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Cross-linked polymer chains: Scaling and exact results

  • Thomas A. Vilgis
  • Michael P. Solf
Conference paper
Part of the Lecture Notes in Physics book series (LNP, volume 492)

Abstract

The paper discusses the size of a randomly cross-linked polymer chain. The calculations are based on an exact theorem for the characteristic function of a polydisperse phantom network that allows for treating the cross-links between pairs of randomly selected monomers as quenched variables without resorting to replica methods. By variation of the cross-linking potential from infinity (hard constraints) to zero (free chain), we have studied the cross-over of the radius of gyration from the branched polymer regime where R gO(1) to the extended regime R gO(√N). In the cross-over regime the network size R g is found to be proportional to (N/M)1/4, where M is the total number of cross-links and N the number of monomers in the system. Our exact results can also be understood in terms of simple scaling arguments.

Keywords

Free Chain Ideal Network Debye Function Replica Trick Kratky Plot 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 1997

Authors and Affiliations

  • Thomas A. Vilgis
    • 1
  • Michael P. Solf
    • 1
  1. 1.Max-Planck-Institut für PolymerforschungMainzF.R.G.

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