Frans_M_Everaerts_Isotachophoresis_378342.pdf

62 MATHEMATICAL MODEL FOR ISOTACHOPHORESIS
A similar expression can be obtained for the sample zone. Calling the right-hand side of
eqn. 4.38, QL and Q, for the leading and Vth zones, respectively, the function RFQ
defined as
must be zero according to eqn. 4.36.
4.3.3. Computer program for calculation of the steady state
4.3.3. I. Compu ration procedure
(4.39)
If all mobilities and pK values are known, and suitable values for the total composition
and pH of the leading electrolyte are chosen, the effective mobilities and the products of
the equilibrium equations (which are constant at a given pH) of both the leading ions and
the buffer ions in the leading zone can be calculated. From an equation similar to eqn.
4.27 9 ‘AL, zAL can be calculated from the total concentration, and with eqn. 4.26 all
partial ionic concentrations of the ionic species A, can be found. With eqn. 4.35, the
total buffer concentration in the leading zone can be obtained and with equations
similar to eqns. 4.26 and 4.27 the partial ionic concentrations of the buffer ions can be
found. Further, QL and the term on the left-hand side of the buffer eqn. 4.34 can be
obtained.
All parameters of the leading zone are now known. Assuming a certain pH for the
following zones, in a similar manner to that indicated for the leading zone, we can
obtain the effective mobilities and products of the equilibrium equations. With eqn. 4.34,
the total concentration of the buffer in the following zones can be found and with
eqns. 4.26 and 4.27 all other partial concentrations. With eqn. 4.35, the total concen-
tration of the sample anionic species in the zones can be obtained. With eqn. 4.38, QV
can be obtained and eqn. 4.39 gives the value of the function RFQ for the assumed pH.
This value must be zero for the correct pH,- In fact, several zero points will be possible,
and the method of finding the correct pH, zero points is dealt with in the next section.
4.3.3.2. Iteration procedure
As mentioned in section 4.3.2.5, the function RFQ must be zero for the correct pH,
value. For several cases this function is calculated as a function of the pH. In Fig.4.9,
the function is plotted for the separation of univalent cations and anions, the buffering
counter ions also being univalent.
In Fig.4.10, the function is plotted for polyvalent sample ionic species and buffer ions
and in Fig.4.11 the function is shown for a system in which, in the leading zone, the
leading ion acts as a buffer instead of the counter ions. Only in the sample zones do the
counter ions act as a buffer and in general this means that there is a large difference in
pH between pHL and pH,. This effect is used in disc electrophoresis according to
Ornstein [18] and Davis [7]. In Figs.4.9,4.10 and 4.1 1, anionic and cationic separations
are indicated by the symbols 8 and @, respectively. The functions are indicated by numbers