ORIGINS OF ENTANGLEMENT EFFECTS IN RUBBER ELASTICITY

The effects of entanglements on a network chain with fixed ends are modeled as hoops through which the chain must pass. This model differs from the tube models which allow no 'chain leakage' from the tube and from the slip-link models which do not conserve monomer along the chain. The strain-dependent portion of the free energy as the chain ends are displaced is shown to arise from three factors: the entropy of the strained unentangled subchains spanning the hoops, the distortion of the hoops with strain, and the narrowing of the distribution of segments required to reach a hoop with increasing extension ratio. An analytical expression for the free energy of the chain can be derived that takes the M minus 1 hoops per chain to be of infinitesimal diameter thereby neglecting this second factor.