Chapter 9
Polymer Phase Separation
9.1 Thermodynamics of Phase Separation
Phase separation is a spontaneous process for polymer chains to segregate from a
mixture into a more concentrated phase with clear boundaries. The decrease of the
system free energy after mixing two components leads to stable homogeneous
polymer mixture. The Flory-Huggins equation for the mixing free energy of
polymer-based mixtures shows that, the mixing entropy is always positive and
favors mixing. Therefore, the total mixing free energy is mainly determined by
the sign and magnitude of the mixing heat. For non-polar polymers, the mixing heat
is always positive, as described by (4.9) (the Scatchard-Hildebrand equation) in
Sect.4.2.1. The mixing heat can be so large that the polymer solution becomes
thermodynamically unstable, and spontaneously transforms into two coexisting
phases: a polymer-rich phase, and a polymer-poor phase.
The condition for a thermodynamic equilibrium between two coexisting phases is
the equivalence of chemical potentials with respect to each component. The mixing
free energy changes with concentrations in the homogeneous mixing states, as
illustrated in Fig.9.1a. Assuming a lattice polymer blend with the total volume
N¼r 1 N 1 þr 2 N 2 , where two polymers with separate molecular weightsr 1 andr 2
are blended with corresponding molecular numbersN 1 andN 2. The free energy
densityDfm¼DFm/N. If we draw a tangent line from a given point on the curve of
Dfmversus the volume fractionf 2 , its intercepts atf 2 ¼0andf 2 ¼1separately
correspond to the chemical potentialsDm 1 andDm 2 for two components, as defined by
Dm 1 @Dfm
@f 1(9.1)
Dm 2 @Dfm
@f 2(9.2)
W. Hu,Polymer Physics, DOI 10.1007/978-3-7091-0670-9_9,
#Springer-Verlag Wien 2013
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