Frans_M_Everaerts_Isotachophoresis_378342.pdf

MATHEMATICAL MODEL FOR THE STEADY STATE
presence of hydroxyl and hydrogen ions, was given by Brouwer and Postema 161. This
model describes the first stage in the Isotachophoretic separation, which is a movingboundary
system.
In Appendix A, a simplified model for moving-boundary electrophoresis is described,
for measuring the effective mobilities of strong electrolytes.
4.3. MATHEMATICAL MODEL FOR THE STEADY STATE IN ISOTACHOPHORESIS
4.3.1. Concept of isotachophoretic separation
In the previous section, the first stage of isotachophoretic separations was discussed.
The formation and migration of zones were described for the case when a stabilize<
electric current is passed across a zone boundary (see Fig.4.2) between a mixture of
anionic and cationic species on one side and a single electrolyte on the other side. In
general, r+ 1 zone boundaries will be obtained for the separation of anionic species
(see Fig.4.3).
No complete separation of the anionic species can be obtained in this way, however.
In the model discussed only those zone boundaries which are formed between the original
boundary and the anode were considered. Essentially, this means that the amount of the
mixture in the cathode compartment is taken to be unlimited (exhausting phenomena
being neglected), and no attention is paid to the influence of the counter ions. For an
isotachophoretic separation, however, a limited amount of sample ions is introduced
between a leading and a terminating electrolyte. The terminating ionic species can never
pass the sample ionic species as its effective mobility is chosen so as to be lower than
those of the sample ions, and hence all sample ionic species will migrate between the
terminating and leading anionic species.
In front of the original sample zone, a series of zones will be formed, as described in
the previous section, but behind the original sample zone a series of zones will now also
be formed, because sample anionic species also remain behind according to their lower
effective mobilities. The last zone formed will contain one anionic species of the sample,
viz., that with the lowest effective mobility of the sample. The last zone but one will
contain two anionic species of the sample with the lowest effective mobilities and each
subsequent zone contains one anionic species more of the sample, in accordance with
their increasing effective mobilities. Analogous to the formation of a series of mixed zones
in front of the original sample, a series of mixed zones will also be formed behind the
original sample, divided into two series of mixed zones.
If an adaptation in concentration according to Ohm’s law has taken place, the whole
system migrates through the capillary tube, during which the separation of the anionic
species continues until a steady state is reached, i.e., all anionic species of the sample
are separated and all sample zones contain only one anionic species of the sample. Only
in this instance can we speak of an isotachophoretic separation.
In Fig.4.6, a very simplified model for the formation of the zones for an isotacho-
phoretic separation of a five-component sample is shown. At zero times, a mixture of
Al . . . is introduced between A, and A,. After a certain time, two series of mixed
55