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We study the phase behaviour of hard rods with length polydispersity, treatedwithin a simplified version of the Onsager model. We give a detaileddescription of the unusual phase behaviour of the system when the rod lengthdistribution has a "fat" (e.g. log-normal) tail up to some finite cutoff. Therelatively large number of long rods in the system strongly influences thephase behaviour: the isotropic cloud curve, which defines the where a nematicphase first occurs as density is increased, exhibits a kink; at this point theproperties of the coexisting nematic shadow phase change discontinuously. Anarrow three-phase isotropic-nematic-nematic coexistence region exists near thekink in the cloud curve, even though the length distribution is unimodal. Atheoretical derivation of the isotropic cloud curve and nematic shadow curve,in the limit of large cutoff, is also given. The two curves are shown tocollapse onto each other in the limit. The coexisting isotropic and nematicphases are essentially identical, the only difference being that the nematiccontains a larger number of the longest rods; the longer rods are also the onlyones that show any significant nematic ordering. Numerical results for finitebut large cutoff support the theoretical predictions for the asymptotic scalingof all quantities with the cutoff length.

Isotropic-nematic phase equilibria of polydisperse hard rods: The effect of fat tails in the length distribution