Analysis of entanglement length and segmental order parameter in polymer networks.

The tube model of entangled chains is applied to compute segment fluctuations and segmental orientational order in polymer networks. The entanglement length N{e} is extracted directly from monomer fluctuations without constructing a primitive path. Sliding motion of monomers along the tube axis leads to reduction of segmental order along the chain. For network strands of length N>>N{e}, the average segmental order decreases approximately (N{e}N);{-1/2} in marked contrast to the 1/N{e} contribution of entanglements to network elasticity. As a consequence, network modulus is not proportional to segmental order in entangled polymer networks. Monte Carlo simulations over a wide range of molecular weights are in quantitative agreement with our theoretical predictions. The impact of entanglements on these properties is directly tested by comparing with simulations where entanglement constraints are switched off.