space-filling, although fluctuating, network of polymer molecules, and
flocculation will not occur.
Also other species may cause depletion interaction. A case in point is
surfactant micelles; for example, if an emulsion has been made with an
unnecessary large concentration of surfactant, so that micelles remain after
emulsification, this may cause aggregation of the droplets. In foods,
however, the surfactant concentrations needed for depletion flocculation to
occur are generally unacceptable.
It may finally be noted that depletion flocculation of particles by a
soluble polymer is closely related tosegregative phase separationof two
soluble polymers—e.g., a protein and a polysaccharide—as described in
Section 6.5.2. It is therefore not surprising that emulsion droplets, covered
with a protein layer, can readily show depletion flocculation due to the
addition of a nonadsorbing polysaccharide.
Question
Assume that to a dispersion of spherical particles in water a given amount of a linear
dextran (see Table 6.1) is added to increase the viscosity. However, the addition of
the polymer also tends to cause depletion flocculation, which is undesirable. What
would be the best value of the molar massMof the polymer—large, small, or
indifferent—if flocculation is to be prevented, while the viscosity becomes as high as
possible?
Answer
Table 6.1 gives for the exponentain the Mark–Houwink equation (6.6) the value of
0.5. This means that intrinsic viscosity will be proportional toM0.5, and viscosity will
thus increase with increasingM. The question is now how the depletion interaction
Vdeplwill depend onM. The radius of gyrationrgis proportional toMn, according to
Eq. (6.4), and from Eq. (6.6) we derive thatn¼(aþ1)/3¼0.5. Using Eq. (12.12) for
h¼0, where the interaction is strongest, we see that the equation will then have a
factord^2 , which will be about equal tor^2 g!M^2 n¼M. We further have to know the
dependence ofPpolonM. In Section 6.2.1 it is shown that forn¼0.5, the solvent
quality parameterb¼0 (‘‘ideal behavior’’), which also means that the second virial
coefficientB¼0. This implies, in turn, thatP!M^1. Thus the value ofVdeplwill
be independent ofM. In conclusion, the molar mass of the dextran should be as large
as possible.
Note IfMis so small that Eq. (6.4) does not apply any more, the
reasoning given breaks down. Below a certain small value of Mno
depletion flocculation occurs.