radius of gyration thus is relatively large. If the molecule is not very long, it
will attain an almost rodlike conformation at very low ionic strength. The
conformation will also depend on thelinear charge density. This is inversely
proportional to the mutual distancebch between charged groups, where
hbchi¼nL=jzj. The extent of expansion of the polyelectrolyte molecule
increases with decrease of the productk 6 bch.
Quantitative theory for the volume occupied by a polyelectrolyte
molecule is available, but it will not be discussed here; there are too many
complications for most of the natural polyelectrolytes. Nevertheless, the
semiquantitative reasoning given provides important understanding. Quite
in general, the presence of charges makes the molecule muchstiffer; cf.
Section 6.2.1, complication 1. Moreover, it causes the volume exclusion
parameterbto be higher (cf. complication 2), or in other words, the solvent
quality is effectively enhanced. The negatively charged polysaccharides, such
as carrageenans, alginates, and xanthan, are all rather stiff and expanded
molecules (unless the ionic strength is high), the powerain Eq. (6.6)
generally being close to unity.
Viscosity. The effects of charge (degree of dissociation) and ionic
strength on expansion (radius of gyration) of polyelectrolytes are, of course,
reflected in the extent by which they increase viscosity. Figure 6.10 gives an
example. It is seen that a higher degree of dissociation and a lower salt
concentration both yield a higher intrinsic viscosity, as expected. However,
it is also seen that at largea;½Zdecreases again, at least at low salt
concentration. This may be explained partly by the contribution of the
polyelectrolyte to the ionic strength. At highz, i.e., higha, this contribution
is considerable, as was discussed in Section 6.3.1, Consequence 3. This
means that an increase inaleads to an appreciable increase in ionic strength,
and at low salt concentration this is sufficient to decrease the radius of
gyration of the molecule and thereby½Z. If the ionic strength is kept
constant at highz, the anomaly is much smaller. Figure 6.11 further
illustrates the effect of ionic strength on intrinsic viscosity of a polyacid.
Notice that the exponent a markedly increases with decreasing ionic
strength, leading to very high intrinsic viscosities.
It can be concluded that charged polysaccharides can be very effective
thickening agents, but that the viscosity of such solutions strongly decreases
with increasing ionic strengthI. At very high salt concentration, charged
polysaccharides behave virtually like neutral polymers.
The kind of counterions present may also affect polyelectrolyte
conformation. At very high salt concentration, part of the ionized groups on
the polymer will become neutralized (due to ion pair formation), causing a
more compact conformation. This depends somewhat on the kind of