Nature of the Rigid-Rod Mesophase

Abstract

The thermodynamic phases of the rigid‐rod gas are re‐examined. Introduced in its present form by Zwanzig, the model postulates elongated molecules of parallelepiped shape with only three allowed orientations (mutually perpendicular). We have added to the virial series the cluster integrals represented by eight‐point bicolored graphs. It is demonstrated that the Padé approximants generated by the truncated cluster expansion provide a much more stable sequence of parameters characterizing the isotropic–anisotropic phase transition. It is similarly shown that there are no stable phases predicted for which the orientational distribution is not axially symmetric. The relative volume change accompanying the transition is still predicted to be larger than that observed in the isotropic–nematic liquid crystal transition.