Cross-linked polymer systems

Cross-linked polymer systems


Michael Lang , Jens-Uwe Sommer , Ron Dockhorn


Cross-linking of polymers leads to a combination of liquid (viscosity) and solid-state features (shape stability, stability in solvents). In modern polymer research, cross-linking processes are applied to control materials properties in combination with structure-formation and self-organization processes. Even though rubber elasticity has been investigated since more than one century, convincing theoretical models that address all the possible structure-property relationships are not at hand. This is due the randomness of the cross-linking process that defines the particular local disorder and heterogeneity of the material.

In our recent work, we put some effort in understanding the effect of entanglements on monomer fluctuations and time average residual bond orientations in entangled networks. In this respect, we were able to develop a theory that allows to compute these properties as function of the local network structure [1].

The analysis of the local network defects was the key to explain the improved stability of tetra-PEG hydrogels [2]. We found that the special structure of the precursor polymers prevents the formation of the most frequent network defects and thus, allows the formation of stable network structures at rather low polymer concentrations. Polymer networks in confined geometries or networks made of stretched chains can be studied simultaneously when analyzing cross-linked polymer brushes [3]. Our work showed that brushes do not collapse upon cross-linking as one might expect from balancing osmotic pressure and modulus. Instead, the ordered chain conformations prevent the film from collapse and only deviations from homogeneous chain stretching drive the changes in the film thickness. Olympic gels are networks that are solely held together by the mutual topological inclusion of overlapping cyclic polymers. Our work on cyclic polymers and Olympic gels focuses on the effect of topology on the conformational properties of cyclic polymers in melts [4] and the corresponding estimates for the elasticity and the swelling equilibrium of Olympic gels, that are currently being developed.


Star-polymer networks

Segmental order and entanglements

Cross-linked polymer brushes

Cyclic Polymers and Olympic Gels
The work on cross-linked polymer brushes [3] was motivated by recent experiments of Dr. Uhlmann (Program Area 2). All other topics are fundamental research related to Program Area 3 of Prof. Heinrich.


  1. M. Lang and J.-U. Sommer
    Analysis of entanglement length and segmental order parameters in polymer networks
    Phys. Rev. Lett. 104 (2010) 177801

  2. F. Lange, K. Schwenke, M. Kurakazu, Y. Akagi, U.-I. Chung, M. Lang, J.-U. Sommer, T. Sakai, K. Saalwächter
    Connectivity and structural defects in Tetra-PEG Hydrogels: A combined proton NMR and Monte-Carlo simulation study
    Macromolecules 44 (2011) 9666-9674

  3. M. Lang, J. Fischer, J.-U. Sommer
    The effect of topology on the conformations of ring polymers
    Macromolecules 45 (2012) 7642-7648

  4. M. Lang, M. Hoffmann, R. Dockhorn, M. Werner, J.-U. Sommer
    Fluctuation driven height reduction of crosslinked polymer brushes: A Monte Carlo study
    Journal of Chemical Physics 139 (2013) 164903

  5. M. Lang, J. Fischer, M. Werner, J.-U. Sommer
    Swelling of olympic gels
    Physical Review Letters 112 (2014) 238001(5)

Cross-linked polymer systems
Cross-linked polymer systems