Recent Advances in the Theory of Filler Networking in Elastomers

  • Gert Heinrich
  • Manfred Klüppel
Part of the Advances in Polymer Science book series (POLYMER, volume 160)


The viscoelastic properties of (mostly carbon black) filled elastomers are reviewed with emphasis on the strain-dependence of the complex dynamic modulus (Payne effect). Considerable progress has been made in the past in relating the typical dynamical behavior at low strain amplitudes to a cyclic breakdown and reagglomeration of physical filler-filler bonds in typical clusters of varying size, including the infinite filler network. Common features between the phenomenological agglomeration/deagglomeration Kraus approach and very recent semi-microscopical networking approaches (two aggregate VTG model, links-nodes-blobs model, kinetical cluster-cluster aggregation) are discussed. All semi-microscopical models contain the assumption of geometrical arrangements of sub-units (aggregates) in particular filler network structures, resulting for example from percolation or kinetical cluster-cluster aggregation. These concepts predict some features of the Payne effect that are independent of the specific types of filler. These features are in good agreement with experimental studies. For example, the shape exponent m of the storage modulus, G′, drop with increasing deformation is determined by the structure of the cluster network. Another example is a scaling relation predicting a specific power law behavior of the elastic modulus as a function of the filler volume fraction. The exponent reflects the characteristic structure of the fractal filler clusters and of the corresponding filler network. The existing concepts of the filler network breakdown and reformation appear to be adequate in describing the deformation-dependence of dynamic mechanical properties of filled rubbers. The different approaches suggest in a common manner that there is a change of filler structure with increasing dynamic strain. However, in all cases additional assumptions are made about the accompanying energy dissipation process, imparting higher hysteresis to the filled rubber. This process may be slippage of entanglements (slip-links) in the transition layer between bound rubber layer and mobile rubber phase, and/or partially release of elastically ‘dead’ immobilized rubber trapped within the filler network or agglomerates.

The theoretical understanding of filled elastomers has been improved to the extent that now a connection can be made between the filler structures on larger length scales and the viscoelastic properties of rubbery materials.


Elastomers Filler networking Fractal filler structures Payne effect Viscoelasticity 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Gert Heinrich
    • 1
  • Manfred Klüppel
    • 2
  1. 1.Continental AG, Strategic TechnologyHannoverGermany
  2. 2.Deutsches Institut für Kautschuktechnologie e. V.HannoverGermany

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