Statistical Mechanics of Rodlike Particles. II. A Scaled Particle Investigation of the Aligned→Isotropic Transition in a Fluid of Rigid Spherocylinders

Abstract

Expressions for the equation of state and the chemical potential are derived as functions of density and temperature for both a perfectly aligned and a completely isotropic fluid of rigid spherocylinders through consideration of the reversible work $\mathrm{W(\alpha ,\; \lambda ,\; \rho )}$ necessary to add a scaled spherocylinder of radius $\alpha$ and cylindrical length $\lambda$ at an arbitrary fixed point in the fluid. A first‐order aligned→isotropic transition is obtained and the transition densities, free volume fractions, and entropy change determined at various values of the radius and cylindrical length of the spherocylinders. Although the densities of the two phases and the density change at the transition depend on the radius of the particles, the entropy change and the free volume fractions of the two phases at the transition depend only on the length‐to‐breadth ratio $x$ , indicating that the transition results from packing effects alone. The behavior of the expansivity and the compressibility of the system near the transition is also determined. The results of this treatment strongly suggest that the molecules of nematogenic compounds do not behave like inflexible rods, but rather must exhibit appreciable flexibility in the nematic as well as the isotropic phase. Some light is also shed on the problem of the relative importance of attractive and repulsive forces in determining the stability of nematic mesophases.