restrictions to volume changes, solvent (water) will be drawn to the region
close to the polyelectrolyte molecule, to even out the osmotic pressure
between that region and the salt solution farther away. It may be noted that
this provides an alternative explanation for the expansion of a
polyelectrolyte molecule at low ionic strength, as discussed in Section
6.3.2. In fact, treatment of polyelectrolyte conformation in terms of osmotic
pressure leads to the same results as that based on electrostatic repulsion,
discussed earlier. The two theories are equivalent.
Consequences. Due to the effect discussed in the previous
paragraph, it is difficult to remove specific ions from a polyelectrolyte. Of
course, the condition of electroneutrality implies that counterions must
always be present, in proportion to the valence of the polymer. They can be
exchanged by other ions, say Ca^2 þby Kþ. However, several ‘‘washings’’ are
needed: at high ionic strength because the ion concentration is high, at low
ionic strength because the volume containing counterions is large. This
means that usually several washings of the polyelectrolyte with a salt
solution of other composition would be needed.
Another consequence of the Donnan effect is that it is difficult, if not
impossible, to calculate ionic strength and composition of a solution of
polyelectrolytes and salts, especially if the polyelectrolyte concentration is
high. One should try to separate a portion of the salt solution from the
mixture, without applying a substantial chemical potential difference. This
can be done, for instance, by ultrafiltration. The ultrafiltrate then contains,
ideally, no polyelectrolyte, but all the salts. It can be chemically analyzed,
and from the result the ionic composition can be calculated (Section 2.3.3).
Note In the derivations given in this section we have assumed
complete dissociation of salt and identical ion activity coefficients
ðg+Þin both compartments. Complete dissociation may not occur
at high ionic strength; see Section 2.3.3. The second conditions will
not be met at very low ionic strength (I). The activity coefficients
will be different owing to the presence of the polyelectrolyte, which
has a very low mass concentration but a very high valence. Taking
the example in Table 6.2 form 2 ¼1 mmolar, Eq. (2.27) yields
I¼51 and 0.67 mmolar for compartments (1) and (2), respectively.
Equation (2.30) then gives for ðg+Þ^2 values of 0.7 and 0.96,
respectively. These complications materially affect the results. The
presence of small ions of higher valence further complicates the
theory.