Theory of Systems of Rodlike Particles: I. Athermal systems

Abstract

An improved treatment of the lattice model proposed in 1956 is presented for a system of hard rods, with axial ratio x, dispersed in a diluent. Interparticle forces, apart from repulsions on contact, are deliberately ignored within the scope of the present paper. The equilibrium distribution of orientations of the rodlike particles in a phase with nematic order is derived and explicitly taken into account. Thermodynamic properties in the asymptotic limit of high degree of order reduce approximately. to those obtained previously. Calculations carried out for equilibrium between anistropic (nematic) and isotropic phases yield ν′_x/ν_x = 1.4653 for the ratio of volume fractions in the respective phases in the limit x → ∞. The product xν_x, expressing the combined covolume of solute species in the isotropic phase at coexistence is 7.89 in the same limit. The calculated critical value of the axial ratio for coexistence of the two phases in the neat liquid is x_crit, = 6.417. Results are compared with those of other theories. Those that rely on the virial expansion are subject to errors implicit in treating the solvent as a continuum.