which the model was verifie'd. A clear
distinction is made between the first stage of the separation by isotachophoresis, which
can be compared with moving-boundary electrophoresis, and isotachophoresis proper, i.e.,
at the steady state if all ionic species of the sample are separated.
For a model as general as possible, all substances will be regarded as amphiprotic
polyvalent molecules, so that the molecules can contain different chemical groups with
different chemical equilibrium constants. For such a molecule, the following equilibria
can be set up:
(In this model, only proton interactions are taken into account. Equilibria referring to other
dissociations, complex formation etc. are neglected.) The symbol A represents an anionic
species and the subscript r characterizes that anionic species. The superscript zA, indicates
the anionic form of the anionic species A,, i.e., it refers to the charge of that ion. The