Cross-linked polymers


Michael Lang, Jens-Uwe Sommer, M. Werner and Ron Dockhorn.


Cross-linking of polymers leads to a combination of liquid (viscosity) and solid-state features (shape stability, no dissolution). 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.


The work on cross-linked polymer brushes [3] was motivated by experiments in 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, M. Hoffmann, R. Dockhorn, M. Werner, J.-U. Sommer
    Fluctuation driven height reduction of cross-linked polymer brushes: A Monte Carlo study

    J. Chem. Phys. 139 (2013) 164903.