Frans_M_Everaerts_Isotachophoresis_378342.pdf

56 MATHEMATICAL MODEL FOR ISOTACHOPHORESIS
zones are obtained. The original sample zone length has been shortened. The whole
system migrates between A, and A,, whereas the mixed zones elongate with time until
the anionic species of the sample are separated. The developed zones are shown that are
present in the narrow-bore tube at different times. As the amount of the sample is
limited, the sample anionic species Al and, for example, As will be separated completely
at a given moment. The two anionic species A, and A5 are separated completely if the
last ion of the ionic species with the highest effective mobility (Al) has overtaken the first
ion of the slowest ionic species (A5).
The length of the original sample zone is taken as Al and the length of the capillary tube
needed for a separation is I (the distance after which Al and AS are separated) (see
Fig.4.7). This means that the time needed for the separation of Al and A5 is obtained as
follows.
Distance covered by Al :
Eml t = li-Ai
Distance covered by A5 :
Em5 t=l
Thus :
A1 = Et (ml -m5)
or
Al
t= -
EAm
(4.24)
After this time 1, the anionic species A, and A5 are not present together in one mixed
zone. The time of separation depends on several factors (see eqn. 4.24) such as differences
in effective mobilities, the concentrations and the amount of the sample. At a certain
moment, each ion of the anionic species Al will have migrated from all other zones and can
be found only in its own zone Al . From this moment, this zone does not elongate further
with time. This procedure occurs for all ionic species and in Fig.4.6, for example, all
ionic species are separated except one mixed zone of A3 +Az at time t =7.
Fig.4.7. The last ion of the anionic species A, will have overtaken the fust ion of anionic species A,
in the original sample zone at point P. The separation time will be t = Al/E Am.