The entropy of a network of rod molecules

Abstract

Although polymer networks are usually studied in the fully flexible case, there are many networks now being synthesized from liquid crystal polymers, where the only freedom lies in the hinging at the junction points. These provide the simplest examples of systems with rigid or nearly rigid members, also of interest in a view of recent neutron scattering experiments from conventional networks. In this paper we study rigid rod networks firstly as an extension of flexible networks, and secondly by new methods invented for this problem. The results show that for small deformations the free energy is very similar to usual Σ λ2i law for conventional networks, but for large deformations the variation is exponential in λ. Entanglements are also studied and a singularity which behaves like log {1 - ξ/a(λ-1)}, where a is the spacing of the rods related to the concentration and ξ the rod length, is predicted from the free energy