On the orientational properties of some one-dimensional model systems

We use the transfer matrix formalism to examine the behavior of some anisotropic hard-core fluids, the centers of whose particles are constrained to a line. At large elongation and pressure, the compressibility factor βp/rho is higher than that for a system with complete alignment by a factor 1+ν that depends upon the molecular geometry. For molecules with a finite radius of curvature, e.g., ellipses, ν = d/2, while for objects with flat sides ν = d; here d is the number of orientational degrees of freedom. A connection is made to some recent studies of hard ellipsoid fluids. We also model the effect of an external field on physical adsorption and show the existence of a phase transition in certain limiting situations