Flory Huggins model

Mixture of polymers and solvents on a grid

The Flory-Huggins model describes the behavior of polymer solutions and was developed by Paul Flory and Maurice Loyal Huggins . It is a grid model .

Polymers dissolve in a solvent when this reduces the Gibbs energy of the system, i. i.e., the change in Gibbs energy (ΔG) is negative. The well-known Legendre transformation of the Gibbs-Helmholtz equation shows that ΔG is composed of the enthalpy of mixing (ΔH) and entropy of mixing (ΔS).

${\displaystyle \Delta G_{\text{mix}}=\Delta H_{\text{mix}}-T\cdot \Delta S_{\text{mix}}}$

If there were no interactions between the substances involved, there would be no enthalpy of mixing and the entropy of mixing would be ideal. The ideal entropy of mixing of several pure substances is always positive (the term - T · Δ S then negative) and Δ G would be negative for every mixing ratio. There would be complete miscibility. From this it follows that miscibility gaps must be explained with interactions between the components. In the case of a polymer solution, polymer-polymer, solvent-solvent and polymer-solvent interactions must be taken into account, as well as the changed entropy of a polymer solution, which is derived by a random walk . The resulting expression for the change in Gibbs energy is based on a term adapted for polymers for the ideal entropy of mixing and an interaction parameter which describes the sum of all interactions.

${\displaystyle {\frac {\Delta G_{\text{mix}}}{RT}}={\frac {\phi _{1}}{m}}_{1}\ln \phi _{1}+{\frac {\phi _{2}}{m}}_{2}\ln \phi _{2}+\chi \phi _{1}\phi _{2}}$

With

• ${\displaystyle R}$= universal gas constant
• ${\displaystyle m}$= Number of occupied lattice sites per molecule (for polymer solutions, m _{1 is} approximately the degree of polymerization and m ₂ = 1)
• ${\displaystyle \phi }$= Volume fraction of the polymer and the solvent
• ${\displaystyle \chi }$ = Interaction parameter

LCST or UCST behavior as a result of the temperature dependence of the interaction parameter

From the Flory-Huggins theory, for example, it follows that the UCST (if present) increases with increasing molar mass and at the same time shifts into the solvent-rich zone. Whether a polymer exhibits LCST and / or UCST behavior can be deduced from the temperature dependence of the interaction parameter (see figure). It should be noted that the interaction parameter contains not only enthalpic elements, but also the non-ideal entropy of mixing (e.g. the very strong hydrophobic effect in aqueous solution). Since the interaction parameter contains both enthalpic and entropic elements, which in turn are composed of many individual components, the classical Flory-Huggins theory makes it difficult to draw conclusions about the molecular cause of miscibility gaps.

Different Flory-Huggins mixing energies as a function of the volume fraction . The different mixing energies result from different interaction parameters . ${\displaystyle \phi }$ ${\displaystyle \chi }$

An extension of the Flory-Huggins model for polymer gels is the Flory-Rehner model .

See also

• Binodal
• Spinodal

Individual evidence

1. ^ Menno A. van Dijk, Andre Wakker: Concepts in Polymer Thermodynamics . CRC Press, 1998, ISBN 978-1-56676-623-4 , pp. 61–65 ( google.de [accessed November 26, 2019]).
2. ↑ Ronald Koningsveld, Walter H. Stockmayer, Erik Nies: Polymer Phase Diagrams . Oxford University Press, Oxford 2001, ISBN 978-0-19-855635-0 .
3. ^ Menno A. van Dijk, Andre Wakker: Concepts in Polymer Thermodynamics . CRC Press, 1998, ISBN 978-1-56676-623-4 , pp. 61–65 ( google.de [accessed November 26, 2019]).