Mixed gels - Physical Gels from Biological and Synthetic Polymers - page 289

Indeed miscibility remains an exception because of the high molecular mass of the
polymers, as explained above. Among polymer properties, the type of polymer, its
molecular mass, the presence of certain functional groups (e.g. ionized or hydrophobic
groups) and the ionic composition are all of crucial importance. The thermodynamics of
such mixtures, in particular the phase diagrams, plays a key role but in general is far from
suf final state of the systems for which they were designed. The

morphologies observed are never in equilibrium: the mechanisms of transport in systems
containing polymers are very slow, but during physical gelation of one of the constitu-
ents, phase separation becomes even slower and the structures that result are the result of
a process which is limited kinetically. This also occurs if one of the phases becomes
glassy, as discussed in Chapter 8 .
The theoretical background for phase separations, devised for small-molecule mix-
tures, was extended to polymer mixtures by the Flory

cient to predict the

Huggins lattice model. Physical
gelation has a profound effect on the kinetics of phase separation, and offers great
potential control of the phase morphology. In this chapter we

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first discuss the mecha-
nisms which affect the kinetics of phase separation, in particular those incipient stages
known to affect the morphologies of the mixture, i.e. nucleation and growth versus
spinodal decomposition, and their in

uence on structure. Next we consider the structure

and properties of mixed-gel systems, first where phase separation follows the usual routes

described here, then where more speci

c molecular interactions begin to in uence the

phase behaviour, as is the case in many polysaccharide polysaccharide mixtures. In the

latter case we give only selected examples, stressing those where research or applications
are of current interest.

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10.2 Equilibrium thermodynamics

The equilibrium thermodynamics of any mixture is determined by the free energy of
mixing (Gibbs energy) as a function of composition and temperature (Ragone, 1995 ),
and the phase diagram can be derived by minimizing the free energy function. The
simplest way to approach the problem is to consider a two-component (A and B) mixture:
at a given temperature, the minima of the free energy diagram de ne the limits of

coexistence of two phases. The locus of such points is the binodal curve, and the
symmetric form of Figure 10.1a is valid for simple mixtures or regular solutions. More
generally, the limit of solubility is determined by the common tangent to the free energy
curve as a function of composition (Cahn et al., 1991 ). The points below the curve of
Figure 10.1a are metastable to local fluctuations in concentration.

Gibbs derived a necessary condition for the stability or metastability of a

'
phase. He showed that a two-component solution will transform spontaneously if
ð∂

' 'fluid'

2 G

=∂

c 2

Þ T ; P 5 0 ;

where G is the Gibbs free energy per mole of solution and c is the
concentration at constant temperature T and pressure P. On a phase diagram, the
boundary of the unstable region is de

2 G

and is called
the spinodal. The spinodal and co-existence curves meet at a single point, the critical
point, and this de

nedbythelocus ð∂ =∂ c 2 Þ T ; P ¼ 0 ;

nes the limit temperature where phase separation takes place. For