Statistical Mechanics of Rodlike Particles. I. A Scaled Particle Treatment of a Fluid of Perfectly Aligned Rigid Cylinders

Abstract

In order to test the suitability of the scaled particle approach for anisotropic fluids of nonspherical particles (this approach had not previously been used with systems of markedly nonspherical particles or with anisotropic fluids of any sort), a scaled particle treatment is applied to a fluid of rigid cylinders of radius a and length l with cylindrical axes all constrained to lie in the same direction but with centers of mass free to move translationally throughout a volume V. Expressions for the equation of state and chemical potential are obtained through consideration of the reversible work W (α, λ, ρ) necessary to add a scaled cylinder of radius α and length λ at some arbitrary fixed point in the fluid. Because of the simple particle shape, the complete arguments used by Reiss, Frisch, and Lebowitz in their original scaled particle treatment of rigid spheres can be extended to aligned cylinders without making any additional approximations, permitting the equation of state to be obtained by two independent methods. Identical expressions for (p / ρkT) are derived from both, demonstrating that the scaled particle approach is capable of yielding self-consistent results for an anisotropic fluid of markedly nonspherical particles.