6.4.3 Viscosity
Polymeric thickening agents used in foods typically are well soluble
polysaccharides, with an excluded volume parameterbclearly above zero.
This implies that especially the dilute and semidilute regimes are often of
importance. Viscosity of very dilute solutions has been discussed in Sections
6.2.2 and 6.3.2. For higher concentrations, the reduced viscosityðZsp=cÞis
higher, as is true for any system (see Figure 5.5), but for polymer solutions
the viscosity increases far stronger with concentration as soon as the chain
overlap concentration is reached.
It has been shown (and made plausible from theory) that a general
relation exists between relative or specific viscosity at very low shear rate
and dimensionless concentration of polymerc½Z 0. This relation is shown in
Figure 6.15 as a log–log plot. Thecritical concentration for chain overlap c
would equal about 4=½Z 0 ; at that concentration,ðZspÞ 0 &10 orZ& 11 Zs(at
very low shear rate).cis mostly expressed in g=100 mL. It may not exactly
correspond to the critical volume fractionjov given by Eq. (6.13). Most
workers usec*, as determined from the break in a log–log plot of specific
viscosity versus concentration.
Note For several polymers, there is a limited concentration region
where the slope gradually changes from small to large and one takes
as the critical concentration that where the steepest slope begins,
often denotedc*. Possibly, the concentrated regime then has been
reached.
For c<c, the slope is 1.2–1.4, i.e., not unity, which would be
expected for dilute solutions. A reason for the discrepancy may be that most
polysaccharides are so stiff that (part of) the molecules are already
somewhat rodlike; they may then already hinder each other in a shear
flow at concentrations well belowjov. Abovec, the slope is close to 3.3 for
most polysaccharides. Galactomannans (guar and locust bean gums) show a
steeper slope, about 4.4. This is supposed to be due to specific attractive
interactions between side groups on the polymer chains. Some further data
are in Table 6.5. Remember that these relations only apply at extremely
small shear rates. At higher shear rates,cremains about the same, but the
slope abovec*is far smaller, e.g., about 2. A steep slope of logðZ=Zs 1 Þ 0
versus logcalso means a very strong dependence of viscosity on molar mass
Mof the polymer. In the ‘‘semidilute’’ regime,ðZ=Zs 1 Þis approximately
proportional toM^3 :^4 , at constant mass concentration. This relation is far
from exact, but the strong dependence ofZonM, much stronger than in the
dilute regime, is unmistakable.