Scaled Particle Theory of a System of Hard Right Circular Cylinders

Abstract

We have applied the scaled particle theory to a system of hard right circular cylinders. By varying the radius to height ratio R, we can study either rod-like molecules (R < 0.5) or disc-like molecules (R < 0.5). We have calculated the packing fraction d_nem, the density jump (δρ/ρ), the order parameters >P_2n<, the entropy change δS/NK, P_vo/KT and the isothermal compressibility β of the isotropic phase at the nematic-isotropic transition point for a range of values of R. By expanding the angle dependent terms occuring in the theory in a series of even Legendre polynomials, it is found that terms at least up to P₄ (cosθ) have to be retained to get qualitatively correct results. The thermodynamic properties at the nematic-isotropic transition point appear somewhat symmetrical for the rod-like and disc-like regions if they are plotted as functions of the ratio (largest dimension/shortest dimension) of the cylinders.