Frans_M_Everaerts_Isotachophoresis_378342.pdf

GENERAL EQUATIONS 43
anionic species A, has n A, pK values, ordered according to increasing pK values. The
particle A?*r, i.e., the ionic form with the highest charge ZA~ is taken as the
reference in all calculations.
Although the difference between anionic and cationic species disappears when this
notation is used, we still use the notation A and B for anionic and cationic species for
the sake of clarity and in order to reduce the number of indices used. Whether a particle
is an anion or a cation depends on its pK values and the pH in the zones.
The electrolyte system has to be chosen such that one of the ionic species acts as the
leading ionic species (anionic for the separation of anions) and another acts as a
buffering counter ion (cationic for the separation of anions) at the chosen pH. The way
in which an appropriate choice can be made will become clear in Chapter 5.
In section 4.2, the equations that describe the first stage in the separation, in fact a
kind of moving-boundary electrophoresis, are derived.
4.2. GENERAL EQUATIONS
For the derivation of the general equations in electrophoretic processes, we shall
consider the formation and movement of zone boundaries when an electric field is
applied over an existing zone boundary between two electrolyte solutions (see Fig.4.2).
On one side of the boundary, a mixture of several anionic and cationic species is
present, and on the other side a 'single electrolyte'. The anode is placed in the single
electrolyte. Only the migration of the anionic species is considered, and the effective
mobility of the anionic species of the single electrolyte is assumed to be higher than
that of any of the anionic species in the mixture. After some time, all of the anionic
species wd1 have the same counter ion B, because the cationic species B1 . . .r are moving
in the opposite direction. The anionic species migrate in the direction of the anode, which
results in a partial separation (moving-boundary electrophoresis). A number of boundaries
will be formed and a situation as shown in Fig.4.3 will be the result.
The anionic species Al, with the highest effective mobility in the mixture, has the
highest migration velocity and will be partially separated from the other anionic species.
It creates its own zone, Al, which becomes elongated in time. In the next zone, the
anionic species Az is separated from A3. . . in a similar way and, together with A1, it
forms the zone Al +Az. Each subsequent zone will contain one anionic species more
- -B
1.. .r
BL
0
'I.. .r-
m < m
A ~ . .r .
AL
Fig.4.2. A zone boundary between a mixture of several anionic and cationic species and a single
electrolyte.