Scaled Particle Theory of a System of Hard Right Circular Cylinders

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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 dnem, the density jump (δρ/ρ), the order parameters >P2n<, the entropy change δS/NK, Pvo/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.