Scaling of entropic shear rigidity

The scaling of shear modulus near the gelation-vulcanization transition was investigated by using heuristic and analytical methods. It was found that the effective chains of the infinite cluster in a dense melt have sizes that scale sublinearly with their contour length. It was also found that each chain contributed k_BT to the rigidity, which lead to a shear-modulus exponent dv. It was observed that the exponent in phantom elastic networks was identical to that of the random resistor network conductivity.