Elastic properties of randomly cross-linked polymers

We have carried out extensive molecular-dynamics simulations of randomly cross-linked polymers and studied the onset of rigidity as the number of cross-links is increased. We find that for our systems, consisting of chains of length N = 10, 20, 30, and 50, the shear modulus E vanishes at a concentration cross-links that is well above the geometric percolation threshold and that it seems to approach zero as E similar to(n-n(c))(f), where the exponent f is considerably smaller than either the classical value f=3 or the corresponding exponent t approximate to 2.0 of the conductivity of random resistor networks.