Statistical Mechanics for Long Semiflexible Molecules: A Model for the Nematic Mesophase

A model system for long semiflexible rods is introduced to investigate the nematic mesophase. The free energy is separated into two parts F = F″ + Δ, where F″ represents a fully aligned, hard system and Δ a correction which in our case is evaluated by the counting technique of DiMarzio extended to the case of nonrigid rods. F″ may be estimated by a variety of techniques. We find several interesting features: (1) for both rigid and flexible cases the anisotropic phase undergoes a second transition at still higher densities to what we take to be the solid phase; (2) for the flexible case sensible values of length-to-breadth ratio and flexibility give the isotropic–anisotropic transition at liquid densities and with Δρ / ρ̄ ∼ 0(1%) in keeping with experiment and in marked contrast to all available results for strictly rigid systems; (3) for a given temperature there is a lower bound to the stiffness energy (associated with making a bend) required for the existence of an isotropic–anisotropic transition. In the present model this energy has the value kT log 2.