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Fig. 3.58  Phase diagram
for a gelling system that can
exist in two states: one-phase
sol and two-phase gel . Gel is
not formed below the critical
concentration x 0
of two homogenous macroscopic phases. In gel, the phase-separated state is micro-
scopically heterogeneous. That is, the solvent-rich phase forms microdroplets inside
the polymer-rich phase. The process of approaching equilibrium in the two-phase
gels is extremely slow so that for all practical purposes such gels are fundamentally
nonequilibrium systems similar to glasses. For this reason, the gel state and struc-
ture depend significantly on the thermal history of its formation. This feature of gels
reveals itself vividly in the gel melting kinetics discussed in Sect. 3.10.3.
Gels cannot form when the concentration of a solution is below some critical
value, x 0 (Fig. 3.58 ). If a solution has lower concentration, cooling it below the
equilibrium temperature results in demixing of the solution without gelation.
Some gelling systems may demonstrate a more complex phase behavior
(Fig. 3.59 ). An example is a solution of atactic PS in carbon disulfide [ 154 ]. Below
Fig. 3.59  Phase diagram
for a gelling system that
can form an equilibrium
one-phase gel
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