Scaled particle theory of hard spherocylindrical fluids

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Abstract
For a system of spherocylindrical particles, an integral equation in the singlet angular distribution function is obtained. The integral equation is solved analytically by an expansion in the reduced density. Two nontrivial solutions appear, one corresponding to a nematic phase where the long axes of the molecules tend to align parallel, and one corresponding to a nonstable pseudonematic phase where the short axes tend to align parallel. The transition from the isotropic to the nematic phase is first order, whereas the transition to the pseudonematic phase is second order. None of the ordered phases can exist for reduced densities below a certain value, which is found as a simple function of the length to width ratio of the molecules.