High-density scaling solution to the Onsager model of lyotropic nematics

We show that the exact orientation distribution function (ODF) of the Onsager model for the nematic liquid crystalline phase of thin hard rod-like particles at high density can be scaled onto a single curve, which needs to be determined numerically only once. The scaling solution is in better agreement with simulation results on a system of sphero-cylinders of length-to-width ratio L/D = 40 than the Gaussian ODF, hitherto believed to be the best representation. The phase behaviour determined from the scaling solution, and from its first-order low density correction, are compared to the exact results.