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the salt counter ions on the surface; and the steric factor () which is the
number of adsorption sites sterically shielded by the adsorbed molecule. The
single component SMA isotherm (40) is
( )( Q
C =
K
C salt
− + Q
)
(1)
where Q and C are the solute concentrations on the stationary and mobile phases,
respectively. C salt is the mobile phase salt concentration and (see Note 2)
is the total ionic capacity of the stationary phase represented. Two approaches
are available to determine and K.
In the first method, isocratic experiments at different mobile phase salt
concentrations are carried out, and the retention times of the proteins or
displacers at these different salt concentrations are recorded. The following
Eq. 2 (41) can then be solved to obtain the linear SMA parameters:
log k ′ = logK − log C salt (2)
where k ′ is the capacity factor and is the phase ratio. Thus, a plot of log
k ′ versus log C salt yields a straight line with a slope of and an intercept of
log(K ).
Alternatively, in the second method, gradient experiments may be used
to obtain the linear parameters. This approach can enable the simultaneous
determination of linear SMA parameters for all components of the feed mixture.
In addition, this technique is more suitable for displacers, as they will have a
high affinity for the stationary phase. Once the retention volumes are obtained,
using at least two different gradient conditions, the values are substituted into
the following equation to solve for the linear parameters (42):
V g =
[ (
x +1
i
+ V )
0K + 1x f − x i
1
]
+1
− x
V i
G
V G
x f − x i
(3)
where V g is the solute retention volume, x i and x f are the initial and final salt
concentrations respectively, V G is the total gradient volume, V 0 is the dead
volume and = 1/ + 1 is the column porosity.
The non-linear parameter, , for displacers or proteins can be determined by
non-linear frontal experiments with the displacer or protein at very low mobile
phase salt concentrations. These experiments can also provide an independent
measure for the characteristic charge in addition to the steric factor (41). The
ratio of the magnitudes of the induced salt gradient to the concentration of the
displacer (d)/protein (p) in the front gives the value of the characteristic charge.
v =
C salt
C displacer/protein
(4)