2 research outputs found

    Entropic Elasticity of Phantom Percolation Networks

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    A new method is used to measure the stress and elastic constants of purely entropic phantom networks, in which a fraction pp of neighbors are tethered by inextensible bonds. We find that close to the percolation threshold pcp_c the shear modulus behaves as (pโˆ’pc)f(p-p_c)^f, where the exponent fโ‰ˆ1.35f\approx 1.35 in two dimensions, and fโ‰ˆ1.95f\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 โˆผ(pโˆ’pc)g\sim(p-p_c)^g, with an exponent gโ‰ˆ2.0g\approx 2.0 and 2.6 in two and three dimensions, respectively.Comment: submitted to the Europhys. Lett., 7 pages, 5 figure

    Elasticity of Gaussian and nearly-Gaussian phantom networks

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    We study the elastic properties of phantom networks of Gaussian and nearly-Gaussian springs. We show that the stress tensor of a Gaussian network coincides with the conductivity tensor of an equivalent resistor network, while its elastic constants vanish. We use a perturbation theory to analyze the elastic behavior of networks of slightly non-Gaussian springs. We show that the elastic constants of phantom percolation networks of nearly-Gaussian springs have a power low dependence on the distance of the system from the percolation threshold, and derive bounds on the exponents.Comment: submitted to Phys. Rev. E, 10 pages, 1 figur
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