Residual bond orientations and monomer fluctuations in (entangled) polymer networks

How entanglements between molecules affect dynamics and conformations of the molecules is one of the most important questions in polymer science, which is still not yet fully answered. The most frequently studied systems are dense polymer melts of molecular weight.


We have shown how one can determine both tube diameter and persistence length of the tube from monomer fluctuations in a polymer network [1,3]. We found that residual bond orientation and modulus are not directly proportional in an entangled polymer network. Based upon this observation, a new scaling law for the time averaged segment orientation was derived.

The key to understand these new results lies in the sliding motion of monomers along the tube axis. The possible sliding length can be computed using a virtual chain length Nk via the phantom model as shown at Figure a). The sliding motion allows the segments to sample the orientations of neighboring tube sections as indicated in Figure b). The sampling of different orientations leads to a reduction of the residual bond orientations in polymer networks as function of chain length and the monomer index k along the chain as shown in the second Figure below. This result is of large importance for understanding nuclear magnetic resonance (NMR) measurements on entangled polymer networks.

Another important point for understanding polymer networks is the effect of network defects on monomer fluctuations and the residual bond orientations. This was elaborated in collaboration with Prof. Saalwächter (Universtät Halle) [2]. We could demonstrate that a precise estimate of network structure is mandatory to extract the effect of the inactive network strands for an improved determination of the cross-link density of polymer networks using NMR.


  1. M. Lang and J.-U. Sommer
    Analysis of entanglement length and segmental order parameters in polymer networks
    Phys. Rev. Lett. 104, 177801 (2010).
  2. Chassé, W.; Lang, M.; Sommer, J.-U.; Saalwächter, K.
    Cross-link density estimation of PDMS networks with precise consideration of networks defects
    Macromolecules 45 (2012) 899-912.
  3. Lang, M.
    Monomer fluctuations and the distribution of residual bond orientations in polymer networks
    Macromolecules 46 (2013) 9782-9797.