Theory of Intrachain Relaxation Spectra for Polymer Networks Possessing a Short- or Long-Scale Ordering. Effects of the Nematic Ordering on the Relaxation Spectrum of a Polymer Network with Included Rods

We discuss the relaxation properties of polymer networks possessing either short-scale ordering caused by rigidity of network strands or long-scale liquid crystalline order. The main topics of the paper are the equilibrium and local dynamic properties of a polymer network ordered due to nematic-like interactions of the network segments with included rod-like particles. A simplified three chain network model is used. Lagrange multipliers in the equations of motion of hard rods are replaced by their averaged values. This approximation corresponds to modelling the rod-like particles by elastic Gaussian springs, their mean-square lengths independent of the ordering. Nematic-like interactions between network segments and rods are taken into account in terms of the Maier-Saupe mean-field approximation. Nematic ordering of rods induces ordering of the network segments. Relaxation spectrum of the ordered network splits into two main branches for the parallel and perpendicular components of the chain segments with respect to the director. We calculate the relaxation times of a polymer network as functions of the wave number. The relaxation spectrum of an isotropic network and that of the ordered network with included rods are compared.