Polymerization-induced phase separation (PIPS) is the occurrence of phase separation in a multicomponent mixture induced by the polymerization of one or more components. The increase in molecular weight of the reactive component renders one or more components to be mutually immiscible in one another, resulting in spontaneous phase segregation.
Types Polymerization-induced phase separation can be initiated either through thermally induced polymerization or photopolymerization. The process generally occurs through spinodal decomposition, commonly resulting in the formation of co-continuous phases.
Thermodynamic Theory of Phase Separation in PIPS The process of polymerization-induced phase separation (PIPS) can be analyzed using classical polymer thermodynamics, most generally via the Flory-Huggins theory. This model provides a framework to quantify the balance between entropy and enthalpy during mixing. It illustrates how this balance changes during polymerization, potentially triggering spontaneous phase separation.
Flory-Huggins Lattice Model and Entropy of Mixing The Flory-Huggins theory considers a lattice model where each site is occupied by either species A or B (e.g., a polymer and a solvent). Assuming equal volume per lattice site, the entropy of mixing is derived from the number of distinct configurations of species on the lattice. For volume fractions ΦA and φB, the entropy of mixing per site is: Δ S mix = − k ( ϕ A N A ln ϕ A + ϕ B N B ln ϕ B ) {\displaystyle \Delta S_{\text{mix}}=-k\left({\frac {\phi _{A}}{N_{A}}}\ln \phi _{A}+{\frac {\phi _{B}}{N_{B}}}\ln \phi _{B}\right)} where:
ϕ A {\displaystyle \phi _{A}} and ϕ B {\displaystyle \phi _{B}} are the volume fractions of each component
N A {\displaystyle \mathbb {N} _{A}} and N B {\displaystyle \mathbb {N} _{B}} are the degrees of polymerization, or the number of monomer units per chain
k {\displaystyle k} is the Boltzmann constant.
As the polymer chains grow during polymerization, N increases, thus reducing the entropy of mixing. This is because the long polymer chains have fewer configurational possibilities compared to individual monomers, thereby reducing disorder, which can be intuitively understood by Figure 1.
Flory-Huggins Free Energy and the Onset of Phase Separation The total free energy change of mixing is given by:
Δ F m i x = Δ U m i x − T Δ S m i x {\displaystyle \Delta F_{mix}=\Delta U_{mix}-T\Delta S_{mix}} . In the Flory-Huggins framework, the enthalpic contribution is modeled using the Flory-Huggins interaction parameter χ {\displaystyle \chi } , yielding the total free energy per lattice site:
Δ F m i x = k T [ ϕ A N A ln ϕ A + ϕ B N B ln ( ϕ B + χ ϕ A ϕ B ) ] {\displaystyle \Delta F_{mix}=kT[{\frac {\phi _{A}}{N_{A}}}\ln \phi _{A}+{\frac {\phi _{B}}{N_{B}}}\ln(\phi _{B}+\chi \phi _{A}\phi _{B})]} where for polymer solutions, N A = N {\displaystyle N_{A}=N} and N B = 1 {\displaystyle N_{B}=1} resulting in the Flory-Huggins equation for polymer solutions:
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