Physical Chemistry of Foods

force will act. The repulsive free energy is very large: several timeskBTfor
each polymer chain involved, and the number of polymer molecules in the
gap between two particles will often be of order 10^3. This means that at very
close approach—roughly speaking forh<d—the repulsive energy between
the particles will always be positive and large; it increases very steeply with
decreasing value ofh.
However, when two particles approach each other,mixingof both
polymer layers will occur forh< 2 d, i.e., before volume restriction comes
into play. This means that the mixing entropy will decrease, and this then
would also lead to repulsion. It mostly does, but not always, since it depends
on thesolvent qualityfor the polymer chains. If the quality is fairly low, just
high enough to allow the chains to protrude into the liquid, the attractive
energy between polymer segments may be large enough to more than
compensate for the decrease in mixing entropy, thereby causing attraction.
Another way to explain these mechanisms is by considering the
osmotic pressurein the liquid between approaching particles. If the pressure
increases in the gap between the particles, solvent will be drawn into the gap
to lower the osmotic pressure again, hence there will be repulsion. Recalling
the equation for the osmotic pressurePpolof a polymer solution in Section
6.4.1,

Ppol¼RT

1

vp

jþ

b

2 vs

j^2 þ

1

3 vs

j^3 þ



ð 12 : 11 Þ

wherejis the net polymer volume fraction andvthe molar volume for
polymer (p) and solvent (s);bmeasures the solvent quality, which is ‘‘ideal’’
forb¼0 (i.e., a theta solvent), and poor forb<0. The values ofjcan
become very high in the gap between approaching particles; say, 0.02 if
h¼ 2 dand 0.4 ath¼d. We can in principle use Eq. (12.11) to explain the
repulsion between the particles. The first term between brackets does not
apply: it stands for the number of species per unit volume, and in the present
case we have only two species, i.e., the pair of particles. The third term can
be interpreted as being due to volume restriction; it is seen to be always
positive and it strongly increases with polymer concentration, i.e., for a
closer approach. The second term is governed by the value ofb; if the latter
is significantly negative, attraction between polymer chains occurs, and this
may result in attraction between particles.
The conformations of the molecules in the polymer layer and the
resulting steric interaction energy can be calculated by means of a numerical
self-consistent field model. The free energy of the polymer layers then is
minimized by considering all possible conformations (including adsorbed
segments) of the chains. We will not discuss the theory because it can rarely