  The isotropic-nematic phase behavior of length polydisperse hard rods with
arbitrary length distributions is calculated. Within a numerical treatment of
the polydisperse Onsager model using the Gaussian trial function Ansatz we
determine the onset of isotropic-nematic phase separation, coming from a dilute
isotropic phase and a dense nematic phase. We focus on parent systems whose
lengths can be described by either a Schulz or a `fat-tailed' log-normal
distribution with appropriate lower and upper cutoff lengths. In both cases,
very strong fractionation effects are observed for parent polydispersities
larger than roughly 50 %. In these regimes, the isotropic and nematic phases
are completely dominated by respectively the shortest and the longest rods in
the system. Moreover, for the log-normal case, we predict triphasic
isotropic-nematic-nematic equilibria to occur above a certain threshold
polydispersity. By investigating the properties of the coexisting phases across
the coexistence region for a particular set of cutoff lengths we explicitly
show that the region of stable triphasic equilibria does not extend up to very
large parent polydispersities but closes off at a consolute point located not
far above the threshold polydispersity. The experimental relevance of the
phenomenon is discussed.
