Mixed gels - Physical Gels from Biological and Synthetic Polymers - page 297

whether charged or uncharged. Another type of phase separation phenomenon is asso-
ciative phase separation or complexation. This occurs when interactions between the two
biopolymers are favoured (negative Flory parameter), for example when the polymers
carry opposite charges, for instance at a pH slightly lower than the isoelectric point of the
protein while the polysaccharide carries a negative charge. One example of this is the
mixture of milk proteins and carrageenans in certain food products.
Consequently the main parameters involved in the phase separation mechanism of
aqueous mixed polymer solutions are pH and ionic strength. During the past three
decades, a signi cant amount of work has been performed on the stability of polysac-

charide protein mixtures. These studies have contributed to an understanding of the

concentrations and conditions under which phase separation processes are expected to
occur. Substantial richness and complexity are introduced to the problem when there is
competition between phase separation and other processes, such as gelation. A similar
case was noted in Chapter 8 for gelation of synthetic polymer solutions via phase
transformations, either in organic solvents or in water. When competition between
phase separation and gelation occurs, stable but non-equilibrium morphologies can be
generated whose characteristics may be strongly dependent on the history of the sample.
The aim of such investigations is often to design systems with pre-speci

-

ed properties, of

value in particular applications, by varying phase morphology.

10.3.7 Rheology of mixed systems

As pointed out in earlier sections, segregative phase separation tends to produce a
structure with one phase dispersed in another. What are the rheological implications of
this? Of course work on the rheology of dispersed systems has a long and detailed history.
The use of fibre-reinforced polymeric materials, for example, has revolutionized modern

construction work. In evaluating the properties of such materials, a number of assump-
tions are made, at least initially. These include (1) that the structure remains constant;
(2) the so-called

, that the properties of a composite material can be
estimated from the volume fractions and, say, moduli of the two phases; and (3) that there
is perfect adhesion between the phases, so stress and strain are not disrupted across the
phase boundary.
Allowing for the above assumptions, observed values of elastic modulus can, in
principle, be compared with those calculated by a formula for composite systems such
as that proposed by Okano ( 1962 ), which in turn is a generalized form of Kerner

' rule of mixtures '

s
formula (Kerner, 1956 ). This was suggested by Watase and Nishinari ( 1980 ) for mixed
gels. There are a number of other models in the literature, but one simple but effective
approach is the so-called polymer blending law, proposed by Takayanagi et al.( 1963 ).
Although this treatment does not give the elastic modulus of the mixture for each
polymer volume fraction explicitly, it does give upper and lower bounds for the moduli
under so-called isostrain and isostress conditions, respectively:

'

G c ¼ x G x þ y G y upper bound ð Þ ð 10 : 7 Þ