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

Abstract

A model system for long semiflexible rods is introduced to investigate the nematic mesophase. The free energy is separated into two parts $\mathrm{F\hspace{0.17em}=\hspace{0.17em}F″\hspace{0.17em}+\hspace{0.17em}\Delta }$ , where $\mathrm{F″}$ represents a fully aligned, hard system and $\Delta$ a correction which in our case is evaluated by the counting technique of DiMarzio extended to the case of nonrigid rods. $\mathrm{F″}$ 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 $\text{Δρ\hspace{0.17em}/\hspace{0.17em}ρ̄\hspace{0.17em}∼\hspace{0.17em}0(1\%)}$ 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 $\mathrm{kT}\log 2$ .