Entropic Elasticity of Phantom Percolation Networks

Oded Farago; Yacov Kantor

doi:10.1209/epl/i2000-00453-y

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Entropic Elasticity of Phantom Percolation Networks

Oded Farago·Yacov Kantor

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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.

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Oded Farago, Yacov Kantor. 2000-09-12. Entropic Elasticity of Phantom Percolation Networks. https://doi.org/10.1209/epl%2Fi2000-00453-y

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