If the curvature of the free energy curve opens to the upside, for instance, the
metastable regions between A and C points and between B and D points shown in
Fig.9.1b, the minute concentration fluctuation will not lead to phase separation, as
illustrated in Fig.9.4b. In this case,
@^2 Dfm
@f^2¼
@m
@f> 0 (9.20)
Fig. 9.5 Illustration of binodal and spinodal phase diagrams of the binary mixing systems. The
regions separated by these curves correspond to two different mechanism NG (nucleation and
growth) and SD (spinodal decomposition) for phase separation
Fig. 9.4 Illustration of mixing free energy changing with the local fluctuations of polymer volume
fractions. (a) The curvature opens to the downside, so fluctuations make lower free energy; (b) the
curvature opens to the upside, so fluctuations make higher free energy
172 9 Polymer Phase Separation