Part of the data presented in Figure 6.15 and Table 6.5 concern
polyelectrolytes, but they were obtained at fairly high ionic strength. It may
be recalled thatcwould be much smaller at low ionic strength. Also the
slope forc>cin plots, as in Figure 6.15, tends to be somewhat higher at
low I. Altogether, the viscosity obtained at a certain polyelectrolyte
concentration is far higher at low than at high ionic strength.
Forc>c, the viscosity is stronglystrain rate thinning, far stronger
than in the dilute regime. This is illustrated in Figure 6.6 for xanthan
solutions. The lower concentration is just below, the higher one well above
c. It is seen that the apparent viscosity decreases by 3.5 orders of
magnitude over the range of shear rates applied. The explanation for this
decrease is somewhat related to the effects discussed in Section 6.2.2, but the
mechanism is a different one. Above the chain overlap concentration, the
polymer chains exhibit entanglements; Figure 6.16 illustrates this. The
smaller the correlation length, which implies the higher the polymer
concentration, the greater the number of entanglements per unit volume.
When applying a shear rate to the solutions, the shearing stress causes
disentangling. This is why the viscosity is so high: the disentangling requires
a relatively large amount of energy. If the polymer molecules become fully
disentangled, the viscosity will be very much smaller. However, Brownian
motion of the polymer chains causes new entanglements to form. The time
available for the formation of entanglements during shearing is roughly the
reciprocal of the shear rate. At very low shear rate, as many entanglements
are formed as are loosened per unit time, and the viscosity is Newtonian,
TABLE6.5 Viscosity of Polysaccharide SolutionsaPolysaccharidec*
g=100 mL slope
Xanthane 0.1 3.9
Na-alginatee 0.2 3.3
Locust bean gum 0.2 4.4
Guar gum 0.25 4.4
Pectine 0.3 3.3
l-carrageenane 0.4 3.3
Dextran (linear) 2.5 3.3
aThe critical concentrationc*for chain overlap and the slope of the
relation logðZsÞ 0 versus logcforc>c*. Actually, results vary among
samples and, for charged polysaccharides, with ionic strength. The
latter is fairly high (about 0.1 molar) for the data presented.
epolyelectrolyte.