If the magnitude ofIis around 0.1 molar, asalted brushcan be
obtained. Due to the Donnan effect, discussed in Section 6.3.3, the
concentration of ions in the brush is high. An important parameter
determining the thickness of the brush then isðs=b^2 chÞ. If its magnitude is
below a critical value, the brush collapses, implying that steric repulsion will
be small. Although the magnitude of the critical value cannot be easily
predicted—it depends, e.g., onI, chain length, and solvent quality—the
effects of charge and number density are clear. For adsorbed polyelec-
trolytes, the magnitude ofswould decrease with increasing solvent quality;
smay also depend on polymer concentration. In most situations in foods,
polyelectrolyte layers will be salted brushes, providing strong ‘‘electrosteric’’
repulsion.
If ionic strength is still smaller, say<0.01 molar, anosmotic brush
would be obtained. Considering for the moment a polyacid, with carboxyl
groups providing the charges, the ions in the brush will be largely restricted
to cations, including protons. It turns out that the degree of dissociation of
the carboxyl groups now greatly depends on ionic strength. The smallerI,
the higher the effective isoelectric pH. This may mean a decreased charge
density, hence decreased repulsion.
Proteins. As an illustrative example, we will briefly discuss some
aspects of the colloidal stability ofcasein micelles. These are proteinaceous
particles to be found in milk, with mean diameter about 120 nm. They
consist predominantly of caseins, calcium phosphate, and water. One of the
caseins present, calledk-casein, has a very hydrophilic C-terminal part of 64
amino acid residues, containing some acidic sugar groups, net charge9to
12.k-casein is at the outside of the micelles, and the C-terminals stick out
into the solvent, forming a ‘‘hairy’’ layer. The value ofsis about 0.03 nm^2 ;
at the ionic strength (75 mmolar) and pH (6.7) of milk, the layer thickness is
d&7 nm. It may be considered as a salted brush of grafted polymer chains.
It provides complete stability against aggregation of the casein micelles. The
van der Waals attraction between the micelles is not strong, because the
particles are fairly small and consist for the most part of water, which
implies that the Hamaker constant is small.
These particles can be induced toaggregateby various means. One is
renneting: the rennet added contains chymosin, a proteolytic enzyme, that
specifically cleavesk-casein, causing its C-terminal end to be split off and
going into solution. Whenshas been reduced to about 30%of its original
value, the particles start to aggregate, and aggregation rate increases assis
further reduced. (There is no clear evidence of collapse of the brush at a
certain stage: it just disappears.) A second cause of casein micelle
aggregation is lowering of the pH. Below a pH of about 5, the net charge