Brownian motion of chains and crosslinks in a permanently linked network: The dynamic form factor

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Abstract
We consider the Brownian motion of crosslinks and chains in a well‐linked network far above the gel point. In a simple mean field approach we model the effect of permanent crosslink constraints by a harmonic potential. The two parameters in this model, the radius of gyration of the mesh and the monomeric friction coefficient, can be determined for most systems. Neglecting entanglements it turns out that the crosslinks and chains are localized within the range of the radius of gyration of a rubber strand between two crosslinks. This is in agreement with the classical phantom model of James and Guth. A crude extension to entanglements shows the restriction of the localization range of the crosslinks. The calculated incoherent scattering can be discussed in the context of experiments recently carried out by Oeser, Ewen, et al., and the coherent scattering is to be compared with current measurements by Oeser, Farago, et al.

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