In many applications, polymer brushes are situated on surfaces that are exposed to a sometimes harsh environment. This exposure and the resulting interactions with the polymer brush lead to a slow destruction of the brush, because more and more chains are broken or torn away from the substrate. Introducing cross-links inside the brush provides a solution to this destruction problem: Should a chain de-graft, then it can be connected to other chains so that it remains inside the brush. On the other hand cross-linking processes can be used to freeze the state of a switchable brush under given solvent conditions, for instance to achieve a patterned switchable substrate.

In our work we are interested in how cross-linking can stabilize a polymer brush. A scaling model was developed [1] that describes the linking between neighboring chains inside the brush. The particular properties of cross-linked polymer brushes can thus be reduced to the distribution of bonds which are formed between the grafted chains.
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 [2].
As a by-product of our investigations, we developed a new self-consistent field model for the properties of a non-cross-linked mono-disperse grafted layer of polymer chains, which is the first to be in full agreement with scaling approaches [3].

Publications:

1. M. Hoffmann, M. Lang, and J.-U. Sommer'
   Gelation threshold of cross-linked polymer brushes
   Phys. Rev. E. 83, 020803 (2011).
2. M. Lang, M. Hoffmann, R. Dockhorn, M. Werner, J.-U. Sommer
   Fluctuation driven height reduction of cross-linked polymer brushes: A Monte Carlo study
   Journal of Chemical Physics 139 (2013) 164903.
3. D. Romeis, M. Lang
   Excluded volume effects in polymer brushes at moderate chain stretching
   Journal of Chemical Physics 141 (2014) 104901.