Scaling of Entropic Shear Rigidity

Abstract

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 dν. 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 dνwhen the percolation length becomes much larger than the density-fluctuation length.

4 pages, 2 eps figures

References in corpus (7)

• Randomly Crosslinked Macromolecular Systems: Vulcanisation Transition to and Properties of the Amorphous Solid State
• Universality and its Origins at the Amorphous Solidification Transition
• Elastic critical behaviour in a 3d model for polymer gels
• Renormalization-Group Approach to the Vulcanization Transition
• On the relevance of percolation theory to the vulcanization transition
• Connecting the vulcanization transition to percolation
• Elasticity of Gaussian and nearly-Gaussian phantom networks

Cited by in corpus (6)

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• Soft random solids and their heterogeneous elasticity
• Finite temperature mechanical instability in disordered lattices
• Dynamics of gelling liquids: a short survey
• Breakdown of disordered media by surface loads
• Solution of Disordered Microphases in the Bethe approximation