Orientational ordering of free chains in a dense polymer network

摘要

The statistics of a polymer solvent in a network are investigated. We find that, without any explicit nematic interaction, the free chains are coupled to the orientation of the network via the excluded volume interaction. Because their conformations are dominated by screening, the minimum in the free energy of the solvent chains is found by following the network. This first paper considers a rigid network frozen from an earlier equilibrium configuration. In the limiting case of the melt the change in the scattering function is Dgr;S(k)=12VcscN(cS+cN)minus;1lminus;2lsqb;(Esdot;k)minus;2minus;kminus;2rsqb;, wherecSandcNare the concentrations of solvent and network,lis the Kuhn length, andEis the strain tensor. In the case of a swollen network, the full scattering pattern may assume the lsquo;lsquo;lozengersquo;rsquo; appearance noticed by several workers.