Entropic elasticity of phantom percolation networks

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 ≈ 1.35 in two dimensions, and f ≈ 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 ∼ (p - p_c)^g with an exponent g ≈ 2.0 and 2.6 in two and three dimensions, respectively.