Internal orientations and elastic properties of non-Gaussian nematic polymer network

Abstract

Elasticity of the polymer network, with nematic interactions between segments of all the system chains, is considered. The Maier and Saupe molecular mean-field is used for description of nematic interactions. Calculations are performed for non-Gaussian network containing chains of finite contour length. The network topological structure is taken into consideration via the system contraction coefficient. Values of thermodynamic parameters, necessary for the existence of the isotropic-nematic equilibrium, are calculated. The system free energy (Helmholtz function) is calculated for any direction of external elongation of the network. A relation between the deformation force and elongation ratio is obtained. The network can have isotropic as well as anisotropic elastic properties. It depends on the system internal orientations and chain lengths. For the network in isotropic phase, defined with respect to orientation of segments, elastic constants have the same values in any direction. It is independent of whether the chain length is finite or infinite. In the nematic phase, the network elastic constants have the same values for chains with infinite length, while they are many in various directions for finite length of chains. The problem of the nematic axis rotation under the system external deformation is considered.