Physical Chemistry of Foods

molar concentration then is negligible. Consequently,bcrwill be very close
to zero for highq, as observed. However, on precipitation of the polymer, it
would loseconformational entropy, by a very large amount (see Section 6.1).
This implies that precipitation will not occur, unlessbis very small (near or
below -1). Instead, phase separation occurs: the solution separates into one
with a low and one with a high concentration of polymer. In both phases,
the conformational entropy still is large. The highly concentrated, and
thereby viscoelastic, polymer solution is often called acoacervate.
The phenomena involved are further illustrated in Figure 6.17 for
simple homopolymers, calculated according to Flory–Huggins theory. It
gives phase diagrams in thebjdomain, for some values ofq. An example
of phase separation is depicted for a polymer–solvent mixture ofq¼100,
j¼ 0 :1, andb¼ 0 :525. What will occur at equilibrium is a separation into
phases A and B, containing a volume fraction of polymer of 10^4 and 0.5,
respectively. The ratio of the volumes of A over B is given by
ð 0 : 5  0 : 1 Þ=ð 0 : 1  10 ^4 Þ¼4, i.e., the (very) dilute part makes up 80%, the
concentrated part 20%. It is also seen that at larger, i.e., more ‘‘normal,’’
values ofq, the low-concentration phase is extremely dilute, almost pure
water. The few polymer molecules in the dilute phase are called collapsed
coils, meaning that they have a relatively small radius of gyration. The
exponentnin Eq. (6.4) is< 0 :5, approaching the minimum value of 1/3.
Ifbis small (highly negative), the high concentration phase is very
concentrated. In such a phase, i.e., in the regime called ‘‘concentrated’’ in
Figure 6.13, other relations hold than in the dilute or ‘‘semidilute’’ regimes.
The correlation length is inversely proportional toj. The viscosity is not
proportional to that of the solvent, but the system behaves like a polymer
melt, containing water as a plasticizer. The viscosity is extremely large for
low water content (small 1j).
Figure 6.17 shows two kinds of curves, ‘‘binodals’’ and one example of
a‘‘spinodal.’’ The binodal is the curve forDGmix¼0, and below that curve
the solution is supersaturated. This does not necessarily mean that phase
separation occurs. The spinodal curve, given by ðq^2 DGmix=q 2 jÞT;p¼0,
bounds a regime in which phase separation is spontaneous. Here, any
thermal fluctuation in the system will lead to the formation of regions of
different composition, which means phase separation. In the regime between
the binodal and the spinodal curves, phase separation depends on a
mechanism of nucleation and growth of a phase. This is discussed in Section
14.2.3; see especially Figure 14.8. The system is thus metastable, and it may
take a long time before phase separation occurs, especially if the initialjis
high (very high viscosity).
According to theory, the solubility will increase if temperature is
increased. The larger value ofTDd!uSmeans thatDHhas to be more