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For simplicity, we do not consider semidilute solutions with large density fluctuations on scales smaller than the correlation length. The results of this paper can be extended to semidilute solutions using scaling concepts, see: de Gennes, P. G. Scaling Concepts in Polymer Physics; Cornell University: Ithaca, NY, 1979.
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The correlations in positions of potential cross-links, which appear because of the coherence through the paths connecting these points, can be neglected in our mean field consideration since such correlations give only small fluctuation corrections to the mean field free energy of the dense network.
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85033164843
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2N. This leads to a tube with oscillating walls. Since we expect topological entanglements to confine the whole strand rather than individual monomers, this case, N > n, is not a good representation of confining potential.
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note
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Note that it has to be modified for deformations affecting the volume in swollen networks. The elasticity of virtual springs depends on the polymer concentration in such nonGaussian phantom networks.
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c = kTc(1 - 2/f)/N, where f is the functionality of cross-links, see section 2.
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