Elastic properties of randomly cross-linked polymers

Abstract

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 of cross-links that is well above the geometric percolation threshold and that it seems to approach zero as E\ensuremath{\sim}(n-${\mathit{n}}_{\mathit{c}}$${)}^{\mathit{f}}$, where the exponent f is considerably smaller than either the classical value f=3 or the corresponding exponent t\ensuremath{\approxeq}2.0 of the conductivity of random resistor networks. \textcopyright{} 1996 The American Physical Society.