Entropic Elasticity of Phantom Percolation Networks

Abstract

A new method is used to measure the stress and elastic constants of purely entropic phantom networks, in which a fraction $p$ of neighbors are tethered by inextensible bonds. We find that close to the percolation threshold $p_c$ the shear modulus behaves as $(p-p_c{)}^f$, where the exponent $f\approx 1.35$ in two dimensions, and $f\approx 1.95$ in three dimensions, close to the corresponding values of the conductivity exponent in random resistor networks. The components of the stiffness tensor (elastic constants) of the spanning cluster follow a power law $\sim (p-p_c{)}^g$, with an exponent $g\approx 2.0$ and 2.6 in two and three dimensions, respectively.

submitted to the Europhys. Lett., 7 pages, 5 figures

References in corpus (3)

• Conductivity Exponent and Backbone Dimension in 2-d Percolation
• Elasticity near the vulcanization transition
• The Elastic Behavior of Entropic "Fisherman's Net"

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