Phase diagrams for systems containing hyperbranched polymers

Sabine Enders*, Kai Langenbach, Philipp Schrader, Tim Zeiner

*Corresponding author for this work

Research output: Contribution to journalReview articlepeer-review


Hyperbranched polymers show an outstanding potential for applications ranging from chemistry over nanotechnology to pharmacy. In order to take advantage of this potential, the underlying phase behaviour must be known. From the thermodynamic point of view, the modelling of these phase diagrams is quite challenging, because the thermodynamic properties depend on the architecture of the hyperbranched polymer as well as on the number and kind of present functional end groups. The influence of architecture can be taken into account via the lattice cluster theory (LCT) as an extension of the well-known Flory-Huggins theory. Whereas the Flory-Huggins theory is limited to linear polymer chains, the LCT can be applied to an arbitrary chain architecture. The number and the kind of functional groups can be handled via the Wertheim perturbation theory, applicable for directed forces between the functional groups and the surrounding solvent molecules. The combination of the LCT and the Wertheim theory can be established for the modelling or even prediction of the liquid-liquid equilibria (LLE) of polymer solutions in a single solvent or in a solvent mixture or polymer blends, where the polymer can have an arbitrary structure. The applied theory predicts large demixing regions for mixtures of linear polymers and hyperbranched polymers, as well as for mixtures made from two hyperbranched polymers. The introduction of empty lattice sites permits the theoretical investigation of pressure effects on phase behaviour. The calculated phase diagrams were compared with own experimental data or to experimental data taken from literature.

Original languageEnglish
Pages (from-to)72-115
Number of pages44
Issue number1
Publication statusPublished - 2012


  • Hyperbranched polymer
  • Lattice cluster theory
  • Miscibility
  • Phase equilibria
  • Wertheim lattice theory

ASJC Scopus subject areas

  • Chemistry(all)
  • Polymers and Plastics

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