Model networks build from molecules with well defined cross-linking units are interesting both theoretically and experimentally. Recently experimental studies of gels made of four-arm star polymers yield unexpected results such as extraordinary breaking strength. In order to analyze the molecular details of these new type of polymer networks we have repeated the cross-linking in solutions of four-arm star polymers in Monte Carlo simulations using the bond fluctuation model.

Our simulations revealed that the microscopic picture of these samples is clearly different to a previous proposal in literature: the linking of symmetric mixtures of two types (identically up to the reactive end-groups which react selectively with the opposite type of star) of four-arm stars should lead to an ordering of the structure upon cross-linking. We found that this ordering is a rather minor correction, but the absence of the shortest dangling loops has a striking effect on the network properties for experiments close to the overlap concentration c* [1]. This is because not only the dangling loop is fully inactive, but also the attached strands contribute less to the modulus of the network. The Figure shows the frequency of these shortest dangling loops in star polymer networks in which this type of defect is still possible. In effect, much more stable networks were produced as compared to previous attempts using the very same precursor stars as building blocks of the network. Our results were confirmed by proton NMR investigations on tetra-PEG Hydrogels and lead for the first time to a quantitative experimental assessment of cyclic structures as part of the active network [2].
In order to describe the change of the network properties as function of polymer concentration, we additionally developed a rate theory approach that monitors the local connectivity of the star molecules [3]. While networks made of one type of star were well captured by mean field models, the networks made of symmetric mixtures showed a clear effect of mixing both species.

These results demonstrate once again that understanding the cross-linking process and the resulting network structure are inevitable to model the network properties.

Publications:

1. K. Schwenke, M. Lang and J.-U. Sommer
   On the Structure of Star-Polymer Networks
   Macromolecules 44, 9464 (2011)
2. F. Lange, K. Schwenke, M. Kurakazu, Y. Akagi, U.-I. Chung, M. Lang, J.-U. Sommer, T. Sakai and 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. Lang, M.; Schwenke, K.; Sommer, J.-U.
   Short cyclic structures in polymer model networks: a test of mean field approximation by Monte Carlo simulations
   Macromolecules 45 (2012) 4886-4895