Nematic Ordering of Hard Rods Derived from a Scaled Particle Treatment

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Abstract
A fluid of hard rods is considered as a model for nematic liquid crystals. A direct application of the scaled particle approach results in an inconsistent thermodynamics. A simplified version which is consistent gives an integral equation for the orientational distribution which has the same form as that used by Onsager in the second virial approximation to the same problem. The coefficients, however, give finite density corrections which change his predicted order and density ratio at the transition in the direction of the experimental values.