Properties of phantom networks and real networks

  • A. J. Staverman
Conference paper
Part of the Advances in Polymer Science book series (POLYMER, volume 44)


The theory of phantom networks by James in 1947 and elaborated by Duiser and Staverman in 1965 and by Flory in 1976 is shown to lead generally to the frontfactor equation for the elastic free energy.

In the state of lowest free energy, called the Θ-state of the phantom network, the chains acquire the random configuration distribution and the frontfactor in the elastic equation is equal to the cycle rank, number of chains minus the number of junctions. The cycle rank depends on the chemical structure of the network and is independent of the number of segments designated as bifunctional junctions.

The number of elastic degrees of freedom is three times the cycle rank. The elastic behaviour of real networks in particular in the unswollen state, deviates from that of phantom networks. A recent theory to explain this deviation is based upon the assumption of a difference between polyfunctional and bifunctional junctions which is alien to the concept of phantom networks and is physically not plausible. An alternative theory is presented based upon the concept of constrained elastic degrees of freedom instead of constrained junctions.


Elastic Energy Equilibrium Position Real Network Elastic Equation Individual Chain 
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 1982

Authors and Affiliations

  • A. J. Staverman
    • 1
  1. 1.Gorlaeus LaboratoriumUniversity of LeidenNetherlands

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