Scaling of Entropic Shear Rigidity

Details Scaling of Entropic Shear Rigidity Scaling of Entropic Shear Rigidity

2004-06-17

arxiv.org/abs/cond-mat/0406411v2

Phys. Rev. Lett. 93, 225701 (2004)

Physics

Condensed Matter

Soft Condensed Matter

4 pages, 2 eps figures

Scientific paper

10.1103/PhysRevLett.93.225701

The scaling of the shear modulus near the gelation/vulcanization transition is explored heuristically and analytically. It is found that in a dense melt the effective chains of the infinite cluster have sizes that scale sub-linearly with their contour length. Consequently, each contributes k_B T to the rigidity, which leads to a shear modulus exponent d\nu. In contrast, in phantom elastic networks the scaling is linear in the contour length, yielding an exponent identical to that of the random resistor network conductivity, as predicted by de Gennes'. For non-dense systems, the exponent should cross over to d\nu when the percolation length becomes much larger than the density-fluctuation length.

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